Validation of OMS II - DHIS

Validation of OMS II A validation of the Margin Model OMS II for equity and index

products used by Nasdaq OMX

December 2014

http://www.nasdaqomx.com/

Author Last update Version Page

Bengt Jansson, zeb/ Risk & Compliance Partner AB 2014-12-09 1.3 2 (38)

Validation of OMS II, 2014

Revision history:

Date Version Description Author

2014-11-18 1.0 Initial draft Bengt Jansson 2014-12-01 1.1 Draft Bengt Jansson 2014-12-08 1.2 Final version Bengt Jansson 2014-12-09 1.3 Adjusted for comments Bengt Jansson




Table of contents

1. Background ......................................................................................................................... 4 1.1 General ........................................................................................................................ 4 1.2 Legal environment ...................................................................................................... 4

2. Input to the validation ........................................................................................................ 4 2.1 Documentation at NOMX Clearing ............................................................................ 4

2.2 Numerical analysis of OMS II .................................................................................... 5 2.3 Discussions .................................................................................................................. 6 2.4 Special issues .............................................................................................................. 6

3. Theoretical framework of the model ................................................................................ 6 3.1 Background on VaR and Margin models .................................................................... 6 3.2 Basic OMS II calculations .......................................................................................... 8 3.3 Purpose & Limitations .............................................................................................. 15

3.4 Statistical significance ............................................................................................... 19 3.5 Risk Factors ............................................................................................................... 20 3.6 Academic and industry references ............................................................................ 20 3.7 Key assumptions ....................................................................................................... 20

3.8 Historical references .................................................................................................. 21

4. Parameters ........................................................................................................................ 21

5. Numerical data .................................................................................................................. 22 5.1 Introduction ............................................................................................................... 22

5.2 Back testing ............................................................................................................... 22 5.3 Stress testing.............................................................................................................. 25 5.4 Sensitivity analysis .................................................................................................... 30

6. Conclusions........................................................................................................................ 35 6.1 Changes from previous validation ............................................................................ 35 6.2 Input to the validation ............................................................................................... 35 6.3 Theoretical framework of the model ......................................................................... 35 6.4 Parameters ................................................................................................................. 35 6.5 Monitoring process.................................................................................................... 36

6.6 Recommendations ..................................................................................................... 36

7. Information ....................................................................................................................... 37 7.1 Tables ......................................................................... Error! Bookmark not defined. 7.2 Figures ........................................................................ Error! Bookmark not defined. 7.3 References ................................................................................................................. 37

8. Appendices ........................................................................................................................ 38 8.1 Appendix 1 Definitions ............................................................................................. 38




Validation of OMS II

1. Background

1.1 General

NASDAQ OMX Clearing AB (“NOMX Clearing”) provides clearing and Central

Counterparty (“CCP”) services. In order to prudently manage these services NOMX Clearing

uses a large number of different models. This report is the validation of the margin model

OMS II.

The purpose of a validation of models is to ensure the theoretical and empirical soundness of

the models used by the CCP. The validation report should ensure transparency on the models

used by the CCP for the benefit of:

Board of Directors, NASDAQ OMX Clearing AB.

Competent Authorities

Internal Audit and Audit Committee

Other stake holders

1.2 Legal environment

NOMX Clearing was at the 19th of March 2014 authorised as Central Counterpart (CCP) to

offer services and activities in the Union in accordance with Regulation (EU) No 648/2012 of

the European Parliament and of the Council of 4 July 2012 on OTC derivatives, central

counterparties and trade repositories1.

The legal framework that governs NOMX Clearing is therefore the EMIR framework,

Regulation (EU) No 648/2012 and supporting delegated Regulations 148/2013, 149/2013,

150/2013, 151/2013, 152/2013, 153/2013, 285/2014, 667/2014, 876/2013, 1003/2013 and the

implementing Regulations 484/2014, 1247/2012, 1249/2012.

The Regulation of particular interest for this validation is Delegated Regulation No 153/2013

“supplementing Regulation (EU) No 648/2012 of the European Parliament and of the Council

with regard to regulatory technical standards on requirements for central counterparties”.

2. Input to the validation

2.1 Documentation at NOMX Clearing

2.1.1 Previous validation of OMS II

In NOMX Clearing’s application for being a authorised as a CCP and to offer services and

activities in the Union in accordance with Regulation (EU) No 648/2012 a validation of the

margin model OMS II was amended. This validation will act as an important building block

for this new validation. The full document name is: “Validation of OMS II ver 1.1, 2013”

1 Usually referred to as “EMIR”




2.1.2 Margin methodology guide for OMS II

This guide is in line with Nasdaq OMX standard when it comes to documentation available

for the member community. It is meant as a general guide and not necessarily as a technical

document describing the actual IT implementation of the model. The full document name is:

“OMS II Margin Guide v 1.0”

2.1.3 OMS II Model Instructions

This is an internal document that describes more of the technical part of the model and the

audience is internal risk management and IT. The document name is: “OMS II model

instructions”

2.1.4 Policies

A lot of policies will be included as input to this validation. The following list will name the

most prominent policies in this aspect:

Policy for the Validation of Models: The starting point for the construction, reporting

set up and the content of the validation is the policy for validating model that is

approved by the Board of Directors at NOMX Clearing. The full document name is:

“Model Validation Policy NOMX (140801)”

Policy for setting risk parameters: NOMX Clearing has developed policies that

regulate how risk parameters should be estimated. The full document name is: “Risk

Parameter Policy NOMX (140319)”

Policy for back testing of models: NOMX Clearing has developed policies that

regulate how back testing should be conducted from a theoretical, and very general,

point of view. More specific guidelines can be found for specific models. The full

document name is: “Back testing Policy NOMX (130513)”

Policy for stress testing of models: NOMX Clearing has developed policies that

regulate how stress testing should be from a theoretical, and very general, point of

view. More specific guidelines can be found for specific models. The full document

name is: “Stress Test Policy NOMX (140228)”

Policy for sensitivity testing of models: Nasdaq OMX has developed policies that

regulate how sensitivity testing should be from a theoretical, and very general, point of

view. More specific guidelines can be found for specific models. The full document

name is: “Sensitivity testing and analysis Policy (130909)”

2.2 Numerical analysis of OMS II

NOMX Clearing has ongoing numerical procedures as place to deliver numerical output from

each margin model that its use. The numerical data can be roughly divided into three separate

parts:

Back testing data

Stress testing data

Sensitivity analysis data




2.3 Discussions

In any validation a large part of the information received must be thoroughly discussed with

the personal at the CCP. The following persons are however prime sources of information to

this model validation:

Karl Klasén, Risk Management department of NOMX Clearing

Torbjörn Bäckmark, Risk Management department of NOMX Clearing

2.4 Special issues

OMS II has been validated (Validation OMS II, NOMX, 2013) in the year 2013 in connection

with the application for being a authorised as a CCP and to offer services and activities in the

Union in accordance with Regulation (EU) No 648/2012. Since a margin model must, and

should, be validated on a yearly basis each validation will be updated with new issues as:

New added functionality to the margin methodology

New types of instruments or markets added to the group of instruments and markets in

which the margin model is used

Changed financial environment as different volatility in the market

New distribution of counterparts as increased risk towards certain firms

New legislation that changes the rules thereby contradicts assumptions made in the

model

A section in the validation will specifically target differences between validations to facilitate

reading.

3. Theoretical framework of the model

3.1 Background on VaR and margin models

3.1.1 Basic VaR methodologies

For a portfolio of investments it is often important to calculate risk measures that try to

capture the risk in one separate number. For the past decade the family of risk measures that

are most used for this is usually referred to as Value at Risk (“VaR”). VaR tries to state the

following:

“With a certain probability X there will be no losses for this portfolio exceeding Y in the next

N days”

Probability: A VaR calculation is made with a confidence level, X. In many cases this

level is quite high (99%) because it is the losses in the distribution tail that are of

interest.

N days: A VaR calculation also needs a time horizon. A longer period will give a

higher value compared to a shorter one.

Y: This is the VaR measure.

The basic principle can easily be shown in the Figure 1 below were the tails of the distribution

represent the extreme gains and losses of a portfolio.




Figure 1: Basic VaR principle

There are a lot of different mathematical methods to calculate a VaR measure, all with

different advantages and weaknesses. The main challenges are to estimate the following:

The volatility of the instruments in the portfolio

The correlation between the instruments in the portfolio

When these challenges have been solved, or rather when the approximations to use have been

decided; the calculations are quite straightforward from a mathematical point of view.

The merits of a VaR model are in its predictability. That means that a model that

overestimates the risk is equally bad as a model that underestimates the risk. This implies that

different models are suitable for different type of underlying markets (gold, currency, etc.),

instruments (derivatives, linear products, etc.) and market states (Low volatile market, high

volatile market, crashing market, etc.).

When a VaR model is chosen as a model to use it is prudent to spend some time

contemplating what market and state it should be used to provide information on. A model

itself can of course be poorly implemented from a mathematical or technical point but the

waste majority of problems come from using the model in a non fitting environment.

