7/30/2019 Copy of MMS Derivatives Lec 4
1/64
Exotic Options
`
7/30/2019 Copy of MMS Derivatives Lec 4
2/64
Exotic Options
Forward Start Option
Compound Options
Chooser Option
Barrier Option Binary Option
Look back Option
Shout Option Asian Option
Basket Options
7/30/2019 Copy of MMS Derivatives Lec 4
3/64
Exotic Options
Forward Start Option A forward start option is the forward purchase of a standard call
option (i.e. right to buy) or put option (i.e. right to sell).
Example : Purchasing a 3 month put option that will come intoexistence 6 months from today
On the forward start date the strike price of the option will be setat a predetermined level. Typically this is the spot price of theasset on the forward start date (i.e. at-the-money).
Alternatively the strike price can be set at a percentage in themoney or out of the money (i.e. a percentage above or below thecurrent spot price of the asset)
They are a common part of employee incentive plan
7/30/2019 Copy of MMS Derivatives Lec 4
4/64
Exotic Options
Compound Options These are option on option
Call on Call: Investor has right to buy a call option at a setprice for fixed period
Call on Put: Investor has right to buy a put option at a setprice for fixed period
Put on Call: Investor has right to sell a call option at a set
price for fixed period
Put on Put : Investor has right to sell a put option at a setprice for fixed period
7/30/2019 Copy of MMS Derivatives Lec 4
5/64
Exotic Options
Chooser Option
The option owner has a choice to decide whether the optionis a call or a put
The choice is to be exercised after a certain period of time
The choice will obviously depend on which option has ahigher value once the fix time period has elapsed
7/30/2019 Copy of MMS Derivatives Lec 4
6/64
Exotic Options
Barrier Option The options payoff is dependent on a barrier level
They have knock in (come into existence) and knock out(cease to exist) features
Barrier level are set either below the current stock rice(down) or above the current stock price (up)
7/30/2019 Copy of MMS Derivatives Lec 4
7/64
Exotic Options
Barrier Option Down
and
Out call (put) :The barrier level is set below
the current stock price and the option (call or put) cease toexist if the barrier level is hit
Down
and
In call (put) : The barrier level is set belowthe current stock price and the option (call or put) comesinto existence if the barrier level is hit
Up- andOut call (put) : The barrier level is set above
the current stock price and the option (call or put) comesinto existence if the barrier level is hit
UpandIn call (put) : The barrier level is set above thecurrent stock price and the option (call or put) comes into
existence if the barrier level is hit
7/30/2019 Copy of MMS Derivatives Lec 4
8/64
Exotic Options
Barrier Option The characteristics of barrier options are different from the
normal standard options
For e.g. Vega, is always positive for a standard option but
may be negative for a barrier option.
Increased volatility on a down and out option and an up andout option does not increase value because the closer theunderlying gets to the barrier price, the greater the chance
the option will expire
7/30/2019 Copy of MMS Derivatives Lec 4
9/64
Exotic Options
Binary Option They pay only a fixed price at expiration if the asset is
above the strike price thus they have discontinuouspayment profiles
It has two states hence binary
State 1: asset above exercise price : pay a fixed dollaramount
State 2: asset below exercise price : pay nothing
Two types
CashorNothing
AssetorNothing
7/30/2019 Copy of MMS Derivatives Lec 4
10/64
Exotic Options
Binary Option
CashorNothing: In CashorNothing Call a fixedamount Q is paid if the asset ends up above the strike price.
AssetorNothing : An AssetorNothing Call pays thevalue of the stock when the contract is initiated , if thestock price ends up above the strike price at expiration .
