Rates FO Training-Session v Products) 20 May 2010

8/9/2019 Rates FO Training-Session v Products) 20 May 2010

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COPYRIGHT 2010 SAPIENT CORPORATION | CONFIDENTIAL 1


Rates FO Training

Session IV (Products)April 15, 2010


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About the training

This training will cover

Products and markets (Session I)

What are interest rates, really ? (Session IV, V)

How are they set, and in which markets are they traded? (Session II, III)

What are the key products used for trading and hedging rates? (Session IV, V)

Processes

What is the front to back process used to trade rates?

What do FO, MO and BO do? What tools and techniques do they use?

What tools and techniques do they use in UBS?

We will emphasize FO concepts, and operations, but cover some MO and BO

What role can, might I play in the process?Mathematics underlying rates trading

Introduction to rates analytics/mathematics (A flavor!)

Valuation and risk management (forward curves, discount curves, and those pesky greeks!)

Typical IT projects, assignments, challenges in FO, and possible solutions (Optional)

So where will it get me?

You will not become an expert, but you will be

Able to talk to a trader, and understand his needs

Able to talk to a BA, and understand his needs

Able to talk rates FO - in weeks, and hopefully, start walking the walk a journey of years!

Where do you want to go?

Assumptions?

For 101 sessions, we dont assume much and start from the basics (time value of money)

For 201 sessions- we will use slightly advance maths not necessary, but very helpful


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Account Plan Topics

Bond basics

What are bonds

Bond valuation

Yield Curve and Term structure of interest rates

Interest Rate products and Risk Management

Futures and Forwards

Swaps

Options

Advanced topics?


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Overview of Bonds

Link between FI and Rates

The rates business is rooted in the fixed income business

We will take a quick pass through the bonds and bond valuation to understand what

interest rates are and how are they set in the markets. (There is a macroeconomic

angle as well, which discusses how interest rates are influenced and determined by

an interaction of the monetary policy in an economy-typically set by the Fed, and the

fiscal policy, typically managed by the federal government. This will be covered in a

201 session)

This will build the foundation for an understanding of various rates products and their

purpose


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What is a Bond?

In its broadest sense, a bond is any debt instrument that promises a fixed income stream to the holder

Fixed income securities are often classified according to maturity, as follows:

Less than one year Bills or Paper1 year < Maturity < 7 years Notes

< 7 years Bonds

A typical bond has the following characteristics:

A fixed face or par value, paid to the holder of the bond, at maturity

A fixed coupon, which specifies the interest payable over the life of the bond

Coupons are usually paid either annually or semi-annually

A fixed maturity date

Note:The coupon rate, the maturity date, par value are all set (fixed) at the time the bond was originally sold The coupon rate will reflect the

required rates of interest at the time of bond issue.

After issue, interest rates, and required rates of return will change. Because everything is fixed except the required rate of return and

the bond price, as rates change, so too will bond prices!


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Bond Valuation: Time Value of Money

Revisiting the time value of money

Future value of an investment at an annual rate r, compounded m times a year is for T years is

Conversely

Setting FV to 1, provides the present value of 1 dollar in the future, and is called the discount factor

Discount factors are of critical importance to finance-it is possible to determine the value of any investment

by applying the appropriate discount factors. For an FI security consisting of known cash flows (Ci), at

various times (Ti)

We will understand its use an application in the relatively simple case (nevertheless important one) of bond

valuation


7/81 COPYRIGHT 2010 SAPIENT CORPORATION | CONFIDENTIAL 7

Bond Valuation: Present Value and Yield to Maturity (YTM)

Bond Valuation

A Coupon Bonds Present Value (PV)/price has Two Components:

Present Value of the Coupon Interest Payments

Present Value of the Future Redemption Value

For a bond with annualized coupon C, m times a year, with N=txM payments due, the value is

The standard bond pricing formula assumes a flat yield, i.e. a single interest rate applicable to

all cash flows. With this assumption

This is the so called Price-Yield Formula



Yield To Maturity (YTM)- rate of return anticipated on a bond if it is held until the maturity date. Or alternatively

put its the IRR (internal rate of return) on a bond

YTM takes into account the current market price, par value, coupon rate and time to maturity. It is also assumedthat all coupons are reinvested at the same rate

When bond investors speak of yield, they are referring to Yield to maturity

Note that when coupon rate equals the yield the price becomes Par

Bond Valuation: Yield to Maturity



Bond Valuation: Yield to Maturity

When the coupon rate is higher than the yield, the bond is at discount, and in reverse at a premium

As the bond approaches maturity, the bond gets closer to par as youd expect. This is called pulling to par effect

Clean vs. Dirty Price

Dirty price is the price youd expect to pay in the market place and takes into account the accrued coupon at

dates between coupon payments. This introduces raggedness in the bond pricing-to get a smoother

measure bond traders prefer to use a different measure

Clean price = dirty price-accrued interest



Factors Affecting Bond Prices

As the price-yield formula suggests

There are three factors that affect the price volatility of a bond

Yield to maturity

Time to maturity

Size of coupon

We will look at each of these in turn.



