exotic derivatives project-lehman

8/8/2019 Exotic Derivatives Project-Lehman

1/28

[Type text] Page 1

IIM, INDORE

2009

Exotic Credit derivatives

and Lehman brothers: Acase analysis

ByV.V.P.Narasimham

E P G P 0 7 - 0 9


2/28

Exotic Credit derivatives and Lehman brothers: A case analysis

V.V.P.Narasimham, EPGP 07-09 Page 2

Table of Contents

1. Introduction5

1.0 Review of Sub prime crisis

1.1 About Mortgage backing business of Lehman brothers

1.2 Factors influenced the Bankruptcy of Lehman Brothers

1.3 Objectives of the study

2. Brief review of Credit derivative swaps..9

2.0 History and future application of CDS

2.1 Application of Credit derivatives

2.2 Types of Credit derivatives

2.3 Market over view of credit derivatives2.3.1 Single type credit default swap

2.3.2 Credit option

2.3.3 Credit linked notes

2.3.4 Synthetic CDO

2.3.5 Basket default swaps

2.3.6 CDO Squared

2.3.7 Hybrid products

3. Pricing and valuations163.0 General considerations for Pricing and valuations of credit options

3.1 Credit default swap3.1.1 Assumptions for pricing the product

3.1.2 Analysis on the effect of Single type CDS on Lehman brothers

3.2 Pricing of Synthetic debt obligation

3.2.1 Analysis of the impact of Synthetic CDO on Lehman brothers3.3 Valuation of credit options

3.4 Valuation of Basket default swap3.5 Valuation of Hybrids

4. Conclusions & Recommendations.27

5. References28


3/28



List of Figures

Figure 1 View of losses suffered by financial institutions and investment Bankers due to subprime crisis

Figure 2 Comparison of Effect of sub price effect with other crisis

Figure 3 Value of commercial properties in 2008

Figure 4 Estimation of revenues by various derivative instruments for investment Bankersunder various scenario's by 2010

Figure 5 Break up of various instruments in credit derivatives marketFigure 6 Frame work of Single type CDS

Figure 7 Frame work of Credit options

Figure 8 Frame work of Credit link Notes

Figure 9 Frame work for Synthetic CDO

Figure 10 Mechanics of Synthetic CDO

Figure 11 Frame work for Basket default Swaps

Figure 12 Probabilistic Valuation model for of Single type CDS

Figure 13 Comparison of PV for Premier leg% & Protection leg

Figure 14 Variation of CBE for change in Spread rate

Figure 15 values of Equity tranche for variation in Rho

Figure 16 CBE values of Equity tranche for variation in Rho

Figure 17 CBE values of Senior tranche for variation in Rho

Figure 18 CBE values of Mezzanine tranche for variation in Rho

Figure 19 CBE values of super senior tranche for variation in Rho


4/28



List of Tables

Table 1 Calculation of PV for Premier leg and Protection leg

Table 2 Calculation of payoff for different probabilities

Table 3 Calculation of PV for default at various times

Table 4 Calculation of CBE for various tranche for different values of Rho

Table 5 Price of pre-defined for variation in spread rate

Table 6 Valuation of Receiver default swap

Table 7 Products of default swaption


5/28



1. Introduction1.0 Review of Sub price crisis:- Sub price crisis of 2007 has shown devastating effect onthe world financial markets. Many financial institutions have suffered heavily due to thiscrisis. Some companies have heavy slash in their revenues while some companies either

closed or forced to merge in other companies. Figures 1 & 2 shows pictorial view of sub pricecrisis on the overall economy and its intensity on the world wide economies.

Figure 1View of losses suffered by financial institutions and investment Bankers dueto sub prime crisis

Figure 2 Comparison of Effect of sub price effect with other crisis


6/28



One of the notable among them was the Bankruptcy of Lehman Brothers. The investmentbanker has filed bankruptcy statement under U.S trade laws on Sept 15, 2008 the day whichWorld wide markets want to forget. Lehman announced will file for Chapter 11 bankruptcyprotection, making it the biggest victim so far of the credit crunch and sub-prime crisis. The

collapse of Lehman one of the biggest financial shocks in years - puts tens of thousands of jobs around the world at risk and in the same week another financial firm Merrill Lynchannounced that it was also facing credit crunch and filed for Bankruptcy and subsequently itwas taken over by Bank of America for $50bn. Further for the first time recession hasoccurred globally and expert are .this crisis has effected heavily Merrill Lynch and Lehmanboth expanded aggressively into property-related investments, including so called sub-primemortgages - loans to people on low incomes or with poor credit histories. The bank has lost$14bn in the past 18 months after being forced to take huge write-downs on the value of those investments. These two investment bankers together held or backed $5.3 trillion inmortgages. What is more, with the mortgage markets facing a credit squeeze over the lastyear, they were providing 70 to 80 per cent of new mortgage loans. To undertake theseactivities, these firms were indebted to a range of creditors; credit from many of thesecreditors would freeze up if these GSEs defaulted on their commitments. Any effort on thepart of these creditors to sell their debt would result in a decline in value that would threatenthe financial viability of many of them. Thus, there were two important reasons, for thissituation.