7/30/2019 Copy of MMS Derivatives Lec 4
11/64
Exotic Options
Look Back Option The option payoffs depend on the maximum and minimum
price of the asset during the life of the option
Look Back Call : At expiration it pays the difference
between expiration price and the minimum stock priceduring the life of option
Thus allowing the investor to purchase the security at thelowest price during the life of the option
Look Back Put : At expiration it pays the differencebetween expiration price and the maximum stock priceduring the life of the option
Thus this option allows the investor to sell the security atthe highest price during the life of the option
7/30/2019 Copy of MMS Derivatives Lec 4
12/64
Exotic Options
Shout Option The owner of the option shouts to the seller of the option as if
he has exercised his option
The owner still gets to keep the option
The difference between the shout price and the stock price is theminimum locked in profit that the owner gets
Even if the stock price falls below the shout price he is entailedto the minimum locked in profit
However if at the end of the option period the intrinsic value(stockstrike) is greater than the difference between ( shoutstock ) the owner gets to keep the higher profit
Most shout option allow for one shout
7/30/2019 Copy of MMS Derivatives Lec 4
13/64
Exotic Options
Asian Options
They are different than the standard option
They have payoff profiles based on average stock price
over the life of the option
Asian call option pay off = max [ 0 , S Average -K ]
Asian put option pay off = max [ 0 , K - S Average ]
Average price will always be less volatile than the actualstock price due to which the price of the option will alwaysbe less than the standard call and put options
7/30/2019 Copy of MMS Derivatives Lec 4
14/64
Exotic Options
Basket Options
Options to sell or purchase basket of securities
The basket can be individual investor specific or can have
specific stocks , indices or currencies
7/30/2019 Copy of MMS Derivatives Lec 4
15/64
Exotic Options
Hedging Issues There are some exotic options that are easier to hedge than
plain vanilla options.
Example: Asian options are easier to hedge because it is
dependent on average stock price and so as time passes,more is known about the prices that will determine theaverage price.
Static option replication involves the construction of a short
portfolio of actively traded options that approximates theoption position to be hedged. The replication portfolio iscreated only once
7/30/2019 Copy of MMS Derivatives Lec 4
16/64
Credit Derivatives
7/30/2019 Copy of MMS Derivatives Lec 4
17/64
Area Do we face creditRisk (Yes/No)
Credit Risk Facedby
Loan extended byBank
Bonds issued bycorporates
Credit extended bycredit card issuer
Credit DerivativeSwaps/Options*
Treasury Securities
Do we have Credit Risk in the following areas?
Yes Bank
Yes
Yes
Yes
Bond holder
BothCounterparties
Card issuer
No None
* As option always have positive value or zero (no negative), option buyer
faces credit risk from option seller.
7/30/2019 Copy of MMS Derivatives Lec 4
18/64
Credit Risk Management Strategies
Risk Taking(Speculative)
Use ofDerivativeslike CDS, TRSand structuredproducts
Risk Transfer(Insurance)
Use ofDerivativeslike CDS, TRSand structured
products.
Risk Mitigation(Hedging)
DiversificationUse ofDerivativeslike CDS, TRSetc.
While Banks are net buyers of protection, Insurance and Hedge Funds are
net sellers of protection.
7/30/2019 Copy of MMS Derivatives Lec 4
19/64
What are Credit Derivatives?
Credit Derivatives are derivatives which are used for either Hedging credit risk involved in loans/bonds (while the loans can
also be sold, it needs borrowers concurrence) or
Speculating changes in credit risk and thus assuming indirect
exposures to credit risks for diversification. E.g., Credit Default Swaps (CDS), CDS forwards and CDS
options, Total Rate of Return Swaps (TROR)
Credit Derivatives can be tailored to lay off any part of thecredit risk exposure i.e., amount, recovery rate and maturity.
Credit Derivatives are not traded on exchanges and arearranged on OTC basis.
7/30/2019 Copy of MMS Derivatives Lec 4
20/64
Credit Default Swap
CDS Buyer(protection
buyer)
CDS Seller(protection
seller)
Referenceobligation
(bond/loan)
CDS is essentially an insurance contract.
If a default occurs on the reference obligation, the CDS
buyer receives a payment from the CDS seller.
The reference obligation is the bond or bank loan on which
the swap is written.
premium
coupon
PaymentOn default
The default swap
premium also known as
default swap spread can
be paid
One time upfront or
Over a period of time
Premium
payment options
investment
7/30/2019 Copy of MMS Derivatives Lec 4
21/64
CDS
CDS Buyer(protection
buyer)
CDS Seller(protection
seller)
Referenceobligation
(bond/loan)
Risk Free
bond
Coupon (a-b)Coupon, a
Prem., b
Note: On condition that there is no counterparty (risk of swap seller
default) risk, liquidity risk and assuming that the interest rate
sensitivity of the risky and risk free bonds are similar
Position of CDS
buyer
7/30/2019 Copy of MMS Derivatives Lec 4
22/64
Chronology of events in CDS
1
Buyer Buys CDS from seller and pays premium regulary.