Factors Affecting Bond Prices: Yield

Inverse Relationship Between Bond Prices and Yields

to Maturity

When interest rates (required rate of return on the

bond) increase, bond prices fall.

The relationship between the coupon rate and thebonds yield-to-maturity (YTM) determines if thebond will sell at a premium, at a discount or at par

Market Yield(%)

Price

($)

If Then Bond Sells at a:

Coupon < YTM Market < Face Discount

Coupon = YTM Market = Face Par

Coupon > YTM Market > Face Premium



Factors Affecting Bond Prices: Yield

Yield to maturity (investors required return)

Bond prices go down when the YTM goes up

Bond prices go up when the YTM goes down

The graph below shows how the price of a 25 year, 10% coupon bond changes as the

bonds YTM varies from 1% to 30%

Note that the graph is not linear instead it is said to be convex to the origin

Price/Yield Re lations

0

50

10 0

15 0

20 0

25 0

30 0

35 0

1 3 5 7 9 1 1 1 3 15 17 1 9 21 23 25 2 7 29

Pe rcent YT

Priceper$100

ofFace

Value


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Other Factors Affecting Bond Prices: Term to Maturity

Long bonds have greater price volatility than short bonds

The longer the bond, the longer the period for which the cash flows are fixed

More distant cash flows are affected more in the discounting process (remember theexponential nature of compoundingand that discounting is the inverse of compounding)

The most distant cash flow from a bond investment is the most important (it is the face valueof the bond) and this cash flow is affected the greatest in the discounting process.


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Other Factors Affecting Bond Prices: Coupon

Low coupon bonds have greater price volatility than high coupon bonds

High coupons act like a stabilizing device, since a greater proportion of thebonds total cash flows occur closer to today & are therefore less affected by a

change in YTM

The greatest price volatility is found with stripped bonds (no coupon payments)


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Change in Interest Rates with Time

Why practically homogeneous bonds of different maturities have different interest rates?

This question is of great significance to both borrowers and lenders.

Should a lender invest in short-term bonds and have to worry about the rates at which toreinvest when short-term bond matures? Or should the lender buy long-term bonds and runthe risk of an uncertain liquidating value if selling is necessary before maturity?

Borrowers are faced with the choice of whether to borrow short-term or long-term. Short-

term borrowing runs the risk that refinancing may be at higher rates. Long-term financingruns the risk that a high rate may be locked in.

A study of the yield-curve and term-structure of interest rates can help borrowers andlenders in making the right decision.


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Whatis a Yield Curve?

A graphical depiction of the relationship between the yield on bonds of the same credit quality, but different

maturities is known as the yield curve.

Term structure of interest rates may be defined as the relation between yield to maturity of zero couponsecurities of the same credit quality and maturities of those zero-coupon securities.

Yield-to-maturity on zero-coupon securities for different maturities is also the spot rate for that maturity.

Therefore, term structure of interest rate may also be defined as the pattern of spot rates for different

maturities.

The yield on Treasury securities is a benchmark for determining the yield curve on non-Treasury

securities. Consequently, all market participants are interested in the relationship between yield and

maturity for Treasury securities.


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Term Structure of Interest Rates

The graphical depiction of the relationship between the yield on Treasury securitiesfor different maturities is known as the yield curve. While a yield curve is typicallyconstructed on the basis of observed yields and maturities, the term structure ofinterest rates is the relationship between the yield on zero-coupon Treasury securitiesand their maturities.

Therefore, to construct term structure of interest rates, we need the yield on zero-coupon Treasury securities for different maturities.

Zero-coupon Treasuries are issued with maturities of six-months and one-year, but

there are no zero-coupon Treasury securities with maturity more than one-year.Thus, we cannot construct such term structure solely from market observed yields.

Rather, it is essential to construct term structure from theoretical consideration appliedto yields of actually traded Treasury debt securities.

Such a curve is called Theoretical Spot Rate Curve


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More risky bonds (e.g. rated Corporate Bonds) will have their own yield curve and it will plot at higher YTMat every term to maturity because of the default risk that they carry

The difference between the YTM on a 10-year corporate bond (say BBB)and a 10-year US Govt bond iscalled a yield spread and represents a default-risk premium investors demand for investing in more riskysecurities.

