MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

1. Summer 07, MFIN7011, Tang Credit Derivatives MFIN 7011: Credit Risk ManagementSummer, 2007Dragon Tang Lecture 9 Credit Derivatives Saturday, July 21, 2007 Readings: Duffie and Singleton Chapter 8 Graveline and Kokalari (2006)

2. Summer 07, MFIN7011, Tang Credit Derivatives Credit Derivatives

3. Summer 07, MFIN7011, Tang Credit Derivatives How Citigroup Survived in Enron Case

4. Summer 07, MFIN7011, Tang Credit Derivatives Caveat: Citigroup and Enron (Yosemite Example)

5. Summer 07, MFIN7011, Tang Credit Derivatives Citigroup Enron Credit Derivative

6. Summer 07, MFIN7011, Tang Credit Derivatives Credit Derivatives: Cure for Credit Risk

7. Summer 07, MFIN7011, Tang Credit Derivatives Usefulness of Credit Derivatives

8. Summer 07, MFIN7011, Tang Credit Derivatives Growth of Credit Derivatives Markets (1996-2008 est., in $ Billions)

9. Summer 07, MFIN7011, Tang Credit Derivatives Participants of Credit Derivatives Markets

10. Summer 07, MFIN7011, Tang Credit Derivatives Participants of Credit Derivatives Markets

11. Summer 07, MFIN7011, Tang Credit Derivatives Types of Credit Derivatives

12. Summer 07, MFIN7011, Tang Credit Derivatives Types of Credit Derivatives by Market Share

13. Summer 07, MFIN7011, Tang Credit Derivatives Total Rate of Return Swaps (TRORS) TRORS is a form of financing TRORS allows an investor to enjoy the cash flow without actually owning the security At the end of the TRORS, the TROR receiver pays any decline in price to the TROR payer and gets the increase in price from the TROR payer He pays a regular floating rate payment on a periodic basis TRORS are off-balance sheet transactions, the highest volume and the most popular sector of the credit derivative market Low-cost borrowers with large global balance sheet are naturally advantaged as payers in TRORS Synthetic financing Synthetic financing

14. Summer 07, MFIN7011, Tang Credit Derivatives TRORS

15. Summer 07, MFIN7011, Tang Credit Derivatives TRORS Total return: Coupons + (final value � original value) Reference Asset: Bond, Loan, Index, Equity, Commodity TROR Receiver is long both price and default risk of the reference asset. Receivers of TROR are often referred to as investors TROR Payer is the legal owner of the reference asset TRORS usually terminates in the event of default Receiver make the net payment of the price depreciation Or, receiver takes delivery of the reference asset and pay the original price to the payer At the maturity of the transaction, the receiver has the right to choose to purchase the reference asset at the then prevailing market price In the event of default, the receiver bears the risk. At the maturity of the transaction, the receiver has the right to choose to purchase the reference asset at the then prevailing market price In the event of default, the receiver bears the risk.

16. Summer 07, MFIN7011, Tang Credit Derivatives Motivation of Receiver The compelling reason to become a receiver of TRORS is �leverage� No initial cash payment is required; cash flows are usually paid on a net basis Hedge funds are eager to be TROR receivers Hedge funds and other lesser credits usually have to deposit collateral Despite the credit implications from a TRORS, the use is primarily that of a financing: funding cost arbitrage. Net basis: the investor�s payments are subtracted in advance from the securities cash flows. Despite the credit implications from a TRORS, the use is primarily that of a financing: funding cost arbitrage. Net basis: the investor�s payments are subtracted in advance from the securities cash flows.