3.1.2 Basic margin methodologies

Early margin models pre-date VaR models by several decades. This can be seen in many of

the architectural decisions that have been done in these models. The pre-conditions for these

models included:

Limited computer power, in some cases the computational force that was necessary to

actual perform the calculations were done on the “super computers” of the time.

Limited research and familiarity of portfolio theory, the introduction of derivatives

might not be entirely new but the scale and organization of the trading and clearing

certainly was.

“Keep it simple” was something that was necessary for the margin models to be

accepted by the member community. No “black boxes”!




All these pre-conditions lead to some joint features of all the traditional commercially

available margin models2.

Mainly designed for linear products (futures)

Step motherly treatment of time dependency for contracts with the same underlying

but different expiry.

Low, or no, correlation between instrument based on different, but correlated,

underlying.

The calculations are very dependent on accurate market prices on exactly those

instruments that can be found in the cleared portfolio. No accurate way to use “price

factors”. In practice these models depend on settlement prices from a corresponding

market place.

It might seem that margin models are very crude, full of drawbacks and of limited value. It is

true that the underlying functionality of a traditional margin model is a little bit blunt but it

gets the job done! The models are resilient against changes in correlation structure and can

easily adopt to high volatility states in the market. They are easy to explain to external parties

and easy to predict.

3.2 Basic OMS II calculations

3.2.1 Instruments

The OMS II model was originally designed for options and only after that forwards was

introduced. The model is used internationally to calculate margins for several types of

instruments but NOMX Clearing uses the OMS II model for Equity and Index products

including futures, forwards and options.

3.2.2 The basic building blocks

3.2.2.1 Vector files

The OMS II model uses a scenario approach for calculation of margins3 by calculating the

worst possible exposure that a portfolio of instruments might reasonably provide over a

specified liquidation period4 and a considered set of scenarios.

It is of course the case that the OMS II margin system can be used to calculate other results

than margins depending on the parameter used, but for this validation the system can be

thought of producing a margin number.

The basic building block in OMS II is what is called the “vector file”. This consists of a

matrix with two dimensions, changes in price is one dimension and changes in implied

volatility in the other dimension.

Building vector files for each position in the clearinghouse5 is the start of all calculations done

by OMS II.

2 Commercial margin models (traditional) are SPAN, OMS II and to some extent TIMS. Of these models “Standard

Portfolio Analysis of Risk”, or SPAN, developed and implemented by the Chicago Mercantile Exchange (CME) in 1988

is the most well known.

3 See Appendix I Definitions for definition of margins

4 See Appendix I Definitions for definition of liquidation period




The implied volatility direction is often called just “volatility” in documentation and data files

so it can be some confusion when it comes to parameters but it is always the volatility used in

option pricing that is discussed when referred to as just volatility.

In the below figure an example of an empty such vector file is shown.

Volatility

Price Point Low Mid High

High price 1

2

3

4

5

.

.

.

27

28

29

30

Low price 31

Table 1 : Basic vector file

For each position in a portfolio the following steps are done to fill the above matrix:

1. For the underlying instrument6 of the position (equity or index futures and forwards)

the margin settlement price is obtained from information vendors (or in the case when

the underlying instrument is traded on Nasdaq OMX directly from the exchange).

2. For the instrument of the position (equity or index options or futures) the implied

volatility is calculated (more on implied volatility calculation later in the document).

3. Parameters for the underlying instrument are taken from CDB (“central data base”).

This defines how much the price of the underlying instrument can move during the

liquidation period.

4. Parameters for the instrument of the position are taken from CDB (“central data

base”). This defines how much the implied volatility can move during liquidation

period.

5. With this information the vector file is created.

A vector file for a sold call option with 6 month to expiry, strike 100 and risk free interest rate

of 2% would look like this in a vector file. Do notice that the implied volatility is divided in

three points. In reality the vector file also have the bid ask spread in volatility. In the

following vector file the “correct” side of the spread is chosen dependent on position to

facilitate reading.

5 Or rather for each position that the clearing house uses OMS II methodology to calculate margin for.

6 Sometimes an underlying instrument is referred to as only ”underlying”.




The basic building block in OMS II is what is called the “vector file”. This consists of a

matrix with two dimensions, changes in price is one dimension and changes in implied

volatility in the other dimension. I a very similar nature to the with spread margin model

SPAN the OMS II algorithm consist of manipulations of the vector files. In the below figure

an example on such vector file is shown.

Volatility

Price Point Low Mid High

110,00 1 -13,17 -15,65 -18,32

109,33 2 -12,65 -15,17 -17,86

108,67 3 -12,14 -14,69 -17,41

108,00 4 -11,64 -14,23 -16,96

107,33 5 -11,15 -13,77 -16,51

. . . .

100,00 16 -6,40 -9,19 -11,97

. . . .

92,67 27 -3,06 -5,57 -8,16

92,00 28 -2,82 -5,29 -7,85

91,33 29 -2,61 -5,02 -7,55

90,67 30 -2,40 -4,76 -7,26

90,00 31 -2,20 -4,51 -6,97

Table 2 : Example on instrument vector file (Call option example)

The negative sign is because a sold option only has obligation and thus a negative market

value. For each underlying that any of the customers has positions in (options, forwards and

futures defined on this underlying) will have a vector file calculated as in Table 2 above.

For each position defined in this underlying a “positional vector” file is created by adding the

individual data to the instrument vector file. In this way each point in the matrix displays the

market value for that specific scenario.

For an option it is only a multiplication of the contact size and number of contracts

that is done.

For a forward the instrument vector file must be used together with the contracted

forward price to create the corresponding P/L for each point.

For a future the situation is exactly as for a forward. The only difference is that in end

of day calculations the market value has been deducted as variation margin. The

market value is therefore by definition zero in standard evening margin calculations.

Now when each position in a portfolio has a corresponding positional vector file next level of

calculation is done. Do notice that up to this point the calculations has been very similar to the

more wide spread margin model SPAN. The really difference between the models are how

correlation is handled.

3.2.3 Correlation in OMS II

3.2.3.1 General

The way correlation is handled in OMS II can be described with the extremes and “something

in between”. Therefore fully correlated, not correlated and correlated cases will be described

in separate sections.




3.2.3.2 Perfectly correlated underlyings

OMS II handle correlation between positions by looking at correlation between the underlying

instruments. This means that all options, forwards and futures that have the same underlying

equity or index are considered to be perfectly correlated.

Do notice that there are parameters that decide if all instruments based on one underlying

instrument should be totally correlated. For an underlying equity as “Ericsson” this means as

an example that NOMX Clearing decide via the parameters if forwards with different time to

expiry should be perfectly correlated or not. Currently the settings of these parameters are that

all instruments based on the same underlying shows perfect correlation. In equity markets this

is not an unusual assumption due to the low time dependencies that instruments based on the

same underlying equity shows compared with more time dependent markets as interest rate or

electricity markets.

Take all positional vector files with this underlying instrument and put them in a “stack” as in

Figure 2. Perfect correlation then means that the same “point” in each vector file is summed

up and a new vector file is created which consists of the sum of all positions in instruments

with the same underlying.

Figure 2: Several instruments with the same underlying

This means that after this step all positions based on one underlying in the portfolio has one

resulting vector file.

3.2.3.3 Perfectly uncorrelated underlyings

In NOMX Clearing perfectly uncorrelated settings are usually set between different

underlyings. This means that the worst case scenario is chosen for each sum vector file per

underlying. In the below example there is two different uncorrelated underlyings X and Y.

Underlying X

Volatility

Point Low Mid High

110,00 1 -1646 -1956 -2290




109,33 2 -1582 -1896 -2233

108,67 3 -1518 -1837 -2176

108,00 4 -1455 -1779 -2119

107,33 5 -1394 -1721 -2064

. . . . .

100,00 16 -800 -1149 -1497

. . . . .

92,67 27 -382 -696 -1020

92,00 28 -353 -662 -982

91,33 29 -326 -628 -944

90,67 30 -300 -595 -907

90,00 31 -275 -564 -871

Table 3 : Total sum vector file for underlying X

The negative sign say that this instrument has a margin for the instrument owner (portfolio).

Underlying Y Volatility

Point Low Mid High

190,00 1 6586 7823 9161

190,67 2 6327 7583 8931

191,33 3 6072 7347 8703

192,00 4 5821 7114 8478

192,67 5 5575 6885 8255

. . . . .

200,00 16 3200 4595 5986

. . . . .

207,33 27 1528 2786 4080

208,00 28 1412 2647 3926

208,67 29 1303 2512 3776

209,33 30 1199 2381 3628

210,00 31 1101 2255 3484

Table 4 : Total sum vector file for underlying Y

Another underlying X that has an all positive vector file (could be a bought option) is then

added to the portfolio. With two uncorrelated underlyings the worst case scenario for each

vector file can be in any point. For underlying X it will be point (1,3) -2 290 and for Y it will

be the point (31,1) 1 101. The sum is be -1 189. From technical perspective a new vector file

is created with the same value in each as in the following Table 5. Do notice that in this

example the volatility part also is treated as totally uncorrelated. If necessary the system can

keep the correlation in volatility to perfect and thereby treat each “column” in the file

separately in the calculations.