Side bar: All publicly traded bonds are assigned a risk rating by a rating agency, such as Dominion Bond

Rating Service (DBRS), Standard & Poors (S&P), Moodys, Fitch, etc.

Bonds are categorized as:

Investment grade top four rating categories (AAA, AA, A & BBB)

Junk or high yield everything below investment grade (BB, B, CCC, CC, D, Suspended)


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Spreads will increase when pessimism increases in the economy

Spreads will narrow during times of economic expansion (confidence)

Corporate Bond Risk Premium and Flight to

Quality

0

2

4

6

8

10

Jan-07

Mar

-07

May

-07

Jul-0

7

Sep-07

Nov-07

Jan-08

Mar

-08

May

-08

Jul-0

8

Sep-08

Nov-08

Jan-09

Corporate bonds, monthly data Aaa-Rate

Corporate bonds, monthly data Baa-Rate

10-year maturity Treasury bonds, monthly data


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Types of Yield Curve

There is no single yield curve describing the cost of money for everybody. The most importantfactor in determining a yield curve is the currency in which the securities are denominated. Theeconomic position of the countries and companies using each currency is a primary factor in

determining the yield curve.Different institutions borrow money at different rates, depending on their creditworthiness. Theyield curves corresponding to the bonds issued by governments in their own currency are calledthe government bond yield curve (government curve).

Banks with high credit ratings (Aa/AA or above) borrow money from each other at the LIBORrates. These yield curves are typically a little higher than government curves. They are the most

important and widely used in the financial markets, and are known variously as the LIBOR curveor the swap curve.

LIBOR rates are widely used as a reference rate for :-

Forward rate agreements

Short term interest rate futures contracts

Interest rate swaps

Floating rate notesSyndicated loans

Besides the government curve and the LIBOR curve, there are corporate (company) curves.These are constructed from the yields of bonds issued by corporations.


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Uses of Yield Curve

Shape of government Yield Curve is a key of economic conditions

Inverted Yield Curve indicates recessions

Article from USA Today Feb 2007Inverted yield curve may no longer be sign of recession

http://www.usatoday.com/money/economy/2007-02-13-curve-usat_x.htm

Steep Yield Curve predicts end of recessions

Benchmark for pricing many other fixed-income securities (Typically LIBOR)


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Construction of Yield Curve

Typically market yield curve used

in I banks (so called LIBOR yield

curve) is constructed from

different instruments at differing

maturities

201 session

This is the yield curve thatunderlies pricing for various

products-appropriately adjusted

for various premiums (risk, cost of

funds etc.)


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Spot Market

A market in which commodities are bought and sold for cash and immediate

delivery.

The spot market refers to instruments that are traded and settle within two

business days* of the transaction.

The spot rate refers to the current market rate

Also called the cash market or physical market


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Forwards

A forward contract

Delivery of a security/ commodity at some future date

Delivery price is determined at the time of contract

It is defined such that it has no initial monetary value

Define the grade and quantity of goods to be delivered

Time and place of delivery are also defined


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Evolution of the forwards/ futures market

17th Century

JapanForward Agreements

Silk and Rice

To Arrive

ContractsShippingIndustry

18th Century

U.SOrganized grain

markets

1848

CBOTMember basedorg

Spot andforward trading

1840

Chicago (center ofrail road network)Natural trading hub

Start of ModernFutures Market

CBOTStandardizedcontracts

Future trading

1898

Chicago Butterand Egg Board

1919Converted to CME

COMFUTURES

1971Currency no

longerPegged to

Gold

IMMestablished.

CurrencyFutures

launched

197690 day US T-Billfuture contract

Most actively tradedfuture

Euro Dollarfuture

contractsCash

Settlement

1982StockIndex

Future onS&P 500

FINFUTURES


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Futures

Definition: A futures contract is a type ofderivative instrument, orfinancial

contract, in which two parties agree to transact a set offinancial instruments

or physical commodities forfuture delivery at a particularprice.

Buyers and sellers in the futures market primarily enter into futures contracts

to hedge risk or speculate rather than exchange physical goods (which is the

primary activity of the cash/spot market).

Buy = Long Position, Sell = Short Position


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Forwards and Futures Contracts

FuturesFutures ForwardForwardAmountAmount StandardizedStandardized NegotiatedNegotiated

Delivery DateDelivery Date StandardizedStandardized NegotiatedNegotiated

Counter-partyCounter-party ClearinghouseClearinghouse BankBank

CollateralCollateral Margin Acct.Margin Acct. NegotiatedNegotiated

MarketMarket Auction MarketAuction Market Dealer MarketDealer Market

CostsCosts Brokerage andBrokerage andexchange feesexchange fees

Bid-ask spreadBid-ask spread

LiquidityLiquidity Very liquidVery liquid Highly illiquidHighly illiquid

RegulationRegulation GovernmentGovernment Self-regulatedSelf-regulated

LocationLocation Central exchangeCentral exchange WorldwideWorldwide


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Need for futures

Hedging need for price certainty in the future.