(Agreement defines nature of reference obligation, creditevent etc)
2 Credit event is triggered (Bankruptcy, failure to pay, restructuring etc)
3 Materiality of the event is verified from the Publicly available
information
4
Credit Event Notice is served by the buyer on seller
5
Seller settles the amount (Physical/cash settlement)
7/30/2019 Copy of MMS Derivatives Lec 4
23/64
CDS Terminology
Reference Entity: It is the corporate, sovereign entity onwhose credit the CDS contract is sold.
Reference Obligation: Reference Obligation is pre-specified obligation issued or guaranteed by the
Reference EntityThe buyer however does not have to deliver this
specific obligation. Any Obligation of the ReferenceEntity, which meets criteria like seniority, currency,tenor etc. can be used as deliverable/referenceobligation.
If no Reference Obligation is specified, SeniorUnsecured obligation is assumed
7/30/2019 Copy of MMS Derivatives Lec 4
24/64
CDS Terminology
The Credit Events: The events that trigger payment from a CDS areformalised by ISDA (International Swaps and Derivatives Association)
a. Bankruptcy: Need not be actual filing, even the steps taken by a corporationto initiate the process is deemed as credit event.
b. Obligation acceleration: Refers to when an obligation becomes payablebefore its scheduled time due to default of the reference entity
c. Failure to pay: When the reference entity does not make the requiredpayment
d. Repudiation/Moratorium: refers to when the issuer disowns its obligation topay
e. Restructuring: refers to when unfavourable events occur, such as reduction
in the payment, reduction in the payments seniority or a postponement inthe payment.
Note: A downgrade from a rating agency, however is not defined as a creditevent.
7/30/2019 Copy of MMS Derivatives Lec 4
25/64
Payment of CDS on Cash
If a credit event occurs, the settlement of CDS can be made on physical andcash basis. In case of physical, the reference obligation is physically delivered to the seller, who will have
to pay the par value.
In case of cash, payment is made as under:
Settlement amount = NP x [reference amount (final price +accrued interest)]
Where
NP = notional principal of the Swap
Reference amount = amount specified at the inception of thecontract (usually 100%)
Accrued interest = percent interest calculated relative to the lastcoupon payment
Final price = percentage price determined by examining thelast bid price (in a poll of five securities dealers)
7/30/2019 Copy of MMS Derivatives Lec 4
26/64
Payoff from CDS - Example
Suppose it has been 60 days since thelast coupon payment. The notionalprincipal of the swap is USD 20 mn andthe reference amount is 100%. The finalprice is estimated at 30% and the annualcoupon was 8%. Calculate the cashsettlement amount.
Settlement amount = 20,000,000 x (100% - [30% + (8% x 60/360)])
= USD 13,733,333
7/30/2019 Copy of MMS Derivatives Lec 4
27/64
Swap Buyer Vs Swap SellerSwap Buyer or Protection Buyer Swap Seller or Protection Seller
CDS acts as a long Put option on the
reference obligation
It is equivalent to writing put option on the
reference obligation (short put)
On default, the buyer receives payment,which limits the buyers downside risk
On default or occurrence of a creditevent, seller is obliged to pay either
Net amountFace value of the ref obligation uponphysical delivery of obligation
It creates a Short position in thereference obligation i.e., he can use it forhedging the existing exposure to referenceobligation orfor taking position in the ref obligationindirectly (speculation)
Creates long position in the referenceobligation
When the credit quality of the referenceobligation declines, CDS become morevaluable and can be traded for profit.
If credit quality of the ref obligationincreases, the swap value decreases thusseller can buy back the swap and realise aprofit.
CDS will not offer protection againstmarket risk (interest risk or currency risk)
7/30/2019 Copy of MMS Derivatives Lec 4
28/64
Types of CDS
Cancelable default swap In this type of swap, the buyer or the seller or both have the
right to cancel the swap
If the buyer of the swap has the right to cancel it, it is calledcallable default swap
If the seller has the right to cancel, the swap is referred to asputtable default swap
Callable are more common than the puttable default swaps.