I. Mortgage credit has dried up, resulting in a collapse of the already declining pricesin the housing market.

II. Fallout could be dire for the viability of other financial firms and the stability of

financial markets.1.1 About Mortgage backing business of Lehman brothers :-At the time of fillingBankruptcy Lehman Brothers it owes more than $600 billion to creditors worldwide. Withmuch of that money being invested in mortgage-backed securities, the collapse in the value of those securities must have increased demands for additional collateral, which Lehman washard-pressed to find. Lehman was a key player in the mortgage securities business and madeits own investments in subprime mortgage securities to boost the return. By borrowingheavily short-term funds at rock-bottom rates (given that Fed had kept rates low for a longtime) and then investing them in subprime mortgages, they were also able to boost theirquarterly profits. All this was driven by the need to pump up earnings to earn theirmanagements compensation payout, even as the firm was taking on enormous debt andhaving to leverage close to 40 times its capital.1.2 Factors influenced the Bankruptcy of Lehman Brothers:- One of the notablesuffers along with Lehman brothers is the AIG insurance which was a profitable well-runinsurance company which found the "easy money" in mortgage business and decided to bethe insurer by offering a product called "credit default swap," basically an insurance to thebuyers of mortgage security that if they dont get their money back for some reason AIG willpay the holder of security. Basically AIG was insuring all the subprime mortgages andearning a premium for doing so. By betting that U.S. housing prices will continue to raise"forever" it assumed estimated a linear growth in mortgages prices. However when the UShousing prices crashed the subprime mortgage business collapsed as the home owners


7/28



defaulted massively on their mortgages which created a ripple effect in making thesemortgage securities worthless. A subprime homeowner had no incentive to pay off amortgage, which was worth more than the house and decided to walk away as they had takena "zero down" mortgage and no equity in the house. The worth of these securities was resting

on the assumption that home prices will not lose value. However, when they did, the entiresubprime market unravelled. Firms like Lehman, Fannie and Freddie, who had enormousinvestments in sub prime securities relative to their capital base, had to book losses and therewas no one ready to buy these securities. The entire mortgage securities market seized, whichspilled over to the broader credit market since no one knows who has how much exposureand what the true value of these securities is. So when one firm starts selling these securitiesat distress prices it triggers a wave of write-downs in other firms as the value of thesesecurities has to be adjusted to reflect market value "using the mark-to-market rule." Thiscreated further selling pressure and soon there was no buyer for these securities. If the cost of funds is minimal and there is plenty of money available, the "free" capital will chase anyinvestment idea that has half a chance of success. This easy money found the perfect partnerin the U.S. mortgage business. Traditionally banks lend money for mortgages to theircustomers after knowing who they are and assessing their credit worthiness. This is to ensurethat the banks get their money back. Even though the mortgages were guaranteed by Fannieand Freddie, their criteria was fairly stringent and it meant mortgages were only given tofolks who had a steady job, a good credit score and a reasonable ability to repay the loan.Then the role of the investment banks like Lehman, which basically found a new business inpackaging the mortgage loans and selling it to investors around the world who wanted ahigher yield. The theory was that since housing prices "only go up" these mortgage backed

securities will always hold their value and if one can earn a better yield particularly since theyield available in treasury was next to nothing this is a very good deal. The credit ratingagencies blessed these securities with high quality ratings and the merry-go-around started.However due to raising inflation many customers have defaulted on one upper side crushingof the mortgage properties on the downer side and which ultimately leads to the bankruptcyof big investment giants like Lehman brothers, AIG insurance etc.Figure 3 shows thevariation of commercial properties in the year 2008.


8/28



Figure 3 Value of commercial properties in 2008

The present document reviews the influence of exotic credit derivatives in Bankruptcy of Lehman brothers and its role in future risk management policies.1.3 Objectives of the study:- Main objectives of the document are to study the impact of exotic credit derivatives in the Bankruptcy of Lehman brothers. For this study themethodology we adopted is as follows:-

a. Frame work and design of the exotic credit derivatives

b.

Pricing and valuationc. Analysis of the instruments based on valuations and derivation of possible reasons forcorrelating to the Bankruptcy of Lehman Brothers.

d. Recommendations.