Price of raw materials

Price of produce goods

Speculation

Making profit by being on the right side of the price move. i.e. if the price is

expected to increase then buy the instrument else short it.

As the prices of commodities and fin instruments change frequently there are alot of opportunities

Day traders, Position traders, Arbitragers


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Contract Terms

Ticker symbol: Initials that identify the contractContract size: The cost per unit of the commodity multiplied by the numberof units specified in the contractTick size: Minimum price increment permitted in the trading processDelivery/expiration monthsSample quote: The terms and format used in reporting price quotesTrading hours: Hours during which a contract may be traded; may differ foropen outcry and electronic tradingPrice limits: Amount of change in price permitted in one day; in cases whenlimits are reached in a day, limits are usually expanded the next dayPosition limits and accountability: Maximum number of contracts a singleentity can hold; explanations required when holding large numbers of asingle contractLast trading day: Final day and time after which the contract cannot betraded

Final settlement rule: Day on which final contract value is determined andsettlement madeTrading venue: Where and how the contract is traded: via open outcry,electronic trading, or both


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Margin

Margins (also called Performance Bonds)

Different from stocks

Instead of borrowed money it is good faith money

Initial Margin

Maintenance Margin

Margin Call

Leverage double edged sword


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T Bill Futures

Defining features

$ one million face

Delivery of a T-bill maturing in 3 months

Price is quoted as the 100 expected discount rate on the 3 month T-bill on

maturity

Invoice price on delivery

$1,000,000 [ 1 (settlement discount on last trading day) X (days to maturity /360)]


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Eurodollars Futures

Defining features

One million principal value

3 month maturity

Price quoted in terms of IMM index for 3-month EDs (100.00 yield)

Cash Settled

Price of ED based on random selection of 20 banks from a predetermined list


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US Treasury Bond and Note Futures Contract

Defining features

The contract requires delivery of $100,000 face value of bonds with at least 15

years to call (i.e. if the bonds are callable) or 15 years to maturity

Future price is quoted as a percentage of the face with a tick of 1/32

Invoice Price on delivery = Future Price * 100,000 * Conversion Factor + AI

Position day: notice of delivery by short, 2 days prior to delivery date

Intention day: short must state precisely which bond will be used for delivery, 1

day before delivery


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US Treasury Bond and Note Futures Contract (cont)

Defining features (cont)

Delivery day: short must transfer bonds to long and long must pay for it.

No trade done on last 7 biz days

Note Contracts and their acceptable maturities

2 year 1 year 9 months to 2 years

5 year 4 years 3 months to 5 year 3 months

10 year 6.5 years to 10 years

Several deliverable bonds

Identify the cheapest to deliver


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Principles of Futures Prices

Parallelism

Futures and Cash markets highly correlated. Similar factors influence each

market

Example: The imminent war in Iraq causes both current and future prices to

increase

Or like monsoon in India

Convergence

Futures and Cash prices tend to converge at the expiration of the futures contract

Due to the fact that carrying costs decrease as the futures contract draws closer

to expiration


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Spread Trading

Buy two related futures contracts, one short and one long

Consists of both a long and short position in different contracts of the same or

related commodities

Takes advantage of the relative movements between two (or more) underlying

contracts

Eliminates sensitivity to absolute price changes

Assumption: The two contracts are highly correlated. (i.e. price increases affect

both commodities)


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Swaps

All swaps involve exchange of a series of periodic payments between two parties, usually through an

intermediary which is normally a large international financial institution which runs a swap book

The two major types are interest rate swaps (also known as coupon swaps) and currency swaps.

The two are combined to give a cross-currency interest rate swap

Other less common structures are equity swaps, commodity swaps

Liability swaps exchange one kind of liability for another

Asset swaps exchange incomes from two different types of assets

Why would a firm want to exchange one kind of liability or asset for another?Capital market imperfection or factors like differences in investor attitudes, informational

asymmetries, differing financial norms, peculiarities of national regulatory and tax structures and

so forth explain why investors and borrowers use swaps.

Swaps enable users to exploit these imperfections to reduce funding costs or increase return

while obtaining a preferred structure in terms of currency, interest rate basis etc.