17. Summer 07, MFIN7011, Tang Credit Derivatives Exercise Three investors want to receive the total rate of return of a given asset. The asset is a BB- bond with a coupon of LIBOR +150 bps, with the current yield 8.30% LIBOR is currently at 5.80% Two of the investors are hedge funds and must pay a funding cost of LIBOR + 100. The third investor is a mutual fund, which pays cash for the investment. The first hedge funds has to put up 5% up front collateral, the second deposits 10%. The collateral earns LIBOR flat. Calculate the net return rate for the three investors See Tavakoli p26; power of leverage Answer: 35.8% for A, 20.8% for B and 8.3% for C. Net swap spread = asset yield (8.3%) � Funding cost (LIBOR + 100bps) = 1.5% Levered swap return = Net Swap spread * 20 (Collateral 5%) = 30% Net return = Levered swap return + interest on collateral (5.8%) = 35.8% See Tavakoli p26; power of leverage Answer: 35.8% for A, 20.8% for B and 8.3% for C. Net swap spread = asset yield (8.3%) � Funding cost (LIBOR + 100bps) = 1.5% Levered swap return = Net Swap spread * 20 (Collateral 5%) = 30% Net return = Levered swap return + interest on collateral (5.8%) = 35.8%

18. Summer 07, MFIN7011, Tang Credit Derivatives Motivation of Payer Creates a hedge for price risk and default risk of the reference asset Effectively creates a short position of the reference asset, without legally shorting it Accounting/Tax Reasons: Can defer unrecognized loss in a bond position, without risking further losses This does not work under the US tax regime: paying the TROR on an asset will be evaluated as a true sale The price risk and default risk are borne by the receiver. Short position: e.g. for a short term, if the investor has a negative view on the asset, he can enter a short term TRORS. Loss deferring: at the maturity of the TRORS, the investor can sell the asset and recognize the loss; in the US, paying the TROR on an asset will be evaluated as a true sale. The price risk and default risk are borne by the receiver. Short position: e.g. for a short term, if the investor has a negative view on the asset, he can enter a short term TRORS. Loss deferring: at the maturity of the TRORS, the investor can sell the asset and recognize the loss; in the US, paying the TROR on an asset will be evaluated as a true sale.

19. Summer 07, MFIN7011, Tang Credit Derivatives Creating Synthetic Assets A financial institution can short credits even in maturities for which no reference asset exists The return of the underlying asset can have a cap or a floor Mismatch maturity: TRORS has shorter maturity than the reference asset Investor of TRORS bears price risk Not the same as the �tranched asset swap�: asset swap package which can be put back to the seller provided the reference bonds are not in default; so the seller is immunized from the default risk but not the market-price risk or credit-spread-widening risk if the put is exercised. Price risk: even if the credit quality of the reference asset does not change, its price may change solely due to the interest rate risk; this risk could be large compared to the gained return Tranched asset swap usually has shorter maturity than the underlying asset swap. The investor is the legal owner of the asset swap package.Price risk: even if the credit quality of the reference asset does not change, its price may change solely due to the interest rate risk; this risk could be large compared to the gained return Tranched asset swap usually has shorter maturity than the underlying asset swap. The investor is the legal owner of the asset swap package.

20. Summer 07, MFIN7011, Tang Credit Derivatives Funding Arbitrage TRORS is a form of financing The figure shows the case when A bank buys the asset outright: on-balance sheet transaction TRORS is a form of financing The figure shows the case when A bank buys the asset outright: on-balance sheet transaction

21. Summer 07, MFIN7011, Tang Credit Derivatives Funding Arbitrage Collateralized loan: equivalent to that AA bank makes loan to A bank, with the reference asset as collateral.Collateralized loan: equivalent to that AA bank makes loan to A bank, with the reference asset as collateral.

22. Summer 07, MFIN7011, Tang Credit Derivatives Funding Arbitrage Benefits to the AA bank: hedge market and credit risk of the BBB asset reduce the capital charge of the transaction: if A- bank and BBB asset are independent, then the implied rating on the effective credit risk to the AA bank is A+ Benefits to the A- bank: lock in a favorable financing rate: 15bps reduction No need to put up any economic capital A leveraged off-balance sheet transaction It works because of the difference in the funding costs of the two institutions leverage: even if the bank is temporarily short of investment cash. Joint ratings of noncorrelated assets and guarantors. leverage: even if the bank is temporarily short of investment cash. Joint ratings of noncorrelated assets and guarantors.