9/28



2.0 Brief review of Credit derivative swaps2.0 History and future application of CDS: - CDS is a credit derivative contractbetween two counterparties. The credit derivatives market is the most exciting anddevastating area in the derivatives markets since 1990.It has changed the landscape of the

financial markets positively and negatively. Though critics are sceptical about the role of credit derivatives after the debacle of Lehman brothers in sept, 08 still credit markets areplaying a great role in the financial markets. As per the estimates of the ISDA notationalprincipal amount for outstanding credit contracts is $182 trillion by dec, 2008. As per therecent estimate of the BCG Revenues from credit instruments will occupy a major share inthe revenues of the Investment bankers by 2010.Figure 4 shows the estimation of revenuesfrom various derivative instruments for investment bankers by 2010 under various scenarios.

Figure 4 Estimation of revenues by various derivative instruments for investmentBankers under various scenario's by 2010

This growth in the credit derivatives market has been driven by an increasing realisation of the advantages credit derivatives possess over the cash alternative, plus the many newpossibilities they present to both credit investors and hedgers. Those investors seekingdiversification, yield pickup or new ways to take an exposure to credit are increasinglyturning towards the credit derivatives market. The primary purpose of credit derivatives is toenable the efficient transfer and repackaging of credit risk. In their simplest form, creditderivatives provide a more efficient way to replicate in a derivative format the credit risksthat would otherwise exist in a standard cash instrument.2.1 Application of Credit derivatives : - A credit derivative is a derivative whose valuederives from the credit risk on an underlying bond, loan or other financial asset. In this way,

the credit risk is on an entity other than the counterparties to the transaction itself. This entityis known as the reference entity and may be a corporate, a sovereign or any other form of


10/28



legal entity which has incurred debt. Credit derivatives are bilateral contracts between a buyerand seller under which the seller sells protection against the credit risk of the reference entity.Main purposes of are as follows:-

Bankruptcy (the risk that the reference entity will become bankrupt) failure to

pay (the risk that the reference entity will default on one of its obligations such asa bond or loan) Obligation default (the risk that the reference entity will default on any of its

obligations) Obligation acceleration (the risk that an obligation of the reference entity will be

accelerated e.g. a bond will be declared immediately due and payable following adefault)

repudiation/moratorium (the risk that the reference entity or a government willdeclare a moratorium over the reference entity's obligations)

Restructuring (the risk that obligations of the reference entity will berestructured).

2.2 Types of Credit derivatives :-Based on the form of credit derivatives can be dividedinto two types.

I. Funded format- The most commonly used is known as swap format, and this is thestandard for CDS. This format is also termed unfunded format because the investormakes no upfront payment. Subsequent payments are simply payments of spread andthere is no principal payment at maturity. Losses require payments to be made by theprotection seller to the protection buyer, and this has counterparty risk implications.

II. Unfunded format- The other format is to trade the risk in the form of a credit linked

note. This format is known as funded because the investor has to fund an initialpayment, typically par. This par is used by the protection buyer to purchase highquality collateral. In return the protection seller receives a coupon, which may befloating rate, i.e, Libor plus a spread, or may be fixed at a rate above the samematurity swap rate. At maturity, if no default has occurred the collateral matures andthe investor is returned par. Any default before maturity results in the collateral beingsold, the protection buyer covering his loss and the investor receiving par minus theloss. The protection buyer is exposed to the default risk of the collateral rather thanthe counterparty.

2.3

Market over view of credit derivatives :-Various types of exist in the marketdepending on the customers needs and the risk perception. Financial engineering also plays agreat role in designing the product. Figure 5 shows the breakdown of the differentinstruments in credit derivatives market.


11/28

Exotic Credit

V.V.P.Narasimham, EPGP 07-09

Figure 5 Break up

2.3.1 Single type credit defaits simplest form is a bilaterThis type of instrument is useor sovereign) from one partCredit protection from the otha credit event. This strategysome specified maturity datpayments, to the protection sThis is known as the premiudate protection seller will pathe CDS. Upon the completiphysical delivery or the cash

Figu

2.3.2 Credit option :-Credit obrothers. This product is verperceived ness of asset & H

$1.75$1.30

$11.10

$0.

erivatives and Lehman brothers: A case anal

of various instruments in credit derivative

lt swap : - A Single type credit swap is a crel contract between a protection buyer andd for transferring the credit risk of a referen

to another. In a standard CDS contract oer party, to cover the loss of the face value ois one of the ways to sell the credit. This p

. For this protection, the protection buyller and until a credit event or maturity, whileg.Supose the credit event does not occursthe amount to the buyer and this is known

n of the maturity period asset will be transf elivery. Figure 6 shows the frame work of S

re 6 Frame work of Single type CDS

ptions are the one of the most vibrant produpopular due to the decreased spread leveldge fund managers for in terms of levera

$35.00

85

Credit def

Credit lin

Options a

Portfolioproducts

Total retu

ysis

Page 11

s market

dit default swap; ina protection seller.e entity (corporate

ne party purchasesan asset following

otection lasts untilr makes quarterlychever occurs first.before the maturityas protection leg of rred in the form of ingle type CDS.

ts sold by Lehman, volatility and thee and asymmetric

ault swaps

ed notes

d hydrids

orreclation

n Swaps


12/28

Exotic Credit


payoff.Furhter this product gamost popular products of Cpurchases debentures from that more than the par rate fro

collateralised to compensate twill be utilised to issue A-2comprise of embedded call oin the form of long term wpurchase the bonds issued byBonds issued by the trust prCovered call option; spread c

Fig

Strategies for selling the bondI. Put call stripping- The

the bond back to thefuture dates.