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Interest Rate Swaps

A standard fixed-to-floating interest rate swap, known in the market jargon as aplain vanillacoupon swap (also referred to as "exchange of borrowings") is an agreement between two partiesin which each contracts to make payments to the other on particular dates in the future till a specifiedtermination date

One party, known as the fixed rate payer, makes fixed payments all of which are determined at theoutset

The other party known as the floating rate payerwill make payments the size of which dependsupon the future evolution of a specified interest rate index

AFIXED-TO-FLOATINGINTERESTRATESWAP

6.75%Fixed 6.5%fixed

Prime-25bp Prime-25bp

Prime+75bp 6.5%Fixed

ToFloating toFixed

RateLenders RateLenders

SWAPBANK

XYZCORP. ABCBANK


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key features of an interest rate swap

The Notional Principal; The Fixed Rate; Floating Rate Trade Date, Effective

Date, Reset Dates and Payment Dates (each floating rate payment has threedates associated with it as shown below

The setting/reset date is the date on which the floating rate applicable for the

next payment is set

Accrual date is the date from which the next floating payment starts to accrue

Settle date is the date on which the payment is due


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Major Types of Swap Structures

A zero-coupon swap has only one fixed payment at maturity

A basis swap involves an exchange of two floating payments, each tied to a different market index

In a callable swap the fixed rate payer has the option to terminate the agreement prior to scheduled maturity whilein aputtable swap the fixed rate receiver has such an option

In an extendable swap, one of the parties has the option to extend the swap beyond the scheduled termination date

In a forward start swap, the effective date is several months even years after the trade date so that a borrower with

a future funding need can take advantage of prevailing favourable swap rates to lock in the terms of a swap to be

entered into at a later date

An indexed principal swap is a variant in which the principal is not fixed for the life of the swap but tied to the level

of interest rates - as rates decline, the notional principal rises according to some formula

A Callable Coupon Swap is a coupon swap in which the fixed rate payer has the option to terminate the swap at aspecified point in time before maturity and a Puttable Swap can be terminated by the fixed rate receiver

Application of callable swap

Transforming Callable Debt into Straight Debt

Swaptions, as the name indicates are options to enter into a swap at a specified future date, the terms of the swap

being fixed at the time the swaption is transacted


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One can view interest rate swaps as:

Long position in bond with a short position in another bond or as a portfolio of forward

contracts.

The value of the swap (for the institution paying floating and receiving fixed), denoted V, is(assume that the financial institution receives fixed payments of C dollars at times s and makefloating payments at the same times):

V ( t ) = b ( t ) b*(t)

b( t ): value of fixed-rate bond underlying swap.

b*( t ): value of floating-rate bond underlying swap.

The discount rates used in the valuation reflect the riskiness of the cash flows. Note that: [r(n) isthe discount rate at date n]:b = C e-r(s) s + Q e-r(T) Twhere Q is the notional principal underlying the interest rate swap, C is the fixed payment andthe summation goes from s=1 to s=T the termination date of the swapb* = C* e-r(t1) t1 + Q e-r(t1) t1where the floating rate bond, b* must have, after the payment at time t1 value equal to thenotional principal , Q , and C* is the floating rate payment due at time t1

Swap Valuation


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Example: Financial institution pays 6-month LIBOR and receives 8% per annum (with semiannual

compounding) on a notional principal of $100 Million. The swap has a remaining life of 1.25 years. The

relevant discount rates are 10%, 10.5%, and 11% for 3 months, 9 months, and 15 months. The 6

month LIBOR rate at the last payment date was 10.2% (and the reset frequency is 3 months).

Note For s= 3/12 = 0.25; r = 0.10 For s = 9/12 = 0.75; r=0.105 For s = 1.25; r = 0.11

t1 = 3 months = 0.25

r ( t1 = 1) = 0.10 [reset frequency discount rate]

C = 0.08 100 = 4 Million [coupon for fixed]

C* = 0.102 100 = 5.1 Million [coupon for floating].

b = 4 (e-0.25 0.1 + e-0.75 0.105) + 104 (e-1.25 0.1) = 98.24 million

b* = 5.1 (e-0.25 0.10) + 100 e-0.25 0.10 = 102.51

The value of the swap to the fixed rate receiver is

98.24 102.51 = -4.27 million.

The value to the fixed rate payer is obviously + 4.27million

Swap Valuation- Example


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What are Options?