Contingent Default Swap Payment is made only if another event occurs besides a credit
event on the reference obligation. The other event can becredit event on another obligation
Protection is weaker and as such trades at low premium
7/30/2019 Copy of MMS Derivatives Lec 4
29/64
Types of CDS
Leveraged Default Swaps The payment in this swap is a multiple of the buyers loss on
the reference obligation.
These swaps are expensive and are undertaken forspeculation
Instead of hedging several obligations, a single leveragedefault swap could be purchased. However, the buyer isexposed to basis risk if the losses on the portfolio are notequivalent to the coverage from the swap.
Tranched portfolio and tranched basket default swaps
In this case, a loan is purchased by a special purpose vehicle(SPV) and transformed into notes with different risk tranches
The investor can then choose the tranche that matches his risklevel
7/30/2019 Copy of MMS Derivatives Lec 4
30/64
Types of CDS
Binary or digital default swap
Swaps final price is set at the inception of the
contract and is based on historical recovery rates
Popular because of their simplicity
Basket Credit Default Swap The reference obligation is a basket of debt
securities.
nth-to-default swap payment is triggered when the
nth reference obligation defaults. If n is set at one, it is called first-to-default basket
credit swap.
7/30/2019 Copy of MMS Derivatives Lec 4
31/64
Basket CDS Effect of Correlation
The spread for basket CDS depends on correlation of thereference entities in the basket.
Low correlation: In a basket of say 100 reference entities,when there is low correlation between entities (diversifiedportfolio), the probability of single default is high as compared
to the probability of 10 defaults. Therefore, the value (spread)of first to default swap will be higher than 10th-to-default swap.
High correlation: However, as the correlation increases, theprobability of multiple defaults also increases. When theportfolio contains similar type of obligations (i.e., correlation isone), either there will not be any default, or all of them willdefault. In this case, the value of first-to-default and nth-to-
default CDS will be same.
7/30/2019 Copy of MMS Derivatives Lec 4
32/64
CDS Credit Indices
Participants in credit derivatives markets have developedindices to track CDS spreads. Among the indices nowused are,
The 5 and 10 year CDX NA IG indices tracking the creditspread for 125 investment grade North Americancompanies
The 5 and 10 year iTraxx Europe indices tracking thecredit spread for 125 investment grade Europeancompanies
For eg., an investment bank acting as markt maker mightquote the CDX NA IG 5 year index as bid 65 bp and offer66 basis points. An investor then could buy CDS at 66bp and sell at 65 bp.
7/30/2019 Copy of MMS Derivatives Lec 4
33/64
Computation of value of CDS
The aim is to determine value of the mid-market (average of bid and ask
prices) CDS spread on the reference entity. The following are the steps
Calculate the present value of the expected payments (payments aremade at the spread rate and multiplied by the reference entitys
probability of survival each year)
Calculate the present value of the expected pay-off in the event ofdefault (assume that the defaults occur half-way through a year. Fromthere the annual probability of default is multiplied by recovery rate anddiscounted to present value)
Calculate the present value of accrual payment in the event ofdefault.(Since the payments are made in arrears, an accrual payment is
required in the event of default to account for the time between thebeginning of the year and the time when the default actually occurs)
Calculate the spread using the following equation
Spread, s = PV Payoff/PV Payments
7/30/2019 Copy of MMS Derivatives Lec 4
34/64
Computation of value of CDS conceptchecker
ABC enters into a 4 year CDS with XYZ insurance to hedge thecredit risk of USD 100 mn bond issued by PQR corporation. Theprobability of PQR corp defaulting during a year, conditional on noearlier default is 3%. Assume that the defaults always happenhalfway through a year and the payments of premium are madeonce in a year at the end of the year. The risk free rate is 6% p.a.,
compounded continuously and the recovery rate in the event ofdefault of PQR is 30%.
Calculate
a. PV of total expected payments made by buyer of CDS
b.PV of expected payoff in the event of default
c. The CDS spread.