II. Price based options- aand receives the undbetween the price of t

III. Spread based options:of the underlying bonbond the payoff is pstrike spread.

IV. Covered call strategymoney call on the sa


ined popularity due to its option of liquidityredit options are the repack trade option.FI/Company at the par rate and issues coupthe trust established by it. This trust is no

he higher par rate issued by it and the excesranche with the option of principal only. Btions. Further a separate call will be sold toarrant. These investors will have the righLehman trust initially and thereafter presetovide various options to the investors likell option etc.Figure 7 shows the frame work

re 7 Frame work of Credit options

s:-se bonds grant the holder the right, but not tissuer at a predetermined price (usually p

t exercise, the option holder pays a fixed aerlying bond the payoff is proportionale bond and the strike price.at exercise, the option holder pays an amoun

calculated using the strike spread and receroportional to difference between the underl

:-an investor who owns the underlying boe face value, receiving an upfront premiu

ysis

Page 12

and high yield. TheLehman brothersns to the investors

mally will be over

capital of the trustoth A-1&2 tranchethe retail investorsnot obligation to

all strike schedule.naked call option,for credit options.

e obligation to sellr) at one or more

ount (strike price)to the difference

t equal to the valueives the underlyinging spread and the

d sells an out-of-. If the bond price


13/28

Exotic Credit


on the expiry date isreceives the strike prithe price. If the pricepremium.

V.

Naked call strategy:-adoes not own but wodate is lower than thecompensates him for nbond price is above th

VI. Default swaption: -Th2.3.3 Credit linked notes :-Aevent, which may be a defaultrelevant credit events must bea credit-default swap with a rlike features, a CLN is aninvestment fund manager willloan defaults. Numerous diff and placed in the past few ydetailed account of these inswell-rated borrower, packageshows the frame work for cre

Figu

2.3.4 Synthetic CDO: - Sylarge number of companies irisk or subordination - eachcredit exposures are taken onphysical assets. Synthetic CCDOs. Synthetic CDOs areThey generate income selling

more companies. One way thswaps". Investors receive reg


greater than the strike, the investor delive. The option premium offsets the investoris less than the strike the investor keeps

n investor writes an out-of-the-money put old like to buy at a lower price. If the bondstrike price, it is delivered to the investor. Tot being able to buy the bond more cheaply ioption strike price, the investor earns the pr

se were protection call and protection put ocredit linked note is a note whose cash flo

, change in credit spread, or rating change. Tnegotiated by the parties to the note. A CLNgular note (with coupon, maturity, redempton-balance-sheet asset, in contrast to apurchase such a note to hedge against possirent types of credit linked notes (CLNs) hears. Here we are going to provide an overuments. The most basic CLN consists of

with a credit default swap on a less creditwit link Notes.

e 8 Frame work of Credit link Notes

thetic CDO is form of credit derivative off a single instrument. This exposure is sold

slice is known as a tranche .In these instusing a credit default swap rather than by hOs can either be single tranche CDOs

also commonly divided into balance sheet aninsurance against bond defaults, typically

ey do so is by entering into contracts knowular payments from credit-default-swap bu

ysis

Page 13

ers the bonds ands loss of upside onthe bonds and the

n a bond which heprice on the expiryhe option premiumn the market. If theemium.tions.

depends upon anhe definition of thein effect combines

ion). Given its noteDS.Typically, an

le down grades, orve been structuredview rather than abond, issued by a

orthy risk. Figure 8

ring exposure to ain slices of varyinguments underlyingving a vehicle buyr fully distributed

d arbitrage CDOs.n a pool of 100 or

n as "credit defaulters, usually which


14/28

Exotic Credit


are banks or hedge funds. Fishows the mechanics of Synt

Figu

Fig

2.3.5 Basket default swapbeing that the trigger is the n t

baskets contain five to 10 ref

and it is the first credit in a baprotection buyer. As with a C


ure 9 shows the frame work for Syntheticetic CDO.