An option is a contract giving the

investor the right, but not the obligation,to buy or sell an underlying asset (a

stock or index) at a specific price on or

before a specific date

The choice has a price Option priceor premium the buyer pays to the seller

for acquiring the right

Like other securities, options are listed

and traded with buyers and sellers

making bids and offers

Buyer acquires no ownership rights in

the underlying asset

Source: http://www.cboe.com


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Types of Options Call

You are interested in buying a house priced at $100,000. However, you donot have sufficient funds to close the deal and need a month to arrange thefunds. As a result, you negotiate a deal with the seller to hold the house foryou for a period of one month in return for a holding fee of $3,000

Call Option right to BUY the underlying asset at a specific price called as strike

price on or before the specified date called as expiration date for a price the option

premium or option price

At the end of the one month period you could:

Walk away from the deal as you realize the house is not worth the price

Pay the seller $100,000 and transfer the house in your name

Sell your right to buy the house in turn for the increase in the price of the house

e.g. say the house is now priced at $130,000. You can give up your right and in

return get $30,000


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Types of Options Put

You want to protect the value of your new car against any damages. Hence

you buy an insurance for a fixed period and in return pay a premium to the

insurance provider for protecting the value of your new car e.g. for a $25,000

car you pay $1500 for a year

Put Option right to SELL the underlying asset at a specific price called as strike

price on or before the specified date called as expiration date for a price, the option

premium or option price

At the end of the year you could:

Regain the insured value from the insurance provider if the car is damaged

during the insurance period

No payments to you as the car is not damaged. Insurance provider keeps the

premium


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Writers and Holders

Writers = Sellers of the option contract. They have obligations

Holders = Buyers of the option contract. They have rights

Buyer (Holder) Seller (Writer)

Call

Put

Right to buy Obligation to sell

Long = Buy, Short = Sell

Right to sell Obligation to buy

What is a Long Call?

Long Call = Buy CallShort Call = Sell Call

Long Put = Buy Put

Short Put = Sell Put


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Option Value In, At and Out of Money

In the MoneyXYZ $75 Call

$75

Share

Price

$60

$90

XYZ $75 Put

Out of Money

At the Money


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Long Call Buy a Call

30

20

10

0-5

30 40 50 60

70 80 90

Profit ($)

Share price ($)

Risk: Premium

Reward: Unlimited

Break Even: Strike Price + Premium

Motivation: When share prices are expected to rise (Bullish)

Buy $60 Call at $5

65


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Short Call Sell a Call

Risk: Unlimited

Reward: Premium

Break Even: Strike Price + Premium

Motivation: When share prices are expected to remain flat (neutral

outlook)

-30

-20

-10

05

30 40 50 60

70 80 90

Profit ($)

Share price ($)

Sell $60 Call at $5

65


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Long Put Buy a Put

Risk: Premium

Reward: Limited (Strike price Share price) Insurance policy

Break Even: Strike Price - Premium

Motivation: When share prices are expected to fall (bearish) or want to use

it has a protective strategy in bearish markets

30

20

10

0

-760504030 70 80 90

Profit ($)

Share price ($)

Buy $60 Put at $7

53

h ll


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Short Put Sell a Put

Risk: Limited (Strike price Share price)

Reward: Premium

Break Even: Strike Price - Premium

Motivation: Share price are expected to remain flat/bullish or purchase at

a pre-determined price lower than the market price

Sell $60 Put at $7

-30

-20

-10

7

060

504030

700 80 90

Profit ($)

Share price ($)

53

C d C ll


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Covered Calls

Sell a call and buy underlying stock

Short Call and Long Stock

Share Price

Profit

Long stock

Short Call

Strike Price

Stock Purchase Price

C d C ll M i i ( i d)


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Covered Calls - Motivation (continued)

Expect market to remain flat

Collect premiums and reduce thecost of holding

Hedge to limit the downside risk

Long stock

Short Call

P i P


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Protective Puts

Buy underlying stock and buy put

Long Stock and Long Put

Share Price

Profit

Long stock

Long Put

Strike Price

Stock Purchase Price

Motivation: Insurance policy on the long stock

O ti V l I t i i V l (IV) Ti V l (TV)


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Option Value Intrinsic Value (IV) versus Time Value (TV)

IV

$75

Strike

P

rice

$70

$80

TV

$70 Call at $7

XYZ Corp. Share price = $75

$75 Call at $4

TV

$80 Call at $1

TV

IV = In the money amount

TV = Opportunity value thatoption may become morevaluable in future

F t ff ti ti i


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Factors affecting option prices

Non Quantifiable

Liquidity

Market sentiment

Corporate Actions

Market news

Supply and demand

QuantifiableUnderlying price

Strike Price

Expiration Date

Volatility

Risk Free Interest Rate

Dividends

St ik d h i


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Strike and share price

Consider two call options which only differ only by strike prices. Which call

would have an higher premium, the one with a lower strike price or higher?

E.g. would XYZ $100 May Call be more valued that XYZ $120 May Call?

Further, what is the impact of the underlying share price on the option price?

Call Put

Strike Price +

Share Price +

Payoff for call = share price strike price

Payoff for put = strike price share price

E i atio Date


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Expiration Date

Consider two options which differ only by the expiration date? Which option would

be more valuable? The one maturing earlier or later? E.g. would XYZ $100 May

Call be more valued that XYZ $100 June Call?