23. Summer 07, MFIN7011, Tang Credit Derivatives Funding Arbitrage TRORS is a form of financing The figure shows the case when A bank buys the asset outright: on-balance sheet transaction TRORS is a form of financing The figure shows the case when A bank buys the asset outright: on-balance sheet transaction

24. Summer 07, MFIN7011, Tang Credit Derivatives Balance Sheet Management The capital market desk of a bank is in the business to issue bonds. Sometimes, it ends up not being able to sell off all the bonds it underwrites. One way to offload the bonds from the balance sheet is to sell them to a conduit of another bank. The conduit purchases the bonds funded with a commercial paper program. The conduit does not want to take the risk of the bonds, therefore it pays the TROR on the bonds to the internal derivatives desk. The derivatives desk then passes the risk by paying the TROR on the bonds to a subsidiary of the original bank End effect: The asset is legally off loaded from the balance sheet, but the risk remains with the originating bank. You want it to appear as if you sold the bonds to a customer. You want it to appear as if you sold the bonds to a customer.

25. Summer 07, MFIN7011, Tang Credit Derivatives Balance Sheet Management 15bps is the fee for renting Bank B�s balance sheet. 15bps is the fee for renting Bank B�s balance sheet.

26. Summer 07, MFIN7011, Tang Credit Derivatives Credit Linked Notes (CLN) The coupons, and/or principal of the note are linked to a credit event. The coupons, and/or principal of the note are linked to a credit event.

27. Summer 07, MFIN7011, Tang Credit Derivatives Why Credit-Linked Notes? There is no need for an ISDA master agreement or confirmation; simple documentation Investor who are not authorized to do derivatives or off-balance sheet transactions can participate Credit lines to the investor, the hedge provider, are not used. This is particularly valuable for very long dated or leveraged transactions It doesn�t matter that the investor is providing a hedge and is highly correlated with the reference credit, as the issuer gets par up front The credit quality of the investor is irrelevant International swaps and derivatives association: documentation is as simple as that for a medium-term note Issuer gets par up front. In the event of default, issuer has the hedge money up front (by paying the investor the defaulted bond value for example) International swaps and derivatives association: documentation is as simple as that for a medium-term note Issuer gets par up front. In the event of default, issuer has the hedge money up front (by paying the investor the defaulted bond value for example)

28. Summer 07, MFIN7011, Tang Credit Derivatives Four Major Structure Types of CLNs Principal-protected notes Receive the credit rating of the issuer The investor risks loss of coupon income in the event of default of a different reference credit Boosted coupon notes Receive the credit rating of the issuer The principal payment is linked to the default event and default value of a different reference credit, with underlying credit risk of a lower-rated credit Boosted coupon notes Receive the credit rating of the issuer The principal payment is linked to the default event of a different reference credit(s) the principal payment may have levered risk or even risk of loss of the entire principal amount in the event of a default of the reference credit(s) Reduced coupon notes Receive the credit rating of the issuer The principal repayment is face amount The termination payment is enhanced by the loss in the event of default of a reference asset Principal is protected, only coupon income is lost. The foregone interest income on the note mitigates the loss in the event of default for the issuer of the note. For boosted coupon, in the event of default, the principal payment may be the market value for the reference asset, paid on an early termination date. Boosted coupon: to compensate for the principal loss risk, the coupons have to be high Reduced coupon: part of the coupon is the option premium paid for the credit protection purchased by the note investor Principal is protected, only coupon income is lost. The foregone interest income on the note mitigates the loss in the event of default for the issuer of the note. For boosted coupon, in the event of default, the principal payment may be the market value for the reference asset, paid on an early termination date. Boosted coupon: to compensate for the principal loss risk, the coupons have to be high Reduced coupon: part of the coupon is the option premium paid for the credit protection purchased by the note investor

29. Summer 07, MFIN7011, Tang Credit Derivatives CDS Indices

30. Summer 07, MFIN7011, Tang Credit Derivatives Pricing Derivatives The dynamic of the underlying asset The payoff of the derivative Then, the price of the derivative B is the discount factor (the savings account) Q is the risk-neutral measure. Expectation is taken with respect to the probability density function of the underlying asset price (or the joint pdf if interest rate is random too) B is the discount factor (the savings account) Q is the risk-neutral measure. Expectation is taken with respect to the probability density function of the underlying asset price (or the joint pdf if interest rate is random too)