X & Y Volatility

Point Low Mid High

1 -1189 -1189 -1189

2 -1189 -1189 -1189

3 -1189 -1189 -1189

4 -1189 -1189 -1189

5 -1189 -1189 -1189

. . . .




16 -1189 -1189 -1189

. . . .

27 -1189 -1189 -1189

28 -1189 -1189 -1189

29 -1189 -1189 -1189

30 -1189 -1189 -1189

31 -1189 -1189 -1189

Table 5 : Total sum vector file for underlying X & Y

Last step for the portfolio is to search the above vector file for the lowest value (-1 189) which

constitutes the margin call for this portfolio (if it only consists of positions defined in

underlying X & Y).

3.2.3.4 Underlyings with some correlation

For instruments based on different underlyings that show significant correlation there is a

method within OMS II that is used to include correlation aspects. This method is called

“window method”. This methodology was primarily developed for interest rate instrument but

can be applied generally for all types of instruments and markets within the OMS II model.

Two instruments vector files based on two different underlyings give the following situation:

Under. X Volatility

Under. Y Volatility

Point Low Mid High

Point Low Mid High

110,00 1 -286 -340 -398

120,00 1 -377 -222 -55

109,33 2 -275 -330 -388

120,67 2 -409 -252 -84

108,67 3 -264 -319 -378

121,33 3 -441 -282 -112

108,00 4 -253 -309 -369

122,00 4 -472 -311 -140

107,33 5 -242 -299 -359

122,67 5 -503 -339 -168

106,67 6 -232 -290 -349

123,33 6 -533 -368 -196

106,00 7 -222 -280 -340

124,00 7 -563 -396 -223

. . . .

230,00 . . . .

100,00 16 -139 -200 -260

130,00 16 -800 -626 -452

. . . .

230,00 . . . .

94,00 25 -77 -134 -191

136,00 25 -978 -815 -650

93,33 26 -72 -127 -184

136,67 26 -994 -834 -670

92,67 27 -66 -121 -177

137,33 27 -1 009 -852 -690

92,00 28 -61 -115 -171

138,00 28 -1 023 -869 -709

91,33 29 -57 -109 -164

138,67 29 -1 037 -886 -728

90,67 30 -52 -104 -158

139,33 30 -1 050 -902 -746

90,00 31 -48 -98 -151

140,00 31 -1 062 -918 -764

Table 6 : Two vector files with different underlyings

If these two instruments are totally uncorrelated the total margin would be calculated

summing up worst cases from both files (-398 + -1 062 = -1 461). If the instruments are

totally correlated the total margin would be calculated summing up the same points from both

files and the worst point is calculated to be (-48 + -1 062 = -1 110).

For the case in between there is a window applied that hinders the different underlyings to

move “too much” from each other. In a way this say that the underlyings can move to any

point in their scanning ranges but if one of the underlyings is in one point the other underlying

is restricted to move “too far away” from this point.




This model is interesting in the way that it does not try to capture the actual behaviour

between two (or several) instruments in one number as the mathematical correlation factor. It

looks at how the correlation effects are in the extreme cases. This makes this model a very

conservative one to use since the effect of the model will be mainly decided by the extreme

movements i.e. the more turbulent days in the historical data.

The downside is that estimating the window sizes is quite complicated and demands much

numerical work. It involves looking at each historical event and estimating the minimum

window size for each date.

This is described in the following Table 7.

Under. X Volatility

Under. Y Volatility

Point Low Mid High

Point Low Mid High

110,00 1 -286 -340 -398 120,00 1 -377 -222 -55

109,33 2 -275 -330 -388

120,67 2 -409 -252 -84

108,67 3 -264 -319 -378

121,33 3 -441 -282 -112

108,00 4 -253 -309 -369

122,00 4 -472 -311 -140

107,33 5 -242 -299 -359 122,67 5 -503 -339 -168

106,67 6 -232 -290 -349

123,33 6 -533 -368 -196

106,00 7 -222 -280 -340

124,00 7 -563 -396 -223

. . . .

230,00 . . . .

100,00 16 -139 -200 -260

130,00 16 -800 -626 -452

. . . .

230,00 . . . .

94,00 25 -77 -134 -191

136,00 25 -978 -815 -650

93,33 26 -72 -127 -184

136,67 26 -994 -834 -670

92,67 27 -66 -121 -177

137,33 27 -1 009 -852 -690

92,00 28 -61 -115 -171

138,00 28 -1 023 -869 -709

91,33 29 -57 -109 -164

138,67 29 -1 037 -886 -728

90,67 30 -52 -104 -158

139,33 30 -1 050 -902 -746

90,00 31 -48 -98 -151

140,00 31 -1 062 -918 -764

Table 7 : Two vector files in the window method

In the upper part of the vector file it is a little rectangle that restricts the area were max and

min combination are compared. The worst case is (-286 + -503= -789). From this situation the

window “slides” down the vector file and produces new values for each position. Here the

volatility part is totally correlated. If treated as uncorrelated the worst case would be (-398 + -

503= -901).

The extreme cases are easy to understand, a window that spans the entire vector file would

equal an uncorrelated case. If the window only covers one row it is fully correlated. Window

sizes are described in percentage of the valuation interval.

3.2.4 Controlling the algorithm

In the previous sections the general calculations were described but there are a lot of settings

in OMS II that really can alter the way margin is calculated.

Risk free interest rate : Risk-free interest rate used when evaluating options. The

simple interest rate is translated to a continuous rate. It is

possible to enter tenor and rate as pair in the system. In this

way a rudimentary yield curve can be constructed. In most set




ups this is not the case since the relative effect of the interest

rate in option pricing is limited.

Dividend yield : Dividend yield used when evaluating options. To properly

evaluate American options on futures, the dividend yield is set

equal to the risk free interest rate.

Adjustment for erosion

of time value

: The number by which the number of days to maturity will be

reduced when evaluating held options. This is a way of

adjusting for the fact that when the defaulting parts positions

are neutralized the time value of the options has decreased.

Valuation points OMS II differs from SPAN in that the numbers of valuation

points are a parameter. For equity products this is 31 points and

when used for interest rate products this was 201 points.

Adjustment of futures : Adjustment factor (spread parameter) for futures. Since futures

have a fixing price there are no bid/ask values that can be used

to treat bought and sold positions on different side of the

spread.

Highest volatility for

bought options

: Applies only to bought options and effectively limits the value

of the option since volatility is one of the most important part

of the valuation.

Lowest volatility for sold

options

: Applies only to sold options and effectively limits the lower

value of the option since volatility is one of the most important

part of the valuation.

Volatility shift parameter : Fixed parameter that determines the size of the volatility

interval. In the previous section a three step interval was used

for volatility. The normal parameter here is 10% (in absolute

terms)

Volatility spread : Defines the spread for options. The spread parameter is a fixed

value.

Highest value bought in

relation to sold options

: Min. spread between the values for bought and sold options if

spread is too small the value of the bought option is decreased

Adjustment for negative

time value

: If the theoretical option value is lower than the intrinsic value,

the price is adjusted to equal the latter.

There are numerous other parameters that decide the behaviour of OMS II but the above

parameters can be considered some of the more important, and interesting, parameters.

3.3 Purpose & Limitations

3.3.1 Instruments and markets

As mentioned before the OMS II the model was primarily designed for options on equities

and index. The scanning range can be divided into a very large number of valuation points

therefore making the model suitable for options and positions were the minimum/maximum

points can be found inside the scanning range area and not always at the end points (as

portfolios with linear products as forwards and futures would show).




Both forward and futures are adequately handled in the model and combination of derivatives

on the same underlying is nicely handled.

Both Equities and index products show limited time dependencies compared with

commodities7 and interest rate markets. In technical terms this mean that forward/futures

prices can be estimated from spot prices by simple discounting. Of course this include taking

into account dividends for both index and equities8. This is also accommodated by the OMS II

model by calculating forward prices from spot prices including time dependent dividend

estimates as parameters in the system.

The OMS II model has been used historically for a large amount of different markets and

instruments but now days it is used for equity and index instruments on the Nordic market.

For this purpose the model is very well suited.

3.3.1.1 Options

Options are the standard premium paid types and no future style options are handled within

OMS II (nor traded on the exchange). The volumes in option contracts are standard American

and European type of options. The behaviour and pricing of these products are considered so

standard that closer descriptions for these are not necessary. It can however be mention that

OMS II has a library of formulas for this purpose that incorporate analytical as well s

common lattice models for the pricing of these options.

There is however currently some position in Cash-or-nothing Binary options. The valuation of

these instruments is not complicated and is done within the Black & Scholes framework

according to the following formulas with standard notation:

( )( ) ( ( ))r T tC t e d t (1)

( )( ) ( ( ))r T tP t e d t (2)

2

ln ( )2

( )

Sr T t

Kd t

T t

(3)

Even though the binary payoff function can be a challenge in the area were strike is close to

market value of the underlying and maturity close to expiry this is manageable because of the

low volumes in these instruments. From Risk Management point of view it is also possible to

hedge these instruments to large extent by using standard option contracts9.