European Options: exercise only at expiration date

American Options: exercise any time up-to the expiration date

Call Put

ExpirationDate + +

Option Decay

Volatility


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Volatility

Measures the un-certainty of future stock price movements

Historical Volatility

The volatility of an asset is the standard deviation of the continuously

compounded rate of return in 1 year e.g. it is the standard deviation of the return

provided by the stock in one year using continuous compounding

Is the unknown variable in the factors affecting the option prices

Expressed as a percentage e.g. XYZ is at $60 with an annualized volatility at

30%. Therefore 1 std dev = .3 * $60 = $18

68.3% prices would fluctuate between $42 and $78



Implied Volatility


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Implied Volatility

Implied by the current market option prices

Volatility that would lead to the current option market price and it derived

from the option pricing model by providing all inputs except the volatility

Can monitor the markets current opinion

Traders calculate implied volatility from active options and apply it to the less

active options

Volatility


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Volatility

Consider two options XYZ.com and ABC. XYZ has a lot of fluctuations in its

share price compared to ABC. All factors similar which option would be more

priced? XYZ.com or ABC

Call Put

Share Price + +

Interest rates


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Interest rates

What happens to option prices when the interest rates go up?

Call Put

Interest rates +

Only true if other factors remain constant especially the share prices

Interest rate increases normally would be followed by decrease in share

prices causing call option prices to reduce

Dividends


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Dividends

XYZ company declares a cash dividend of 50% with an ex-date in May.

What impact would it have on the XYZ May Call?

Call Put

Dividends +

Summary of factors affecting option prices


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Summary of factors affecting option prices

Call Put

Strike Price +

Share Price +

Volatility

Expiration

Dividend

Interest rate + +

+ +

+ +

Advanced strategies


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Advanced strategies

Spread Strategy involves taking a position in two or more options of the

same type (call or put) on the same stock but varying strike prices or

expiration dates

Bull

Bear

Butterfly

Calendar

Combinations Strategy involves taking position in both calls and puts on

the same stock

Straddle

Strips

StrapsStrangles

Summary


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Summary

Strike

Sell call

Buy call with higher maturity

S1 = Buy Call

S3 = Buy Call

S1 = Sell Call

S2 = Buy Call

S1 = Buy Call

S2 = Sell Call

S2 = Sell Call

BullBear

Butterfly

Calendar

Summary


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Summary

Strip

S1 = Buy Put

S2 = Buy Call

S = Short Call and Put

S = Buy Call and Put

Strap

Bottom straddle Top straddle

Strangle

Option Prices Sensitivities - Greeks


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Option Prices Sensitivities Greeks

Underlying PriceUnderlying Price

VolatilityVolatility

Strike PriceStrike Price

Expiration DateExpiration Date

Interest RatesInterest Rates

DividendsDividends

DeltaDelta

VegaVega

ThetaTheta

RhoRho

GammaGamma

Option Sensitivities or Greeks

Delta


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Delta

How much does an option premium change in value as the underlying stock

price changes?

Delta ( ): The rate of change of the option price with respect to the

underlying stock price i.e. ratio of change in option price to change in stock

price

Optionprice

A

B Slope =

Stock price

Indicator of the options sensitivity to

the change in the underlying stockprice

XYZ June 60 Call

At T1, XYZ = 59.5, Option = 5.5

At T2, XYZ = 60.5, Option = 6.0

Delta = 6.0 5.5 / 60.5 59.5

Delta = 0.5 or 50% or 50

Delta Calls, Puts and Stock


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Delta Calls, Puts and Stock

Delta for underlying stock = 1

Long Short

Call

Put

Positive Delta Negative Delta

Negative Delta Positive Delta

Delta Hedging


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Delta Hedging

Delta hedging entails continuously re-balancing the portfolio by maintaining

a delta neutral for the position

Position/portfolio with delta = 0 is delta neutral

For the above call option, assume, delta = 0.6 which means for every $1

share price change the option price changes by $0.6

To maintain a delta neutral position, XYZ can hedge by buying 0.6 (delta) *

1000 (contracts) * 100 (lot size) = 60,000 shares60,000 shares would lead to a gain of $60,000 for $1 price increase

1000 contracts would lead to a loss of $60,000 for $.6 price increase

Net delta = 0

If stock price increases causing delta to increase by 0.05 then we buy 0.05 (delta

change) * 1000 (contracts) * 100 (lot size) = 5000 shares

Gamma


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Gamma

How does the options delta change in value as the underlying stock price

changes?