7/30/2019 Copy of MMS Derivatives Lec 4
35/64
Concept checker
a. PV of expected payments in the event of survival (no
default)
Note: probability of survival at the end of second year =0.97x0.97
PV of expected payment at the end of 1 year =
Time (years) Survivalprobability
Expectedpayment
PV of expectedpayments
1 0.9700 0.9700s 0.9135s
2 0.9409 0.9409s 0.8345s3 0.9127 0.9127s 0.7624s
4 0.8853 0.8853s 0.6964s
Total (a) 3.2068s
)106.0(97.0
es
7/30/2019 Copy of MMS Derivatives Lec 4
36/64
Concept checker
b. PV of accrual payment in the event of default
Note: probability of default in second year = 0.97x0.03
Since we are assuming that default occurs halfway through a year, the accrual
payment for each year is 0.50s. The expected accrual payment for year0.5 = 0.0300 x 0.50 s = 0.0150s
PV of expected payment at the end of year = 0.0150sx
Therefore, PV of expected payments = a + b = 3.2068s + 0.0511s = 3.2579s
Time (years) Defaultprobability
Expectedaccrualpayment
PV of expectedaccrualpayment
0.5 0.3000 0.0150s 0.0146s
1.5 0.0291 0.0146s 0.0133s
2.5 0.0282 0.0141s 0.0121s3.5 0.0274 0.0137s 0.0111s
Total (b) 0.0511s
)50.006.0( e
7/30/2019 Copy of MMS Derivatives Lec 4
37/64
Concept checker
c. PV of expected pay-off in the event of default
As 3.2579s = 0.0716 i.e., s = 0.0220 or 2.20%.
Therefore, mid market spread for the CDS should be 220 bp per year.
Time (years) Defaultprobability
1-Recoveryrate
ExpectedPayoff ($)
PV ofexpectedpayoff ($)
0.5 0.3000 0.70 0.0210 0.0204
1.5 0.0291 0.70 0.0204 0.0186
2.5 0.0282 0.70 0.0197 0.01703.5 0.0274 0.70 0.0192 0.0156
Total 0.0716
7/30/2019 Copy of MMS Derivatives Lec 4
38/64
Marking the Market of CDS
At inception, the value of CDS is zero i.e., the CDS is priced so that
PV of payments made by the buyer of swap is exactly equal to thePV of expected payouts in the event of default (otherwise it will leadto arbitrage opportunities)
In the previous example, presume that CDS was originallynegotiated 5 years ago at a spread of 175 bp. Calculate the current
marked to market value of the CDS for both the buyer and seller. For CDS buyer, M2M value of CDS = PV expected payout recd -
PV of payments made
= 0.0716 (3.2579[0.0175]) = 0.0146 times the NP
For CDS seller M2M value of CDS =PV of payments recvd PVof payouts made
i.e., -0.0146 times NP i.e., loss. (zero sum game)
7/30/2019 Copy of MMS Derivatives Lec 4
39/64
CDS Forwards and Options
CDS Forward: It is the obligation to buy or sell aparticular CDS on a particular reference entity at aparticular future time, T. Thus a bank could enter into a forward contract to sell 5 year
protection on TATA Motors credit for 150 bp starting in 1 year. If
Tata Motors defaults during the next year, the banks obligationunder forward contract ceases to exist.
CDS Option: It is an option to buy or sell at a particularCDS on a particular reference entity at a particular futuretime. As in the above referred example, a buyer can buy
a call option for buying CDS at 150 bp. If the 5 year CDS spread for Tata Motors in one year turn out to
be more than 150 bp, the option will be exercised. The cost ofthe option would be paid upfront.
7/30/2019 Copy of MMS Derivatives Lec 4
40/64
Total Rate of Return (TROR) Swap
In a TROR swap, the TROR payer transfers totalreturn (coupons, interest and the gain or lossover the life of the swap) on a risky debt securityto the TROR receiver.
In turn, TROR receiver pays a return that istypically LIBOR plus some spread.
Thus credit risk is transferred from the TROR
payer to the TROR receiver.
7/30/2019 Copy of MMS Derivatives Lec 4
41/64
TROR Swap
TRS Payer TRSReceiver
Reference
obligation(bond/loan)
Libor + spread
TROR
TROR
investment
When payer owns the reference
obligation, payer can hedge thecredit risk as well as interest rate
risk by buying a TROR swap.
When the payer does not own the
reference obligation, TROR
creates a short position for the
buyer and a long position for thereceiver.
While the coupon payments are
exchanged periodically like an
interest rate swap, the change in
the value of the bond either gain or
loss is transferred at the end of the
swap.