re 9 Frame work for Synthetic CDO

re 10 Mechanics of Synthetic CDO

s:- A basket default swap is similar to a Ch credit event in a specified basket of referenrence entities. In the case of first-to-default

sket of reference credits whose default triggeDS, the contingent payment typically involv

ysis

Page 14

DO and Figure 10

DS, the differencece entities. Typical(FTD) basket, n=1,

rs a payment to thes physical delivery


15/28

Exotic Credit


of the defaulted asset in retassuming the nth-to-default rithe position as a series of regis sooner. The advantage of a

than any of the credits in thetheir credit risk. Figure 11 shthe frame work of Basket def

Figure 1

2.3.6 CDO Squared: - A spform of tranches. A collateraliof collateralized debt obligatiassets securing the obligtranches. CDO-squared allowCDOs.Typically this is a meof a mixture of asset-backed slosses are incurred if the sumtranches exceeds the attachme2.3.7 Hybrid products:- H

other market risks such as icontingent instruments linkeswap or an FX option.


urn for a payment of the par amount insk, the protection seller receives a spread pailar cash flows until maturity or the nth credFTD basket is that it enables an investor to

asket. This is because the seller of FTD protows the frame work of Basket default swapult swaps.

1 Frame work for Basket default Swaps

ecial purpose vehicle (SPV) with securitizatized debt obligation squared (CDO-squared)on (CDO) tranches. This is identical to aation. CDO-squared arrangements ares the banks to resell the credit risk that tzanine super tranche CDO in which the c

ecurities and several sub tranches of syntheof the principal losses on the underlying p

nt point of the super-tranche.brid credit derivatives are those which com

terest rate or currency risk. Typically, theto the value of a derivatives payout, such

ysis

Page 15

ash. In return foron the notional of

it event, whicheverearn a higher yield

ction is leveragings. Figure 11 shows

on payments in theis backed by a poolDO except for theacked by CDOhey have taken inllateral is made uptic CDOs.Principalrtfolio of synthetic

ine credit risk with

se are credit eventas an interest rate


16/28



3 Pricing and valuations3.0 General considerations for Pricing and valuations of credit options: - Generallypricing of credit options depends on the following factors.

a. Default probability rate

b. Recovery ratec. Spread valued. Asset correlationse. Protection on the premium and protection legs.f. Asset Quality

Based on these factors pricing and valuations can be modelled for various credit instruments.Considering the time and availability of the resources both pricing and valuations was donefor three instruments (Single type CDR, Synthetic CDO & Credit options) only and for theothers only pricing exercise was done.3.1 Pricing of Credit default swap:- Pricing of single type CDRs can be done in structuralform or reduced form. In the structural approach, the default is characterised as theconsequence of some event such as a companys asset value being insufficient to cover arepayment of debt. This approach is based on the assumption that bonds should be traded onthe internal structure of the company. However this approach lacks flexibility. The otherapproach uses in valuation of the CDS is the probabilistic approach. This approach based onthe occurrence of credit event. Pricing of single CRS depends on several factors like hazardrate, default rate, swap spread and the Quality of asset. Pricing of CDS depends on the break even spread which depends on the values of premier leg and protection leg. Figure 12 showsthe probabilistic valuation model for Single type CDS.

Premium PV = Protection PV

Where


17/28

Exotic Credit


Figure 12 Prob

3.1.1 Assumptions for priciasset will be recovered in capoor recovery rates at the lainterest rate curve as well assubprime crisis in this considreduced) and this made hugassumed from the historical dplayed a great role in the lossSingle type CDS and figurevalues for different rates of as


bilistic Valuation model for of Single typ

g the product :-For pricing the product it ie of default. However it suffered heavily iner stages. Further while deciding the pricehe recovery rate of the asset is flat. Howeveerably reduced the recovery rates of the asse losses for the Lehman brothers.Furhterata which is not much related to the presents of Lehman brothers. Tables 1-3 shows the13 shows the comparison of premier leg

set correlations.

ysis

Page 17

CDS

s assumed that thethis stream due toit is assumed that

r conditions due toet (Prices of assetsdefault rates werecrisis and this alsovaluation done for

and protection leg


18/28



Table 1 Calculation of PV for Premier leg and Protection leg

TimeRecovery

rateHazard

rateInterest

rate SpreadPV of Protection

legPV of Premium

leg0.5 0.4 0.02 0.965605 0.012 0.009811 0.009811

1.5 0.8 0.02 0.900325 0.004 0.001643 0.0016432.5 0.8 0.02 0.839457 0.004 -0.00047 -0.000473.5 0.8 0.02 0.782705 0.004 -0.00315 -0.003154.5 0.8 0.02 0.729789 0.004 -0.00647 -0.00647

0.001359 0.001359

Table 2 Calculation of payoff for different probabilities

Calculation of defaultprobabilities

Exp. Pay from buyerin case of no default

Exp. Pay from Sellerin case of default

Exp. Pay frombuyer in case of

default

TimeHazRat.

Def.Prob

Sur.Prob

Exp.Pay.

Dis.Fact

PV of Exp.Pmt.