Gamma: The rate of change of the option delta with respect to the

underlying share price

2120 22 2423 25 26

6

5

4

3

2

Underlying

Va

lue

U

Gamma=

Second derivateof the portfolio

value with respect

to the underlyer

price

Gamma neutral


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G

Underlying stock gamma = 0

Asset price is linear to the underlying price

How would we make a portfolio gamma neutral?

Use derivative since price is non-linear with the underlying asset price

Gamma of portfolio = ( P), Gamma of hedge option = ( H)

New Gamma = Contracts hedge * ( H) + ( P)

To make portfolio Gamma neutral we need to add position of option hedge =- ( P) / ( H)

Adding new option position causes the delta of the portfolio to change and

hence make it delta neutral to changing position of the underlying stock

Since Gamma is not constant, re-balance the portfolio to maintain gamma

neutrality. This is called as gamma trading

Gamma Trading


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Gamma Trading

If we buy options, (calls or puts) then we are said to have POSITIVE

GAMMA. This works in our favour because

The Gamma makes our portfolio longer in a rising market and shorter in a fallingmarket

If we are gamma trading, this forces us to Sell High and Buy Low to remain Delta

Neutral

If we sell options, (calls or puts) then we are said to have NEGATIVE

GAMMA. This works against us because

The Gamma makes our portfolio shorter in a rising market and longer in a falling

market

If we are gamma trading, this forces us to Sell Low and Buy High to remain Delta

Neutral

Vega


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g

How does the option value change as the underlying stock becomes more or

less volatile?

Vega: The rate of change of the option price with respect to the underlying

stocks volatility

Indicator of the options sensitivity to underlying volatility

10%5% 15% 25%20% 30%35%

65

4

3

2

Implied Volatility

Va

lue P

VVega =

Vega characteristics


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g

Option premium rises with increasing volatility and falls with decreasing

volatility

Positive Vega for buyers and negative Vega for writers

High Vega indicates higher changes to portfolio value for small changes in

underlying volatility

Vega for underlying stock = 0

Vega neutral by adding option position = V Portfolio / V HedgeRepresented as dollar amount the option is expected to change for a 1%

increase in volatility e.g. $$$/1% an option with a Vega of 0.2 would gain

(lose) $0.20 in value for each 1% increase (decrease) in volatility

Theta and Rho


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Theta

How much does the passage of time affect the option value?

Theta: The rate of change of the option price with respect to the time

Indicator of the options sensitivity to passage of time

As expiration approaches, time value of option decreases. Theta measure

this option time decay

Rho

Rho is the rate of change of the value of the option with respect to the

interest rate

Greek Summary


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y

PositiveNegativeNegativePositiveShort Put

NegativePositivePositiveNegativeLong Put

PositiveNegativeNegativeNegativeShort Call

NegativePositivePositivePositiveLong Call

ThetaVegaGammaDeltaInstrument

What are Exotics?


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Exotic options are non-standard products whose pay-off is dependant on the path

realized by the underlying asset

All Exotic options are customized as per client requirements (also called structuredproducts) and hence are always OTC products

Carries significant credit risk apart from the usual market risk that any options portfolio

shall always carry

Example of Exotics


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Binary (Digital) Options

Cash-or-nothing Call here, the payoff is zero if the price of the underlying assetends up below the strike price at time T (maturity time) and pays a fixed amount

Q if it ends up above the strike price.Cash-or-nothing Put here, the payoff is Q if the underlying price ends up belowthe strike price at maturity and zero if it is above the strike price at maturity.

Similarly, Asset-or-nothing options can be set up the only difference is that thepayoff in this case is the value of the underlying price at maturity

Barrier Options

Barrier option will knock in or knock out depending on whether the barrier has

been hit during the life of the option and the type of the option.

A knock-out option ceases to exist when the price reaches a certain barrier

A knock-in option comes into existence only when the underlying price reaches a

certain barrier

Example of Exotics


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Lookback Options

Payoff from Floating Strike Lookback options depend on the maximum or

minimum price reached during the life of the option

The payoff from a Floating Strike European style Lookback Call is the amount that

the final price exceeds the minimum price during the life of the option

The payoff from a Floating Strike European style Lookback Put is the amount by

which the maximum price achieved during the life of the option exceeds the final

price.

Barrier Options

Payoff depends on the average price of the underlying asset during at least somepart of the life of the option

Now, the average can be looked at in two respects:

Fixed Strike, Average Price:

Payoff from an average price Calloption is max (0, Save

X)

Payoff from an average price Putoption is max (0, X Save

),

Average Strike:

Payoff from an average strike Callis max (0, ST

Save

)

Payoff from an average strike Putis max (0, Save

- ST)

Documents

Rates FO Training-Session v Products) 20 May 2010