31. Summer 07, MFIN7011, Tang Credit Derivatives Risks in Underlying Assets Interest risk Default risk Recovery risk Spread risk (changes of the rating) Liquidity risk

32. Summer 07, MFIN7011, Tang Credit Derivatives Spread Models Spread models do not break down the spread into default risk and recovery risk components It is easier to directly model the spread itself This approach is ideal in modeling credit spread options Reduced form models Spread = PD * LGD Spread is the underlying variable in such options Reduced form models Spread = PD * LGD Spread is the underlying variable in such options

33. Summer 07, MFIN7011, Tang Credit Derivatives Spread Models The spread is assumed to follow where s is the spread, k is the rate of mean reversion, ? is the long run mean of the spread, s is the volatility coefficient, and dz is the Wiener increment. In the simplest case, the model assumes that interest rates are constant, which is a reasonable assumption to make when the spread option has short maturity The real world dynamics, NOT risk-neutral The real world dynamics, NOT risk-neutral

34. Summer 07, MFIN7011, Tang Credit Derivatives Spread Option Pricing European spread option pricing where R is an appropriate discount rate, K is the threshold spread or exercise price, and f(sT) is the probability function R depends on which probability measure is used. R depends on which probability measure is used.

35. Summer 07, MFIN7011, Tang Credit Derivatives A One-Factor Spread Model Two-period model with each period equal to one year Term structure of riskless rate r=[0.08,0.09] Term structure of spread rate s=[0.010,0.015] Then Term structure of risk rate r+s = [0.09,0.105] The price of a risk zero coupon bond of maturity two yeas (face value $100) 81.8984 = 100/(1+0.105)2 The riskless forward rate f12 = 1.092/1.08 � 1 = 0.1001 The riskless rate r is the spot rate The riskless rate r is the spot rate

36. Summer 07, MFIN7011, Tang Credit Derivatives A One-Factor Spread Model A simple discrete binomial representation of the model In order to undertake pricing without violation of arbitrage, under a risk-neutral regime, it is necessary to risk-adjust the stochastic process above by modifying its drift term by adding ? s(t) can take one of two values (with equal probability) This is the risk-neutral process This is the risk-neutral process

37. Summer 07, MFIN7011, Tang Credit Derivatives A One-Factor Spread Model Assumptions s(0)=0.010 k=0.2 ?=0.02 s=0.03 With equal risk-neutral probability(0.5)

38. Summer 07, MFIN7011, Tang Credit Derivatives A One-Factor Spread Model The price of a 2-year risky zero B(0) is from the initial term structures of credit spread and interest rate: see before In computing B(1), we use forward rate B(0) is from the initial term structures of credit spread and interest rate: see before In computing B(1), we use forward rate

39. Summer 07, MFIN7011, Tang Credit Derivatives A One-Factor Spread Model Then ? =0.0081 Spread call option (K=0.02) = Face Value*(0.0231-0.02)*0.5/1.08 0.5 is the probability 0.5 is the probability

40. Summer 07, MFIN7011, Tang Credit Derivatives Extensions Extend these models to multi-periods Incorporate an additional factor Make the interest rate stochastic and correlated with the credit spread

41. Credit Derivatives 41 Counterparty Risk Many contracts are traded over-the-counter between default-prone parties Each side of the contract is thus exposed to the counterparty risk of the other party When you�re in the money. Collateral/margin, etc. Issuer riskWhen you�re in the money. Collateral/margin, etc. Issuer risk

42. Summer 07, MFIN7011, Tang Credit Derivatives Credit Risk of Derivatives Unilateral default risk European option The option writer may default on his obligations The default risk of the option holder is manifestly not relevant Bilateral default risk Defaultable swaps Swap agreements between two default-prone entities Note: a defaultable swap should not be confused with a default swap, which is a credit derivative, a form of insurance against the reference risk unilateral: for the option holder, the option value cannot fall below zero. unilateral: for the option holder, the option value cannot fall below zero.

43. Summer 07, MFIN7011, Tang Credit Derivatives Summary