Rec.Rate

Exp.Pay.

PV of Exp.Pay

Exp.Pay

PV Of Exp.Pmt

0 1.00 1.18 0.97 1.14 0.40 1.20 1.16 0.01 0.010.5 0.02 0.02 0.98 1.15 0.90 1.04 0.40 1.18 1.06 0.01 0.011.5 0.02 0.02 0.96 1.13 0.84 0.95 0.40 1.15 0.97 0.01 0.012.5 0.02 0.02 0.94 1.11 0.78 0.87 0.40 1.13 0.88 0.01 0.013.5 0.02 0.02 0.92 1.08 0.73 0.79 0.40 1.11 0.81 0.01 0.01

4.5 0.02 0.02 0.90PV 4.78 PV 4.88 PV 0.05

Table 3 Calculation of PV for default at various times

Time

Case-ICase-II Case-I

Case-II Case-I Case-II Case-I Case-II

Recovery rate SpreadTotal PV to DefaultProtection Buyer:

Total PV to DefaultProtection seller

0.5 0.7 0.7 0.006 0.006

4.924 6.776 2.4388 2.4573

1.5 0.6

Assetdefaulted

0.0082.5 0.4 0.0123.5 0.1 0.018

4.5Asset

defaulted

3.1.2 Analysis on the effect of Single type CDS on Lehman brothers:- a. Decrease in Quality of assets with timeb. Decreased recovery rates and subsequent default of lender.c. Problems in calibrating in recovery rates and default rates.d. Prevailing low interest rates gives less chances for increasing spread.


19/28



Figure 13 Comparison of PV for Premier leg% & Protection leg

3.2 Pricing of Synthetic debt obligation :-The performance of a synthetic CDO is linked tothe incidence of default in a portfolio of CDS. The CDO redistributes this risk by allowingdifferent tranches to take these default losses in a specific orderThis risk is redistributed into three tranches as given in previous chapters. Out of these threetranches, the equity tranche has the greatest risk and is paid the widest spread. It is typicallyunrated. Next is the mezzanine tranche which is lower risk and so is paid a lower spread.Finally the senior tranche is having less risk perception & is normally protected bysubordination debt clause. The advantage of CDOs is that by changing the details of thetranche in terms of its Attachment point and width, it is possible to customise the risk profileof a tranche to the investors specific profile Attachment point: This is the amount of subordination below the tranche. The higher the attachment point, the more defaults arerequired to cause tranche principal losses and the lower the tranche spread. Figure 14 & Table4 shows effect of spread rate on the Break even point. (CBE) Spread depends on the

following factors:-a. Tranche width: The wider the tranche for a fixed attachment point, the more losses to

which the tranche is exposed. However, the incremental risk ascending the capitalstructure is usually declining and so the spread falls.

b. Portfolio credit quality: The lower the quality of the asset portfolio, measured byspread or rating, the greater the risk of all tranches due to the higher defaultprobability and the higher the spread.

c. Portfolio recovery rates: The expected recovery rate assumptions have only asecondary effect on tranche pricing. This is because higher recovery rates implyhigher default probabilities if we keep the spread fixed. These effects offset each otherto first order.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 0.2 0.4 0.6 0.8 1

P V o

f t h e a s s e t

Recovery rate

PV of Protection leg

PV of Premium leg

More payments has to paid by the premier sellerdue to the poor recovery rate of asset


20/28



d. Swap maturity: This depends on the shapes of the credit curves. For upward slopingcredit curves, the tranche curve will generally be upward sloping and so the longer thematurity, the higher the tranche spread.

e. Default correlation: If default correlation is high, assets tend to default together and

this makes senior tranches more risky. Assets also tend to survive together making theequity safer. To understand this more fully we need to better understand the portfolioloss distribution. Table 5 shows the effect of correlation on the CBE.Table 4 Calculation of CBE for various tranche for different values of Rho

Equity 0-3 rho=10% rho=30% rho=70%MCValue

MCst.dev

MCValue

MCst.dev

MCValue

MCst.dev

Floating leg value 2,292.42 2.56 1,771.89 3.57 931.79 3.77

Fixed leg value 6,657.61 11.12 8,258.19 13.5210,844.22 12.87

Total Price with predefined coupon 1,959.54 3.06 1,358.98 4.19 389.57 4.38Break Even coupon (CBE) 63.128% 0.216% 58.022% 0.2792% 35.156% 0.267%

Mezzanine 3-10 rho=10% rho=30% rho=70%MCValue

MCst.dev

MCValue

MCst.dev

MCValue

MCst.dev

Floating leg value 1,516.19 6.14 1,515.42 7.23 1,162.22 7.27

Fixed leg value 28,811.0 13.97 28,190.03 19.75 28,484.6 22.25Total Price with predefined coupon 75.64 6.79 105.92 8.15 (262.02) 8.04Break Even coupon (CBE) 7.1857% 0.040% 11.301% 0.1005% 15.196% 0.169%