If there is default on the bond, the
swap is terminated and final
payment is made.
TRS
Payer
TRS
ReceiverTROR on
reference
obligation
Libor + spread
7/30/2019 Copy of MMS Derivatives Lec 4
42/64
Total Return Swap - Example
Exotic Hedge fund will enter into a $100 mn total return swap on theS&P 500 index receiver (i.e., total return receiver). The counterparty(i.e., total return payer) will receive 1 year LIBOR + 400 bp. Thecontract will last two years and will exchange cash flows annually.Given the following information, determine the cash flows at contractinitiation, in one year and two years. Assume LIBOR remains flat.
Current LIBOR = 5%
Current S&P 500 value = 1,000
S&P 500 in 1 year = 1,200
S&P 500 in 2 years = 900
7/30/2019 Copy of MMS Derivatives Lec 4
43/64
Total Return Swap payoff
At the beginning:
Similar to other OTC contracts, there will not be any cashflowexchanged in the beginning
After 1 year:
S&P Index has increased by 20%. Hence Swap receiver will receive $
20 mn and will pay $ 9 million ( @5% + 400 bp on $100 mn).Therefore, net cashflow will be $11 mn to hedge fund.
After 2 years:
S&P index dropped by 25% (from 1200 to 900). Therefore swap payerhas to pay 25% in addition to 9% floating rate. Hence swap payer
i.e., hedge fund will pay $ 34 mn to swap receiver.
7/30/2019 Copy of MMS Derivatives Lec 4
44/64
TROR Swap Points to remember
TROR creates a long position in the assets for the receiver.
Alternative for the receiver would be to buy the bond or theloan itself. However TROR provides the following advantages Does not require upfront purchase of the asset, resulting in savings on
finance costs.
Off-balance sheet exposure for the receiver requiring no capital. Hence
leveraging is resorted to. It may be more liquid than the underlying asset.
The spread over LIBOR received by the payer iscompensation for bearing the risk that the receiver will default.The payer will lose money if the receiver defaults at a time
when the reference bonds price has declined.
The spread therefore, depends on credit quality of thereceiver, the credit quality of the bond issuer and the defaultcorrelation between the two.
7/30/2019 Copy of MMS Derivatives Lec 4
45/64
Credit Spread Options
Credit spread is the difference in the yield between a risky bond and
a risk free bond. In Credit Spread Options, the option buyer has the right but not an
obligation, to exercise the option when credit spread diverges from apre-specified strike spread.
In a Credit Spread Put Option (CSPO), the put writer makes a
payment if the credit spread is greater than the strike spread.
In Credit Spread Call Option (CSCO), the option has value when thecredit spread is less than the strike spread. The payoffs are asunder:
CSPO payoff = NP x duration x max (credit spreadstrike spread, 0)
CSCO payoff = NP x duration x max (strike spreadcredit spread, 0)
7/30/2019 Copy of MMS Derivatives Lec 4
46/64
Structured Products
Credit Linked Notes (CLN) and
Collaterised Debt Obligations (CDOs)
7/30/2019 Copy of MMS Derivatives Lec 4
47/64
Credit Linked Note
Protection
Buyer
Special Vehicle (Trust)
Funds its balance sheet by issuing
Notes to investors
Uses the proceeds to acquire cash
collateral (risk free bonds) @Libor +x
Sells default protection and passes the
yield on the collateral plus the swap
premium to investor
Investor
Premium
@ y Certificates @
Libor + x+y
On default,
100% recovery
to buyer
If reference credit
defaults, cash
collateral will be
liquidatedIn practice, the SPV may retain a small percentage of the coupon to meet
the expenses.
7/30/2019 Copy of MMS Derivatives Lec 4
48/64
Credit Linked Notes
A SPV is set-up to issue notes/certificates
The proceeds are invested to acquire cash collateral (riskfree bond) equal to the amount of protection sought by the
protection buyer.
The yield from collateral plus the fees paid for the
protection are passed onto the investorsIf there is default, the cash collateral is liquidated to satisfy
the claim of protection buyer and remaining proceeds are
distributed to the investors. Thus CLN provides payment that
varies with the credit risk of an underlying bond
In case there is no default, the collateral is liquidated the
satisfy the claims of note holders.