3.3.2 Market conditions for the model

3.3.2.1 General on market state

The financial market is not a quiet, stable and calm system. On the contrary, markets tend to

have different states that are defined in different volatilities and correlation structures for the

underlying prices in the market.

7 Especially power markets as electricity or gas

8 Both decided dividends but also future estimates of dividends

9 A vertical spread is a position that consists of a multiple number of options. Given the same underlying, expiry date but

different strikes as the binary option this position would give a rough hedge.




A very crude way of connecting different models to market states can be done according to

the following picture:

Figure 3: Market movements and correlation

This is only indicative on the usage of models but can be useful for the validation since it

points at interesting areas which should be investigated in this document. A VaR model has

its merits by its ability to accurately predict risks. Its usual usage is very much focused on day

to day markets. Sometimes used as risk mandate calculation in funds or trading environment.

This means that the model is used were market movements are small, or rather were the larger

amount of market movements can be found.

Traditional margin models tend to treat correlation very step motherly and concentrate on

individual volatility on separate underlying. The movements are in many cases caused by

individual events for the underlying and uncorrelated with the rest of the market. This could

be before annual reports or media coverage attributed to certain company specific events.

OMS II is a traditional conservative margin calculation model. The areas were the model

show strengths is exactly that area when market movements are “large”. The margin

calculated typically show resilience against these large movements.

This feature also indicates that when margin models are accused for “over margining” it is in

some situations only a misconception on what market state the model should be used. A

traditional margin model will always (and should also have this feature) produce higher

numbers than a traditional VaR when used in a normal day to day market environment.

Stress test models are used in those rare events when market crashes lurks. In these areas the

number of observations is very rare making statistical measures uncertain10

. For these stress

tests it is usual to consider high positive correlation in the methods, “everything moves

together in a crash”.

3.3.2.2 Correlation within on underlying instrument

For all risk models, which margin models are a part of, the issue of correlation is always the

most debated and questioned aspect of the design.

10 This is the usual objection when using a VaR model as stress test model with high confidence level.

Market movements

Correlation

Margin models

VaR models Stress test

models




For OMS II the correlation has two aspects, and one of them is correlation within instrument

defined on the same underlying but with different time to expiry. As an example the question

could be asked if a forward with one month to expiry based on equity is perfectly correlated

with a forward based on the same equity but with two years to expiry. In OMS II the current

setting11

is that these products are treated as perfectly correlated. As discussed before this

implies that there are no time dependencies in these products. Equities and Index products are

certainly the most stable underlying markets in this aspect and movement in equity spot price

will influence the forward price directly. The changes in forward price that are not caused by

changes in the spot price are caused by changes in future dividend expectations, tax issues etc

but there is not a perfect correlation between the two instruments.

Would this lead to situations were OMS II under margining situations were two forwards

based on the same underlying but with opposite direction are present in a portfolio? Yes

definitely! Would it lead to situations where this would be a problem? From the perspective

of the clearing house this would not be the case. Individual equities could show this from time

to time but on average for all equities in the market this would not lead to significant under

margin situations.

It is also the case that OMS II has minimum spread parameters that would cushion this effect

because the instruments would be priced on separate sides of the spread.

The alternative is to include correlation effects12

within equity, and index, products with the

same underlying. This would lead to a significantly more complex set up for the customers to

handle when it comes to replicating margins. It would also increase the difficult task of

explaining margin behaviour for counterparts in NOMX Clearing. The benefit would be very

limited from the clearing house perspective.

It is important to identify that this is the same discussion that takes place if looking at an

interest rate product. If the underlying is the spot rate of a credit provider (as STIBOR as an

example) then the term structure is a way of linking the future value to the spot rate. For

interest rate products this is the normal mind set and this is also what makes it quite difficult

to accommodate traditional interest rate products in traditional margin models. In most cases

clearing houses construct different interest rate index products and have futures defined on

these indexes to be able to use the traditional margin models without constructing very

complex margin parameter set ups.

3.3.2.3 Correlation between instrument

This aspect of correlation is what people ordinary means with correlation in equity markets.

This is also one area which is hard to “solve”. Using a covariance-variance methodology as an

analytical VaR model would do is not really an option for clearinghouses for these types of

models.

OMS II has no correlation between different underlyings. In Figure 3 it can be seen that OMS

II is used in an area where it is hard to actually know which correlation to use because of the

changes in correlation structure for larger movements in the underlying values.

11 As discussed this is really a parameter setting but OMS II within NOMX Clearing this is the way this situation has been

handled since the creation of the model and therefore this issue is discussed here as part of the model

12 That would be to include the window methodology for products with different time to expiry but the same underlying

equity.




3.3.3 Calculation issues

In history all margin models were used to calculate margin numbers. During the last year the

models has also been used in looking at intraday risk. A margin model looks at how much

margin a counterpart should pay at a certain point in time (end of day) even if the actual

calculations are mad intraday. A risk model on the other hand calculates the risk at that

specific moment.

The set up for intraday margin calculation compared with end of day calculations differs in

some aspects. In the end of day calculations it is perfectly clear which options that have been

exercised or not. This is especially true on the expiry date since at the end of the day the

position exists as a delivery position or does not exist at all (not exercised and therefore it is

removed).

All intraday calculations must do some decisions regarding expiring options and also for

options that have exercise opportunities build in as American style options. Also forwards that

expiry must be dealt with in the calculations.

NOMX Clearing has historically worked a lot in this area and the OMS II system has many

parameters that are used to optimize the usage of the OMS II model in the intraday

calculations.

The other area in which intraday margin calculations has a challenge is in the prices used. End

of day calculations use official prices that in most cases are provided by exchanges. Intraday

prices mean that the clearing house must use some sort of technique to get prices for

instruments. In NOMX Clearing there are a system called “price server system” that handles

this issue. This system is not within the scope of this validation but in short the system does

calculate accurate real time prices for all instruments that are cleared. This is very much as a

larger bank would handle their intraday need for accurate prices.

In late 1980th

when OMS II was implemented the calculating power was limited and therefore

OMS II was run on high end machines at the time. This was a long time ago and the

calculation time of OMS II is not really an issue, except for more extreme intraday

calculations that would be used for supervising risk for HFT trading.

NOMX Clearing does not use the OMS II model in such a way and therefore the current use

of OMS II has no limitations when it comes to time issues connected to CPU usage.

3.4 Statistical significance

As previously discussed a traditional margin model has not a statistical predictability as a

VaR model would have. The purpose for the model is to calculate a “high enough” margin

that ensures the stability of the clearing house.

The parameters for scanning ranges, which are the main risk parameter for most margin

models, are usually calculated using some sort of statistical method. There are some trusted

methods in this area:

Pure normal distribution (or log normal) where standard deviation is calculated for the

look “back period”13

Actual historical distribution

Some chosen extreme value distribution technique

13 See Appendix I Definitions for definition of look back period




All these models do have a statistical significance to them and can be evaluated with back

testing techniques.

For a margin model the back testing for small portfolios with a limited number of underlyings

would then in effect show the back testing for the scanning risk parameter methodology.

When the portfolios shows a larger number of underlyings the lack of correlation between

these underlyings would show a back testing pattern with very few “testing exceptions”14

.

3.5 Risk Factors

When designing a risk model in general the key decision is to decide what factors that do, and

should, affect the result of the model. This will of course be governed by what instruments

that is traded and on what type of markets.

For equity and index markets where forwards, futures and standard options are traded the

obvious risk factors are movements of the underlying equity and index together with

movements in implied volatility for options on these equities and indices.

Other risk factors as interest rate used in option pricing, dividend estimations, etc are other

risk factors that could be candidates to include in a risk model given another more

complicated set of products.

For OMS II the chosen risk factors (underlying equity and index together with movements in

implied volatility for options on these equities and indices) works well and has been used

since the introduction of the model at NOMX Clearing.

3.6 Academic and industry references

There are no direct academic research that functioned as the beginning of traditional margin

model. The usage of this model predates the interest on risk model that was introduced with

VaR at the end of the 1980th

.

There is of course academic references for all the option and forward instrument pricing

formulas that is used in the OMS II calculation library but all these models are (as previously

stated) quite standard and wide spread.

When it comes to industry standard OMS II sets its own foot print here because the model has

been extensively used by, and sold to, numerous foreign clearinghouses since early 1990th

.

3.7 Key assumptions

The OMS II model is as previously stated a rather old model with few assumptions build into

the model, there are two basic assumptions:

All instruments that the model calculates margin for have accurate market prices

externally given15

.

The parameters that define the generation of vector files should describe as accurately

as possible the future risk factor movements in the environment in which the model is

used.

14 See Appendix I Definitions for definition of testing exception

15 There are actually some Tailor made instruments that gets valuated within the OM;S II margin model but that is very

conservatively done and relies entirely ob internal parameters.




3.8 Historical references

All mathematical models should be evaluated based on the usage of the model. It is virtually

impossible to have an opinion on a margin model if it is unclear what is expected of it.

OMS II was developed in late 1980th

and does live up to the description of margin

methodologies made in section 3.1.2.

