Copy of MMS Derivatives Lec 4

7/30/2019 Copy of MMS Derivatives Lec 4

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Exotic Options

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Exotic Options

Forward Start Option

Compound Options

Chooser Option

Barrier Option Binary Option

Look back Option

Shout Option Asian Option

Basket Options


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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


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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


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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


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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)


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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


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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


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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


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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 .


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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


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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


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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


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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


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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


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Credit Derivatives


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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.


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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.


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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.


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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


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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


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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)


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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


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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.


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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)


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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


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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)


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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


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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


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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.


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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.


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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.


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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


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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.


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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


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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


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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


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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)


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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.


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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.


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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


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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


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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.


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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.


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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)


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Structured Products

Credit Linked Notes (CLN) and

Collaterised Debt Obligations (CDOs)


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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.


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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.


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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


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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.


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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.


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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.


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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.


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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


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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)


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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


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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


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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.


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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


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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.


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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.


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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


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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.


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Thank You !

Documents

Copy of MMS Derivatives Lec 4