Senior 10-15 rho=10% rho=30% rho=70%MCValue

MCst.dev

MCValue

MCst.dev

MCValue

MCst.dev

Floating leg value 111.22 1.77 354.66 3.48 542.89 4.49

Fixed leg value 22,314.7 2.53 21,798.50 8.04 21,135.8 12.82Total Price with predefined coupon (1,004.5) 1.88 (735.26) 3.84 (513.90) 5.08Break Even coupon (CBE) 0.6229% 0.011% 3.3341% 0.0547% 9.1068% 0.130%

Super Senior 15-30 rho=10% rho=30% rho=70%MCValue

MCst.dev

MCValue

MCst.dev

MCValue

MCst.dev

Floating leg value 16.85 0.76 281.42 4.87 861.24 9.56

Fixed leg value 67,283.7 0.86 66,839.96 10.22 65,469.0 25.15Total Price with pre


21/28



defined coupon (3,347.3) 0.80 (3,060.5) 5.35 (2,412.2) 10.72Break Even coupon (CBE) 0.0266% 0.001% 0.6622% 0.0175% 3.6394% 0.072%

Figure 14 Variation of CBE for change in Spread rate

Table 5 Price of pre-defined for variation in spread rate

Correlation

Total price with predefined [email protected]%Spread

Total price with predefined [email protected]%Spread

Total price with predefined [email protected]% Spread

10% (4,153.37) (1,999.89) 768.7420% (5,093.28) (3,126.84) 1,803.4530% (6,136.64) (4,355.87) 1,803.4540% (6,941.09) (5,413.34) 3,999.3150% (8,012.32) (6,343.96) 5,008.7860% (8,766.73) (7,288.27) 5,989.3070% (9,667.55) (8,250.81) 7,250.8180% (10,307.18) (9,223.04) 8,323.1690% (11,239.19) (10,304.99) 9,563.13

3.2.1 Analysis of the impact of Synthetic CDO on Lehman brothers:- Following weresome of the possible reasons that triggered the losses of Lehman brothers:-

a. Equity tranche which promised great returns has incurred great losses due tothe volatility in the market and this may be the possible reason behind thelosses of Lehman brothers.(Equity tranche is effected by 30-70% due tochanges in Rho value) Figure 15-18 shows the affect of rho value of varioustranches.

b. Most of the assets were occupied the lower correlation portions withoutrecognizing the composition of the tranche.

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

140.00%

-10% 10% 30% 50% 70% 90%

C B E %

Correlation

CBE-1.5% Spread

CBE-2.5% Spread

CBE-3.5% Spread


22/28



c. Assets were purchased at the time of lowest interest regime/.However sub-prime crisis causes the upward sloping curve which leads to the increase inspread rate and this ultimately leads to the increase of default of assets.Futhermost of the assets taken as collatereral in equity tranche is in the anticipation

of increase in the value of the mortgages in case of default of lenders.However this strategy backfired due to fall in assets price. This can be seen inthe effect of Rho on the equity tranche.

d. In this anticipation of the more returns width of the tranche also increased(Equity, Mezzanine tranche).This resulted in more defaults.

Figure 15 CBE values of Equity tranche for variation in Rho

0%

10%

20%

30%

40%

50%

60%

70%

10% 30% 70%

C B E

Rho

Equity CBE


23/28



Figure 16 CBE values of Senior tranche for variation in Rho

Figure 17 CBE values of Mezzanine tranche for variation in Rho

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

10% 30% 70%

C B E

Rho

Senior CBE

0%

2%

4%

6%

8%

10%

12%

14%

16%

10% 30% 70%

C B E

Rho

Mezzanine CBE


24/28



Figure 18 CBE values of super senior tranche for variation in Rho 3.3 Valuation of credit options :- Valuation of credit options depends price, yield or creditspread. The exercise price is constant for options struck on price, but for options struck onyield it depends on the time to maturity of the underlying bond and has to be determined froma standard yield-to-maturity calculation curve. Bond options struck on spread are different.