7/30/2019 Copy of MMS Derivatives Lec 4
49/64
Position of CLN Buyer
CLN allows investors who are otherwise restricted from buyingunderlying bond/loan/derivative, to invest in synthetic security.
Benefits
Buyer earns high return if there is no default
Risks
Buyer earns lower return if there is downgrade or default. Buyer has counterparty risk, as CLN issuer may default in their
obligation to pay the coupon or par value.
The risk is high if there is significant correlation between the CLNissuer and bond issuer.
CLNs are often privately traded, illiquid
7/30/2019 Copy of MMS Derivatives Lec 4
50/64
Collaterised Debt Obligations (CDOs)
CDOs are similar to CLNs as in that the issuer
transfers a credit risk related return to aninvestor.
Unique features of CDO are
CDO issuer is transferring his exposure to a basket ofsecurities (200 or more)
CDOs are typically issued by Special Purpose Vehicle(SPV) or Special Purpose Entitity (SPE). These are
trusts set-up by investment banks with a rating of AAA(legally separate from parents)
CDOs usually provide tranched returns, with investorschoosing tranche that best suits their risk profile.
7/30/2019 Copy of MMS Derivatives Lec 4
51/64
Cash CDO with N underlying securities
Bond 1
Bond 2
Bond N
SPV
Junior tranche
Ist 15% loss
Yield =20%
MezzanineTranche
2nd 25% loss
Yield=12%
Senior Tranche
Residual loss
Yield=6%
cash cash
return return
Average
Yield8.5%
At the outset, return is paid at the agreed rate on the
principal. However, when there is loss, the return is paid on
the remaining principal.
7/30/2019 Copy of MMS Derivatives Lec 4
52/64
Cash CDO with N underlying securities
SPV has invested in several bonds and then pays the returns to different
tranches. There can be a senior tranche, one ore more mezzanine tranches and a
junior tranche.
Junior most tranche incurs the most credit risk and losses are first assignedto this tranche and are also called equity tranche.
They sometimes have threshold where losses are only applied only whenthe losses exceed threshold. Junior tranche behaves like equity securitiesand hence expected returns are larger. Sometimes, a portion of juniortranche is retained by the SPV
Large part of the CDO is typically the senior tranche carrying an AA or AAAcredit rating.
Mezzanine tranches, which sustain losses after the junior tranche hasabsorbed losses, usually have credit ratings of B to AA.
The issuer of CDO earns a fee for originating, structuring and managingCDO.
7/30/2019 Copy of MMS Derivatives Lec 4
53/64
Cash flow Vs Synthetic CDOs
Cash flow CDO: SPV makes an investment in the actual
securities that are used to generate payment to thetranches.
Synthetic CDO: SPV does not invest in actual securities.Instead the exposure to these securities is created by
selling a default swap. (this is similar to synthetic CLN) Very popular as compared to cash CDOs
Off-balance sheet exposure
Does not have operational risk with regard to underlying assets
Other variants can be part cash and part synthetic. TheCDO could be invested in foreign securities with foreignexchange risk hedged by the SPV with a currency swap.
7/30/2019 Copy of MMS Derivatives Lec 4
54/64
Synthetic CDO with N underlying securities
CDS Buyer 1
CDS Buyer 2
CDS buyer N
SPV
Junior
tranche
MezzanineTranche
Senior
Tranche
Payment if
default cash
Swap
premium
return
Risk free
bond
return investment
7/30/2019 Copy of MMS Derivatives Lec 4
55/64
Types of CDOs
Balance Sheet Vs Arbitrage CDOs (Based on
Type)Primary objective of Balance sheet CDO is to move
loans off the balance sheet of commercial banks tolower regulatory capital requirements.
Arbitrage CDOs are designed to capture the spreadbetween the portfolio of underlying securities and thatof the highly rated tranches. (Senior tranches alsoseem attractive for investors as they pay relatively
higher premium as compared to corporate bonds ofcorresponding rating too much belief in creditratings)
7/30/2019 Copy of MMS Derivatives Lec 4
56/64
Various types of CDOs
Tranched PortfolioDefault Swaps
Unlike syntheticCDO, the defaultswap exposure for
the SPV istranched.
SPV does not haveexposure to SuperSenior Tranche.