Calculation power was limited at this time so the basic set up with 31 valuation points for

equity products was really something that could not be set to large. The design of the model

could therefore not be to numerically complicated, because of constrains in computational

power. Since the model was developed in parallel with the introduction of exchange traded,

and cleared, derivatives in Sweden it was also important that the model could be explained to

members and external stakeholders. So a rather simple and efficient model was the priority

over a complex “black box” model.

In Sweden the options were introduced prior to forward and futures and the decision to use

something else than SPAN was primarily because of that SPAN was mainly designed for

linear products as futures.

OMS II has been, and is still used, for OTC equity and index contracts that are admitted from

clearing members for clearing. The contract is however very similar to the exchange traded

ones and pose no really challenge for NOMX Clearing when it comes to pricing.

Using OMS II as a general margin model for more complicated OTC products with high

degree of tailor made feature would on the other hand be very hard and the usage of OMS II

margin model will most likely be limited to current usage.

4. Parameters

NOMX Clearing uses a numerical methodology for estimating scanning range parameters.

The look back period is one year and a confidence level of 99.2%. On top off this there is a

procyclicality buffer off 25% for scanning ranges were not 10 years of historical data is used.

The numerical approach does rely on history to estimate future behaviour but do not make any

assumptions16

on actual distribution of the equity market.

16 As a Gaussian approximation as an example




5. Numerical data

5.1 Introduction

The OMS II margin model has been in use for a very long time and to accurately draw

conclusions from the data there must first be some feeling for the composition of the market17

were the model is used. The following table and graph show the distribution on different

instrument types.

Instrument type Initial Margin (SEK)

Index future -5 812 064 042

Stock option -2 745 734 357

Index option -1 127 118 672

Stock forward -626 977 858

Sum -10 311 894 930

linear -6 439 041 900

Non linear -3 872 853 030

Sum -10 311 894 930

Table 8 : Margin per instrument type Figure 4: Margin per instrument type

The currency distribution is as follows:

Currency % of IM IM / Currency (SEK)

SEK 96,3% -9 933 969 463

DKK 2,4% -247 394 958

EUR 1,1% -111 257 178

NOK 0,2% -19 273 331

Sum 100% -10 311 894 930

Table 9 : Currency mix in the equity and index market

One can see that even if there are instruments defined in other currencies than SEK it is not

any volumes in them.

5.2 Back testing

5.2.1 General

Back testing is a technique that is used to control that the behaviour of a mathematical model

behaves as expected/desired. NOMX Clearing has an automated back testing functionality

that produces data on a daily basis. The back testing results are presented on a monthly basis

to the NASDAQ OMX Clearing Risk Committee. The implemented back testing functionality

is a clean back testing were the composition of the tested portfolio is adjusted for the

following parts:

17 In this section on numerical data all markets that OMS II is used in will jointly be referred to as the “market”




Changes in market prices for underlyings

Changes in the portfolio composition as trading and contracts that expires, during the

period i.e. new trades are removed and trades that have expired are artificially

included in the market value.

Do notice that implementing a clean back testing functionality in a clearing house is virtually

impossible to do without development in the clearing system. Having access to normal margin

calculations and market values in a data warehouse will not be sufficient.

Another thing that is important is that the x days period do not become a “sliding” window.

Technically this will cause auto correlation to the time series. In practice autocorrelation (and

clustering of breaches) is present in most financial data but overlapping periods should be

avoided to not count price movements several times in the analysis. In the figure beneath one

can see that each breach will be counted x times for a sliding x day period.

Figure 5: Overlapping test periods

For the back testing presented for the OMS II methodology the sliding effects have been

adjusted for.

NOMX Clearing has two different automatic back testing set ups:

Traditional enterprises back testing which is a daily check of how the calculated initial

margin of actual portfolios copes with the actual market movements.

A relatively new model level back testing in which the initial margin of theoretically

constructed positions checks against the actual historical market movements.

There is a broad range of different reports that aim at describing the results from the back

testing program at NOMX Clearing. This involves both types of back testing and both will be

included in this additional validation.

5.2.2 Data

The back testing analysis is conducted with one year of data (20131031 – 20141031).

Considering that the model has been in use for a considerable amount of time means that the

drawbacks of not analysing a longer period is limited.

The current markets that are margined using OMS II are Nordic equities and indices. The data

is of course limited to these markets.

5.2.3 Enterprise level back testing

There are two aspects of the OMS II margin methodology that will be investigated here.

Firstly the size of the portfolios is divided in three categories with an equal amount of

portfolios: The division is made with Initial Margin as a measure.

Size group nr Average Initial Margin




1 -20 301 070

2 -86 987

3 8 272

Table 10 : Size of the groups for back testing

Before the actual stress test calculations a definition is needed.

Offset percentage, “OP”: A portfolio can have positions that will give off set between

positions in different derivatives series but with the same underlying. In many circumstances

this is referred to as Time Spread effect. It is also the case that options that differs by strike or

time to expiry also will be correlated in both underlying but also in implied volatility18

.

By looking at the difference between naked margins (NM) i.e. margin without correlation

effects between series and Initial margin (IM) the correlation effect can be measured

NM IM

OPNM

(4)

This measure will divide the portfolios according to the following table.

OP Nr OP

1 0%

2 >0 < 10%

3 > 10% < 50%

4 >50% < 80%

5 > 80%

Table 11 : Size of the groups for back testing

It is an interesting measure and the different groups will have different types of counterpart

according to size and trading. To have a high OP number for one underlying the trading

strategy needs to be quite hedged but with a large number of different series with this

underlying. Large counterparts are usually not hedged in all underlyings and since this factor

is calculated for the whole portfolio larger counterparts typically can be found in the middle.

Size group NR OP Nr Breaches Nr Observations NR CONF_LEVEL

1 1 65 254 329 99,97%

1 2 3 34 511 99,99%

1 3 11 93 647 99,99%

1 4 3 17 456 99,98%

1 5 7 3 732 99,81%

2 1 132 330 069 99,96%

2 2 4 15 461 99,97%

2 3 9 44 481 99,98%

2 4 0 10 984 N/A

18 Actually this is a parameter setting for implied volatility. It is doable to run OMS II with no correlation for implied

volatility.




2 5 9 2 609 99,66%

3 1 173 349 617 99,95%

3 2 3 4 270 99,93%

3 3 10 14041 99,93%

3 4 4 6935 99,94%

3 5 104 6093 98,29%

Sum 537 1 188 235

Table 12 : Back test table

A breach is defined as an increase (or decrease) in the market value of the portfolio in any day

during liquidation period currently two days.

The analysis is quite straight forward. First of all it can be concluded that the amount of

breaches is quite low. The increase in breaches with OP is very small and this is what should

be expected (and of course wanted) because the OMS II margin methodology do give

correlation within one underlying and this table give confidence that this is appropriate. If not

the number of breeches would be significantly higher than the table show. Summing over OP

Nr give the following:

Size group NR OP Nr Breaches Nr Observations NR CONF_LEVEL

1 N/A 89 403 675 99,98%

2 N/A 154 403 604 99,96%

3 N/A 294 380 956 99,92%

Sum 537 1 188 235

Table 13 : Back testing table with summed OP Nr

The behaviour of the OMS II methodology does give the desired behaviour for the stress test.

Note: It could probably be more beneficial to exclude accounts with positive or very small (in

absolute number) Initial margin since these accounts will show peculiarities from the

beginning. Positive numbers mean sold options and numbers in the area of zero will create

breaches just from rounding numbers.

5.2.4 Model level back testing

In a model level back testing theoretical portfolios are created and then back tested against

history to look for vulnerable combinations of instruments that might be handled in a les

optimal way by the OMS II margin model.

9 different portfolios are created with OMX positions which will be investigated. They

consists of both futures and options and are all tested during the period 2013-11-05 - 2014-03-

31.

The back testing is done for one and two days. The margin coverage (MC) is calculated and is

how much more margins there is compared to the market value on the back testing. A margin

coverage of 100% means that the margin is just enough. A value over 100% means that here

is more than sufficient margin to cover for the back testing losses.

Port. Port. name 1-day BT 2-day BT IM MC 1 day MC 2 days




1 Front month future vs back month future

-251 -289 -1 382 551% 478%

2 Front month future vs one-year-out future

-917 -713 -1 382 151% 194%

3 Front month future vs front month ATM option

-1780 -1593 -8 738 491% 549%

4 Front month future vs six-months-out ATM option

-1651 -1799 -9 706 588% 540%

5 Front month call-put spread -2517 -3703 -9 256 368% 250%

6 Six-months-out call-put spread -2815 -3468 -9 708 345% 280%

7 Front month ATM option vs six-months-out ATM option

-1707 -1957 -2 746 161% 140%

8 Front month ITM option vs front month OTM option

-1884 -2964 -3 358 178% 113%

9 Six-months-out ITM option vs six-months-out OTM option

-677 -821 -2 141 316% 261%

Table 14 : Back test of theoretical portfolios, 2013-11-05 – 2014-03-31

From the above table one can see that none of the portfolios breached in the back test. Since

NOMX Clearing allow for spread positions with spread parameters it is interesting to

investigate if these parameters can be a cushion for spread positions. From the tale it can be

concluded that spread positions can be handled appropriately within OMS II.