For credit spread options the exercise price depends both on the time to maturity of the bondand on the term structure of interest rates at the exercise time. A credit spread strike iscommonly specified as a yield spread to a Treasury bond or interest rate swap, or as an assetswap spread. credit spread strike is commonly specified as a yield spread to a Treasury bondor interest rate swap, or as an asset swap spread. Option payoff after timet is

Where the PV01 T is the value at T of a risky 1bp annuity to time T M or default, and S T is the

market spread observed at T on a CDS with maturity T M.If suppose two assets A& B whose ratio of payments after time t equal to present ratio of present payments then if Suppose A be the swaption, in which case AT is 0 if defaulthappens before T and PST otherwise. The value of the swaption today is then the value of theswaption today is

If we make the assumption that log (S T) is normally distributed with variance 2T,corresponding to the spread following a log-normal process with constant volatility , then

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

10% 30% 70%

C B E

Rho

Super Senior CBE


25/28



with the requirement E(S T) = F 0 (the forward spread), we have determined the distribution of ST to be used to find E[max{S T K,0}]. It is easy to calculate this expectation and we arriveat the Black formula

Table 6 Valuation of Receiver default swap

Receiver default swaption:-Buyer (Lehman brothers) Seller (FI)

Type of contract Short by the seller (FI)Time 3 monthsPV 4.39Premium 120 BP to be paid by Lehman brothersScenarios:-(I).Spread >265 BP Not exercise (Loss only

be premium)Gets 120 BP paid by Lehmanand can retain option.

(II).Spread strike price CDS spread at expiry < strike priceCredit view Short credit forward Long credit forwardKnockout May trade or without Not relevant

3.3 Valuation of Basket default swap:- This type of products are based on redistributingthe credit risk of a portfolio of single name credits across a number of different securities.The portfolio may be as small as five credits or as large as 200 or more credits. Theredistribution mechanism is based on the idea of assigning losses on the credit portfolio to thedifferent securities in a specified priority, with some securities taking the first losses andothers taking later losses. This exposes the investor to the tendency of assets in the portfolioto default together, i.e., default correlation. The simplest correlation product is the basketdefault swap. air-value of spread paid by a credit risky asset is determined by the probabilityof a default, times the size of the loss given default. FTD baskets leverage the credit risk byincreasing the probability of a loss by conditioning the payoff on the first default among

several credits. The size of the potential loss does not increase relative to buying any of theassets in the basket. The most that the investor can lose is par minus the recovery value of the


26/28



FTD asset on the face value of the basket. Value of n: An FTD (n=1) is riskier than an STD(n=2) and so commands a higher spread. The other factor affects the correlation sensitivity isthe default probability of premier leg & Protection leg. Following affects the valuation of Basket default swap.

a.

Number of credits: The greater the number of credits in the basket, the greater thelikelihood of a credit event, and so the higher the spread.b. Credit quality: The lower the credit quality of the credits in the basket, in terms of

spread and rating, the higher the spreadc. Recovery rate: This is the expected recovery rate of the nth-to-default asset

following its credit event. This has only a small effect on pricing since a higherexpected recovery rate is offset by a higher implied default probability for a givenspread. However, if there is a default the investor will certainly prefer a higherrealised recovery rate.

d. Default correlation: Increasing default correlation increases the likelihood of assets to default or survive together. The effect of default correlation is subtle andsignificant in terms of pricing.

3.5 Valuation of Hybrids :-The behaviour of hybrid credit derivatives is driven by the jointevolution of credit spreads and other market variables such as interest and exchange ratesdefault protection on the MTM of an interest rate swap. Suppose an investor has entered intoa receiver swap with fixed rate k with a credit risky counterparty. If the MTM of the receiverswap, R St is positive to the investor at the time of default, this is paid by the protection seller.If RS t is negative, the investor receives nothing, so that the payoff at default is max (R St, 0).This is an option to enter into a receiver swap with fixed rate k for the remaining life of the

original trade at default. For simplicity, we assume that default can only take place at times ti.If B denotes the price process of the savings account, then computing the expecteddiscounted cash flows gives the value V0 for the price of the default protection, where

This means that the value of default protection is a probability weighted strip of receiverswap, where each swap is priced conditional on default happening at t.The parameters neededfor pricing hybrids are essentially volatility and dependence parameters.Main factors required for pricing the product are

a. Calibration of volatilitiesb. Determination of dependency between credit spreads and other market variablesc. Correlation between rate and credit process


27/28



4 Conclusions& Recommendations4.0 Based on the valuations and pricing of the exotic credit derivative products following

conclusions can draw.a. Portfolios have to be more diversified for avoiding the risk involved in the credit

derivative instruments. This can be understandable considering the risk exposureto the various assets lesser/negative correlations can reduce the market effect onthe Portfolio. However care has to taken while designing the product.

b. More quantitative techniques has to applied for deriving the better resultsc. Investors have to under stand the risk involved in the credit products and have to

evaluate the Quality of the assets before investing in the Portfolio.d. Role of the rating agencies has to more regulated for avoiding the over rating of

the assets.e. Application of better risk practices.


28/28


5. References1. Collateral damage: Facing robust actions in the face of growing crisis.BCG Report

Oct 082. Investment and capital markets Market report second Quarter 2008:BCG Report

3. Lehman brothers guide to exotic credit derivatives4. Options futures and other derivatives by John C.Hull5. Wikipedia.com6. www.google.com-General searches on credit derivatives in google

exotic derivatives project-lehman

Documents