Losses in respect
of other tranchesare passed ontothe investors.
Tranched BasketDefault Swaps
The exposure of aninvestors trancheis defined by the
number of defaults,not the amount.
It is a hybrid of N-to-default swapand a CDO
Attachment and
detachment pointsas explained in thediagram will governthe exposure
CDO squared
It is a CDO thatinvests in otherCDOs.
Yield is higher thanthat available fromordinary CDOs.
However, CDO2investments arecomplicated and
difficult tounderstand
7/30/2019 Copy of MMS Derivatives Lec 4
57/64
TPDS
Super Senior
Tranche
Mezzanine
Tranche
Junior Trance
SPV
Junior
tranche
MezzanineTranche
Senior
Tranche
Payment if
default cash
Swap premium return
Risk free
bond
return investment
Senior
Tranche
7/30/2019 Copy of MMS Derivatives Lec 4
58/64
TBDS
SPV
Junior
tranche
1 to 7
MezzanineTranche
8 to 11
Senior
Tranche
12 to 15Payment if
default cash
Swap premium return
Risk free
bond
return investment
Basketcontaining
15 assets
The higher the number of the assets and lower the default
correlations, the higher the investors risk in respect of
Junior tranche.
7/30/2019 Copy of MMS Derivatives Lec 4
59/64
CDO squared with Inner CDO and ABS positions
Security 2
Security 3
Security 4
CDO trancheB
ABS
CDO tranche
A
Security 1
CDO tranche
C
2CDO
Inner CDO Outer CDO
7/30/2019 Copy of MMS Derivatives Lec 4
60/64
Valuation of a Basket CDS and CDO - Correlation
Suppose a basket of 100 reference entities is used to define a 5-year nth-to-defaultCDS and that each reference entity has a risk neutral probability of 2% defaulting in 5years.
When the default correlation is zero, the probability of one or more defaults during the5 years is 86.74% (binomial distribution) and 10 or more defaults is 0.0034%.Therefore, a first-to-default CDS is therefore, quite valuable whereas a tenth-to-default CDS is worth almost nothing.
As default correlation increases, the probability of one ore more defaults declines and
the probability of 10 or more defaults increases. In an extreme case, where the default correlation is perfect, the probability of one or
more defaults equals the ten or more defaults and is 2%. Because in this extremesituation, all the entities are the same and either they all default (2%) or none of themdefault (98%).
The valuation of CDO is similarly dependent on default correlation. If the correlation is
low, junior equity tranche is very risky and senior tranches are safe. As the default correlations increase, the junior tranche becomes less risky and senior
tranche becomes more risky and when the assets perfectly correlated, all tranchesare equally risky.
7/30/2019 Copy of MMS Derivatives Lec 4
61/64
Gaussian Copula Model to measure the time to default
Because Q1 and Q2 and
cumulative probability
distributions, the inverse
cumulative standard normal
function returns variables which
are normally distributed: x1 and
x2.
7/30/2019 Copy of MMS Derivatives Lec 4
62/64
Credit Risk of Credit Derivatives
Counterparty RiskWhen an institution has transferred credit risk in respect of
underlying asset to another institution through derivative, it isexposed to the risk of joint default by the counterparty and theunderlying asset.
If only one defaults, there is no credit risk
The joint probability of default is given by the following equation.
Model Risk
Legal Risk Parties may not agree on the terms of trade in case of default,
even with full confirmation of the trade (use of ISDA confirmationagreements help resolve some of this uncertainty)
)()())(1)(())(1)((),()( BPAPBPBPAPAPBACorrABP
7/30/2019 Copy of MMS Derivatives Lec 4
63/64
Credit Derivatives Facts to know
While banks are net buyers of credit protection, insurers
and Hedge funds are net sellers of credit protection. Derivatives like CDS are more liquid than the underlying
bonds and provide price discovery. The transactionprices of CDS provide useful information about the cost
of credit to outside observers. On the downside, the growth of credit derivatives has
created operational risk because of backlogs in theprocessing of trades.
The Lehmans failure (was very active in CDS market)and rescue of AIG (too much exposure to CDS and otherderivatives) point to the need to have centralisedclearing house to eliminate the counterparty risk.
7/30/2019 Copy of MMS Derivatives Lec 4
64/64
Thank You !