These kinds of reports are currently produced by NOMX Clearing on a regular basis which is

a very nice addition to the overall margin framework.

5.3 Stress testing

5.3.1 Set up

Stress testing is to test how a model behaves if “large” changes are made in the basic

assumptions. First an investigation is done regarding how the model works if the market

values are stressed. In a way this is a back testing against fictive market movements. Secondly

an investigation is made to deduct if the model works within the desired financial

environment. Is it used for the type of distribution of instruments and positions that the model

is meant to work within?

5.3.2 Stressed market conditions

Back testing the model against actual market movements decides if the model works as

desired on a day to day basis. By constructing a time series of “fictive” very large market

movements the behaviour of the model within a much stressed market can be observed.

NOMX Clearing performs stress testing with two different sets of stress test scenarios:

A structured scenario approach called CCaR (Clearing Capital at Risk) where the

entire equity market moves up or down. Each equity moves according to maximum

movements for some time period back. Changes in Implied volatility are treated as

individual scenarios.

Historical stress scenarios from three actual historical occurrences are also used as

scenarios.

Four of the biggest portfolios in terms of initial margin is chosen for this investigation. The

Initial margin and market value looks like this:




DATE ID MV IM MARGIN

2013-11-11 n -584 429 -214 965 002 -215 549 430

2013-11-12 n -228 056 -208 640 257 -208 868 313

2013-11-11 x 242 200 153 -207 450 598 34 749 554

2013-11-12 x 219 643 107 -189 023 126 30 619 981

2013-11-11 y 107 330 -196 656 186 -196 548 856

2013-11-12 y 214 215 -188 136 458 -187 922 243

2013-11-11 z -67 451 244 -560 325 093 -627 776 337

2013-11-12 z -58 622 330 -552 047 004 -610 669 334

∙ ∙ ∙ ∙ ∙

∙ ∙ ∙ ∙ ∙

∙ ∙ ∙ ∙ ∙

2014-11-25 n -17 296 283 -541 955 528 -559 251 810

2014-11-26 n -17 237 889 -544 853 362 -562 091 251

2014-11-25 x 406 914 833 -675 931 836 -269 017 003

2014-11-26 x 387 094 339 -668 751 454 -281 657 115

2014-11-25 y 0 -476 945 695 -476 945 695

2014-11-26 y 0 -505 336 678 -505 336 678

2014-11-25 z -117 152 608 -647 208 026 -764 360 634

2014-11-26 z -103 330 796 -636 276 060 -739 606 856

Table 15 : Stress test table with market value, initial margin and margin, SEK

Now the three different historical scenarios are defined:

Date Name Historical Extreme Event Affected markets Market move summary

1987-10-29 SMV 1987 Stock market crash Equity Equities down

2008-12-09 SMV 2008 Post Lehmann unrest Equity and F/I Equities up, rates down

2012-06-07 SMV 2012 Euro crisis aftermath F/I Rates up

Table 16 : Historical Stress test scenarios, SEK

Running the above defined stressed markets for the four clients will produce potential losses

for some scenarios. If the margin in an account cannot cover for the market value that the

account get for a scenario, then the portfolio get a potential loss. For each scenario all the four

portfolios are ordered according to losses. It is expected that the first scenario will produce

largest losses since it is defined in equity movements and the other have interest rate parts.

The result is the following:

DATE ID MV IM MARGIN SMV 1987 SMV 1987 Loss

2014-06-09 n -8 319 062 -822 973 145 -831 292 207 -1 438 291 645 -606 999 437

2014-06-10 n -7 731 265 -820 893 564 -828 624 829 -1 432 840 124 -604 215 294

2014-11-20 x 307 573 384 -655 815 833 -348 242 449 -759 424 419 -411 181 970

2014-11-25 x 406 914 833 -675 931 836 -269 017 003 -669 845 060 -400 828 057




2014-08-12 y 0 -167 427 000 -167 427 000 271 379 130 438 806 130

2014-06-30 y 0 -168 850 752 -168 850 752 281 417 920 450 268 672

2014-10-24 z 78 149 936 -481 765 559 -403 615 623 602 878 042 1 006 493 665

2014-10-27 z 75 811 128 -482 371 334 -406 560 206 628 401 539 1 034 961 745

Table 17 : Stress test losses for SMV 1987, SEK


2014-10-16 n -27 437 294 -385 722 602 -413 159 895 541 153 242 954 313 138

2014-10-15 n -31 466 323 -405 425 123 -436 891 446 569 447 305 1 006 338 751

2014-08-08 x 63 334 935 -127 530 211 -64 195 276 218 121 790 282 317 066

2014-08-07 x 61 821 375 -137 039 016 -75 217 641 225 609 451 300 827 092

2014-11-27 y 0 -508 166 910 -508 166 910 -914 654 220 -406 487 310

2014-11-26 y 0 -505 336 678 -505 336 678 -909 550 560 -404 213 882

2014-08-11 z -31 336 654 -649 345 068 -680 681 722 -1 022 598 443 -341 916 721

2014-08-08 z -9 430 646 -640 230 304 -649 660 950 -987 508 869 -337 847 919



2014-10-16 n -27 437 294 -385 722 602 -413 159 895 130 096 467 543 256 362

2014-10-17 n -21 086 444 -402 209 253 -423 295 697 145 810 875 569 106 572

2014-08-08 x 63 334 935 -127 530 211 -64 195 276 102 431 575 166 626 851

2014-08-07 x 61 821 375 -137 039 016 -75 217 641 104 534 815 179 752 456

2014-08-12 y 0 -167 427 000 -167 427 000 -101 606 400 65 820 600

2014-06-30 y 0 -168 850 752 -168 850 752 -101 316 992 67 533 760

2014-10-24 z 78 149 936 -481 765 559 -403 615 623 -113 272 226 290 343 397

2014-10-27 z 75 811 128 -482 371 334 -406 560 206 -115 799 459 290 760 747


The result is as expected for the different scenarios. At the same time NOMX Clearing uses

internal scenarios that are constructed. These are the scenarios:

Name Stressed scenario Affected markets Market move summary

SMV B1 Vol 0 Nordic equity market moves up Equity Equities up SMV B2 Vol 0 Nordic equity market moves down Equity Equities down

Table 20 : Constructed Stress test scenarios, SEK




Do notice that “Vol 0” indicates that the implied volatility is not changed in this scenario.

There are several scenarios where the implied volatility is shifted too. For this investigation

though the implied volatility is left as is. These scenarios are now applied exactly as the actual

historical scenarios previously investigated.

DATE ID MV_SEK IM_SEK MARGIN_SEK SMV B1 Vol 0 SMV B1 Loss

2013-11-13 n -5 544 966 -201 050 012 -206 594 977 217 172 764 423 767 742

2013-11-14 n -5 706 495 -197 593 468 -203 299 963 246 596 379 449 896 341

2014-08-08 x 63 334 935 -127 530 211 -64 195 276 200 177 742 264 373 017

2014-08-07 x 61 821 375 -137 039 016 -75 217 641 212 186 460 287 404 101

2014-11-27 y 0 -508 166 910 -508 166 910 -914 654 220 -406 487 310

2014-11-26 y 0 -505 336 678 -505 336 678 -909 550 560 -404 213 882

2014-03-14 z 44 077 561 -540 311 907 -496 234 346 -979 486 720 -483 252 374

2014-03-26 z -965 774 -686 761 452 -687 727 226 -1 139 305 771 -451 578 545

Table 21 : Stress test losses for SMV B1 Vol 0, SEK

DATE ID MV_SEK IM_SEK MARGIN_SEK SMV B2 Vol 0 SMV B2 Loss

2014-05-30 n -10 933 112 -852 135 806 -863 068 918 -1 489 508 799 -626 439 881

2014-06-02 n -11 449 472 -840 590 158 -852 039 631 -1 469 843 215 -617 803 585

2014-11-20 x 307 573 384 -655 815 833 -348 242 449 -777 114 891 -428 872 442

2014-11-24 x 379 005 124 -651 654 992 -272 649 867 -683 746 881 -411 097 014

2014-08-12 y 0 -167 427 000 -167 427 000 271 379 130 438 806 130

2014-06-30 y 0 -168 850 752 -168 850 752 281 417 920 450 268 672

2013-12-18 z -72 491 457 -430 919 664 -503 411 121 416 394 805 919 805 926

2013-12-13 z -45 560 749 -450 662 206 -496 222 955 427 902 591 924 125 546

Table 22 : Stress test losses for SMV B2 Vol 0, SEK

An interesting fact is that the portfolios behave very similar to the SMV of 1987 and the

generated scenario B2 Vol 0. This is at least an indication that at much stressed markets the

movement tends to be much correlated as is the assumption that scenario B2 Vol 0 is

constructed from.

From this investigation it is clear that by adjusting the scanning ranges and keeping no

correlation between underlyings in OMS II the model as such can easily be adjusted to supply

a cushion for very large movements in the markets.

It is further on also clear that the present scanning ranges that are used at OMS II is not

designed to withstand that type of market shock. It is capital preservation models that are

needed in these area and NOMC Clearing do have such a model called CCaR which is used as

a complement to the varies margin models used by NOMX Clearing.




From the standpoint of the validation the OMS II produced margin levels behaves as expected

and give the expected cushion at extreme market movements.

5.4 Sensitivity analysis

5.4.1 Set up

Sensitivity analysis is made to investigate what the margin model is sensitive to. The goal of

this is to find were small differences in calculation method or parameter input causes large

movement in the output (if any). The composition of positions and exposure is relatively

constant and the sensitivity tests are therefore done for an arbitrary date, 2014-10-30.

5.4.2 Enterprise level sensitivity testing

The sensitivity analysis will investigate if “small” changes in scanning range and volatility

range will lead to “small” changes in the resulting Initial Margin calculations. Included is also

if “large” changes in scanning range and volatility range will lead to “large” changes in the

calculations.

To measure this, a simple directional coefficient k can be calculated for the differences as in

the following definition:

Increase IM Increased scanning range k (5)

This k will be the % change in Initial margin given change in parameters. One question that is

important to ask is if this is a linear relation for margin calculations. I.e. would a 1% change

and a 100% change lead to the same k? To measure this a measure in percentage called

difference scan is introduced. 0% is a perfect relation between 1% and 100% changes. Higher

number of Difference scan means that the relation is weaker.

The number of accounts for this day is 4 583. Looking at all accounts would however not be

accurate because of the majority of small accounts for which this relationship will be distorted

by positive margin etc. The validation will therefore compare three separate groups dependent

on initial margin:

Type Nr of accounts Minimum IM (abs) Maximum IM (abs)

Large 47 50 000 000 n/a Medium 605 500 000 49 999 999 Small 1957 50 000 499 999

Table 23 : Dividing portfolios in groups according to Initial Margin

In the following table it can be seen how much initial margin calculations changes with a 1%

and 100% change in scanning range.

Portfolio size

Nr of accounts

Average Initial Margin

Average change in IM 1% scan range change

Average change in IM 100% scan range change

Average of Difference scan

Large 47 -188 353 959 -0,79% -79,18% -0,14%

Medium 605 -3 756 597 -0,95% -104,99% -10,10%

Small 1957 -180 396 -0,98% -110,02% -11,98%

Table 24 : Scanning range sensitivity, 2014-10-30




The column “Average change in IM 1% scan range change” says that if the scanning range is

increased with1% (multiplied with 1.01 not increased by adding 1% to the absolute value of

the scanning range) this is the average increase in initial margin for that offset factor and size

of portfolio.

The column “Average change in IM 100% scan range change” says that if the scanning range

is increased with100% (multiplied with 2 not increased by adding 100% to the absolute value

of the scanning range) this is the average increase in initial margin for that offset factor and

size of portfolio.

Interestingly the behaviour of large portfolios is very stable and differences in initial margin

dependent on differences in scanning ranges are the same for small differences as for large

differences. This would be suspected since large portfolios tend to have a large amount of

positions and even if specific underlyings can have positions that will lead to non linearity the

majority of underlyings will show this behaviour.

For changes in implied volatility the situation looks like this:

Portfolio size

Nr of accounts

Average Initial Margin

Average change in IM 1% voll range change

Average change in IM 100% voll range change

Average of Difference scan

Large 47 -188 353 959 -0,08% -7,69% 0,77%

Medium 605 -3 756 597 -0,13% -14,33% -0,93%

Small 1957 -180 396 -0,12% -13,16% -0,91%

Table 25 : Implied volatility sensitivity, 2014-10-30

Since implied volatility ranges only effects portfolios with options it is not expected that the

relation between changes in volatility range and changes in Initial margin will be as

pronounces as for scanning ranges.

The low Difference scans suggests that the changes in volatility are very linear. This indicates

that even if options can show nonlinearity for individual instruments on average this is not a

problem for the OMS II model.

From the standpoint of the validation this is a very nice behaviour since this implies that the

model is quite predictable from changes in both scanning risk and volatility ranges.

5.4.3 Model level sensitivity testing

By creating theoretical positions and changing some of the risk factors one can draw

conclusions on how sensitive works for interesting combinations of instrument which might

not yet have been found.

To be able to do this investigation the option series is divided into groups19

Time to expiry

Moneyness <1 month 1 month - 3 months 3 months - 9 months > 9 months

> 30% ITM 10% ITM - 30% ITM

ATM +/- 10%

19 ITM is “In The Money”, ATM is “At The Money, OTM is Out of The Money”




10% OTM - 30% OTM

> 30% OTM

Table 26 : Groups for model level sensitivity testing, 2014-11-05

The option series in each of the moneyness groups will have the initial margin calculated for 7

different sub scenarios according to the following table:

Sub scenario, short Sub scenario, long

Av sc par*1,01 d Average of scaning range parameter *1,01

Av sc par*2 d Average of scaning range parameter *2

Av sc par*3 d Average of scaning range parameter *3 d

Av vol par*1,1 d Average of volatility parameter *1,1 d

Av vol par*2 d Average of volatility parameter *2 d

Av vol par*3 d Average of volatility parameter *3 d

Av sc par*2, vol Par*2 d Average of scaning range parameter *2 and volatility parameter *2 d

Table 27 : Sub scenario for a group in model level sensitivity testing, 2014-11-05

This means that the investigation will be done for 5 * 4 * 7 = 140 different groups. In each

group the increase in initial margin expressed as percentage will be calculated and inserted in

a large table.

Time to expiry

<1 month 1 month - 3 months 3 months - 9 months > 9 months

> 30% ITM

Av sc par*1,01 d 0% 0% 0% 0%

Av sc par*2 d 0% 18% 0% 15%

Av sc par*3 d 0% 37% 0% 29%

Av of vol par*1,1 d 0% 0% 0% 0%

Av of vol pa*2 d 0% 0% 0% 3%

Av of vol pa*3 d 0% 0% 0% 6%

Av of sc pa*2, vol pa*2 d 0% 18% 0% 17%

Sum of OI% 0% 2% 0% 0%

10% ITM - 30% ITM

Av sc par*1,01 d 0% 0% 0% 0%

Av sc par*2 d 36% 33% 29% 22%

Av sc par*3 d 71% 66% 59% 46%

Av of vol par*1,1 d 0% 0% 1% 1%

Av of vol pa*2 d 0% 3% 7% 12%

Av of vol pa*3 d 1% 7% 16% 25%

Av of sc pa*2, vol pa*2 d 36% 34% 34% 34%

Sum of OI% 0% 4% 0% 1%

ATM +/- 10%




Av sc par*1,01 d 1% 1% 0% 0%

Av sc par*2 d 149% 77% 46% 28%

Av sc par*3 d 323% 171% 101% 60%

Av of vol par*1,1 d 1% 2% 2% 3%

Av of vol pa*2 d 11% 21% 25% 27%

Av of vol pa*3 d 22% 43% 50% 54%

Av of sc pa*2, vol pa*2 d 154% 93% 68% 53%

Sum of OI% 17% 30% 6% 7%

10% OTM - 30% OTM

Av sc par*1,01 d 2% 1% 0% 1%

Av sc par*2 d 823% 156% 64% 33%

Av sc par*3 d 3100% 453% 155% 74%

Av of vol par*1,1 d 11% 8% 5% 5%

Av of vol pa*2 d 134% 83% 57% 45%

Av of vol pa*3 d 324% 178% 117% 89%

Av of sc pa*2, vol pa*2 d 1109% 264% 125% 77%

Sum of OI% 7% 12% 3% 2%

> 30% OTM

Av sc par*1,01 d 0% 1% 1% 0%

Av sc par*2 d 0% 407% 103% 49%

Av sc par*3 d 0% 2624% 295% 118%

Av of vol par*1,1 d 0% 21% 12% 9%

Av of vol pa*2 d 0% 644% 144% 98%

Av of vol pa*3 d 0% 3037% 333% 209%

Av of sc pa*2, vol pa*2 d 0% 2528% 297% 158%

Sum of OI% 0% 7% 0% 0%

Total Sum of OI% 24,79% 54,89% 9,87% 10,45%

Table 28 : Sub groups for model level sensitivity testing, 2014-11-05

From the above table there can be some conclusions drawn. First the volume weighted open

interest (OI) is added to each group as measure eon how large the positions within each group

are for NOMX Clearing. Secondly when a sub group show 0% percentage it means that there

are no option ser5oies with open interest at that date for that sub group.

ITM options do function as linear instruments the more ITM they are and the difference in

scanning range is nearly linear. They are insensitive for changes in volatility.

ATM options show a larger moment when scanning ranges change but still within

expectations. They are sensitive for volatility movements but rather small changes. Both

scanning ranges and volatility changes are quite large for short options because that’s where

options are most sensitive.

OTM options do show large swings for changes in both scanning ranges and volatility. This

because if the normal scanning range is not large enough to “kick in” the options into ATM or




even ITM then the increased scanning range might do just that. The effect will be a very large

increase in option value thus a large difference in initial margin.

Since this sensitivity analysis is made on naked options series this is of course nothing that

surprises the reader. This behaviour is natural to options and is a a part of all basic courses in

option theory.

The interesting part is the open interest numbers that show that the bulk of open interest

resides in ATM area between 1 month and 3 month time to expiry. This indicates that the bulk

of the options are in an area that shows a very nice behaviour in changes for scanning ranges

and volatility. This investigation is in the line of similar investigations in last validation; see

(Validation OMS II, NOMX, 2013, ss. 23-24) .

It would be interesting in next validation to look more on the effect in actual numbers. Very

much OTM options can have an initial margin of 1 SEK and then a increase to 10 SEK is very

large in percent but can be moderate if looked upon in the environment of a portfolio.

From the validation stand point the model do behave as expected and in line with previous

validation.




6. Conclusions

6.1 Changes from previous validation

Since the previous validation of the OMS II model (Validation OMS II, NOMX, 2013) there

has been very little changes to the model or the way the model is used.

It is still Nordic equity market which is the market for which this model is used as margin

model.

6.2 Input to the validation

From discussions with key personnel it is evident that the knowledge of the model is good and

the risk of misconception in usage of the model or setting of parameters is limited.

The OMS II model has been used for almost 30 years and there is an abundance of

documentation to use in validation process and almost an infinite volume of historical data.

The documentation of the model, with the OMS II model instructions (OMS II MI, 2014) and

OMS II Margin methodology guide (OMS II MMG, 2014) as main reference material, is very

good. Updated, clear and with a mathematical standard that explains and motivates the

different decisions made in the implementation makes this an excellent aid in understanding

the model.

6.3 Theoretical framework of the model

The OMX II model is one of the oldest models in use. It is wide spread around the world and

used at many clearinghouses for a number of different instruments. The model has been

designed for exchange traded instruments but later other more tailor made contracts20

has

been added to the instrument cleared at NOMX Clearing.

OMX II has no specific statistical measure linked to it. Even if scanning ranges have

statistical significance when estimated, the margin model will only show similar behaviour

for very small portfolios with derivatives based on one underlying.

The way correlation is handled is very step motherly leading to a very robust model with little

difficulties to withstand changes in correlation structure or high volatility periods.

The model itself requires external market prices for its positions which make it less suitable to

be used extensively for pure OTC market. Given current markets, instruments and usage of

the model it performs well and can certainly continue to be a central margin model for

NOMX Clearing.

The model is well known in the financial community.

The analysed data is generally of good quality and can be easily imported from the existing

data warehouse. The validation of the data does have the expected findings (due to the

simplicity of the model) and do support the theoretical conclusion drawn by the validation.

6.4 Correlation

The current use of OMS II when it comes to correlation is that different indices and equities

are treated as perfectly uncorrelated. This is a very conservative approach in this area and

fulfils by definition the demands on portfolio margining given by (Del.Reg 153/2013 EMIR,

20 In reality tailor made instruments re very much like standardized derivatives but some of the parameters has been

changed as strike or time to expiration.




s. Art 27). For instruments based on the same underlying (same risk factor) NOMX Clearing

allows for correlation between positions based on these instruments. This effectively means

that a long position with a short time to expiry is perfectly correlated with a short position

with a long time to expiry when the positions are based on the same underlying instrument

(risk factor). NOMX Clearing applies spread parameters in order to avoid combinations for

which initial margin would have been very low. As an example on numerical investigation

please see Table 14 : Back test of theoretical portfolios, 2013-11-05 – 2014-03-31.

The equity market is a market with very high dependencies between spot price and forward

price. Equities can be bought and hold with very low “cost of carry” implying that price

difference between forward and spot is directly related to interest rate costs and corporate

action expectations. Changes in these factors will affect the price relation but related to

margin these are very small differences and would be adequately covered by the effect of the

spread parameters.

From the stand point of the validation the usage of OMS II when it comes to correlation meet

all criteria’s set by the EMIR frame work.

6.5 Parameters

The methodology for setting scanning ranges and other clearing parameters is well described

in the documentation and communicated to the stake holders. The OMS II model is a very

parameter driven model in the sense that most of the behaviour of the model can, and must, be

decided with parameters.

The volume of parameters is manageable to handle manually but file transmission is

supported by the model implementation.

6.6 Monitoring process

NOMX Clearing has an ambitious back testing and sensitivity testing program at place which

facilitates the monitoring of the model. Changes in the way the model behave or changes in

the surrounding environment would quickly be discovered.

6.7 Recommendations

The recommendation from the previous validation (Validation OMS II, NOMX, 2013) was to

improve documentation, which has been done.

When it comes to data the recommendation is to create a package of data for usage as input to

investigations. Today the data exists but the flexibility of the report system is also hard for

externals to comprehend. More set reports with explanation of the content will facilitate the

monitoring of the margin model.




7. Information

7.1 Figures

Figure 1: Basic VaR principle .................................................................................................................................. 7

Figure 2: Several instruments with the same underlying ....................................................................................... 11

Figure 3: Market movements and correlation ........................................................................................................ 17

Figure 4: Margin per instrument type .................................................................................................................... 22

Figure 5: Overlapping test periods ......................................................................................................................... 23

7.2 Tables

Table 1 : Basic vector file ........................................................................................................................................ 9

Table 2 : Example on instrument vector file (Call option example) ...................................................................... 10

Table 3 : Total sum vector file for underlying X ................................................................................................... 12

Table 4 : Total sum vector file for underlying Y ................................................................................................... 12

Table 5 : Total sum vector file for underlying X & Y ........................................................................................... 13

Table 6 : Two vector files with different underlyings ............................................................................................ 13

Table 7 : Two vector files in the window method .................................................................................................. 14

Table 8 : Margin per instrument type ..................................................................................................................... 22

Table 9 : Currency mix in the equity and index market ......................................................................................... 22

Table 10 : Size of the groups for back testing ........................................................................................................ 24

Table 11 : Size of the groups for back testing ........................................................................................................ 24

Table 12 : Back test table ....................................................................................................................................... 25

Table 13 : Back testing table with summed OP Nr ................................................................................................ 25

Table 14 : Stress test table with market value, initial margin and margin, SEK .................................................... 27

Table 15 : Historical Stress test scenarios, SEK .................................................................................................... 27

Table 16 : Stress test losses for SMV 1987, SEK .................................................................................................. 28



Table 19 : Constructed Stress test scenarios, SEK ................................................................................................. 28

Table 20 : Stress test losses for SMV B1 Vol 0, SEK ............................................................................................ 29

Table 21 : Stress test losses for SMV B2 Vol 0, SEK ............................................................................................ 29

Table 22 : Scanning range & Implied volatility sensitivity testing for all counterparts, 20141030Error! Bookmark not defined.

Table 23 : Average Scanning range & Implied volatility sensitivity testing for all counterparts, 20141030Error! Bookmark not defined.

7.3 References

OMS II MI. (2014). OMS II Model instructions.

OMS II MMG. (2014). Margin methodology guide OMS II.

Validation OMS II, NOMEX. (2013). Validation of OMS II ver 1.1 2013.




8. Appendices

8.1 Appendix 1 Definitions

To facilitate reading the definitions of COMMISSION DELEGATED REGULATION (EU)

No 153/2013, CHAPTER I, GENERAL, Article 1 Definitions is included in this appendix to

the validation.

For the purposes of this Regulation, the following definitions apply:

1) ‘basis risk’ means the risk arising from less than perfectly correlated movements

between two or more assets or contracts cleared by the central counterparty;

2) ‘confidence interval’ means the percentage of exposures movements for each financial

instrument cleared with reference to a specific lookback period that a CCP is required

to cover over a certain liquidation period;

3) ‘convenience yield’ means the benefits from direct ownership of the physical

commodity and is affected both by market conditions and by factors such as physical

storage costs;

4) ‘margins’ means margins as referred to in Article 41 of Regulation (EU) No 648/2012

which may include initial margins and variation margins;

5) ‘initial margin’ means margins collected by the CCP to cover potential future

exposure to clearing members providing the margin and, where relevant, interoperable

CCPs in the interval between the last margin collection and the liquidation of positions

following a default of a clearing member or of an interoperable CCP default;

6) ‘variation margin’ means margins collected or paid out to reflect current exposures

resulting from actual changes in market price;

7) ‘jump to default risk’ means the risk that a counterparty or issuer defaults suddenly

before the market has had time to factor in its increased default risk;

8) ‘liquidation period’ means the time period used for the calculation of the margins that

the CCP estimates necessary to manage its exposure to a defaulting member and

during which the CCP is exposed to market risk related to the management of the

defaulter’s positions;

9) ‘lookback period’ means the time horizon for the calculation of historical volatility;

10) ‘testing exception’ means the result of a test which shows that a CCP’s model or

liquidity risk management framework did not result in the intended level of coverage;

11) ‘wrong-way risk’ means the risk arising from exposure to a counterparty or issuer

when the collateral provided by that counterparty or issued by that issuer is highly

correlated with its credit risk.

Documents

Validation of OMS II - DHIS