FRM Jorion 22 Credit Derivatives

Financial Risk Management Zvi Wiener Following P Jorion, Financial Risk Manager Handbook http://pluto.huji.ac.i l/~mswiener/zvi.html FRM 972-2-588-3049 Chapter 22 Credit Derivatives Following P Jorion 2001 Financial Risk Manager Handbook http://pluto.huji.ac.i l/~mswiener/zvi.html FRM 972-2-588-3049 Credit Derivatives From 1996 to 2000 the market has grown from $40B to $810B Contracts that pass credit risk from one counterparty to another Allow separation of credit from other exposures Ch 22, Handbook Zvi Wiener slide Credit Derivatives Bond insurance Letter of credit Credit derivatives on organized exchanges: TED spread = Treasury-Eurodollar spread (Futures are driven by AA type rates) Ch 22, Handbook Zvi Wiener slide Types of Credit Derivatives Underlying credit (single or a group of entities) Exercise conditions (credit event, rating, spread) Payoff function (fixed, linear, non-linear) Ch 22, Handbook Zvi Wiener slide Types of Credit Derivatives November 1, 2000 reported by Risk Credit default swaps 45% Synthetic securitization 26% Asset swaps 12% Credit-linked notes 9% Basket default swaps 5% Credit spread options 3% Ch 22, Handbook Zvi Wiener slide Credit Default Swap A buyer (A) pays a premium (single or periodic payments) to a seller (B) but if a credit event occurs the seller (B) will compensate the buyer premium A - buyer Contingent payment B - seller Reference asset Ch 22, Handbook Zvi Wiener slide Example • The protection buyer (A) enters a 1-year credit default swap on a notional of $100M worth of 10-year bond issued by XYZ Annual payment is 50 bp • At the beginning of the year A pays $500,000 to the seller • Assume there is a default of XYZ bond by the end of the year Now the bond is traded at 40 cents on dollar • The protection seller will compensate A by $60M Ch 22, Handbook Zvi Wiener slide Types of Settlement Lump-sum – fixed payment if a trigger event occurs Cash settlement – payment = strike – market value Physical delivery – you get the full price in exchange of the defaulted obligation Basket of bonds, partial compensation, etc Definition of default event follows ISDA’s Master Netting Agreement Ch 22, Handbook Zvi Wiener slide Total Return Swap (TRS) Protection buyer (A) makes a series of payments linked to the total return on a reference asset In exchange the protection seller makes a series of payments tied to a reference rate (Libor or Treasury plus a spread) Ch 22, Handbook Zvi Wiener slide 10 CLN A buys a CLN, B invests the money in a highrated investment and makes a short position in a credit default swap The investment yields LIBOR+Ybp, the short position allows to increase the yield by Xbp, thus the investor gets LIBOR+Y+X Ch 22, Handbook Zvi Wiener slide 17 Credit Linked Note Credit swap buyer par CLN = Xbp AAA note + Credit swap Contingent payment par L+X+Y investor Contingent payment LIBOR+Y AAA asset Asset backed securities can be very dangerous! Ch 22, Handbook Zvi Wiener slide 18 Types of Credit Linked Note Type Asset-backed Compound Credit Principal Protection Enhanced Asset Return Ch 22, Handbook Maximal Loss Initial investment Amount from the first default Interest Pre-determined Zvi Wiener slide 19 FRM 1999-122 Credit Risk (22-4) A portfolio manager holds a default swap to hedge an AA corporate bond position If the counterparty of the default swap is acquired by the bond issuer, then the default swap: A Increases in value B Decreases in value C Decreases in value only if the corporate bond is downgraded D Is unchanged in value Ch 22, Handbook Zvi Wiener slide 20 FRM 1999-122 Credit Risk (22-4) A portfolio manager holds a default swap to hedge an AA corporate bond position If the counterparty of the default swap is acquired by the bond issuer, then the default swap: A Increases in value B Decreases in value – it is worthless (the same default) C Decreases in value only if the corporate bond is downgraded D Is unchanged in value Ch 22, Handbook Zvi Wiener slide 21 FRM 2000-39 Credit Risk (22-5) A portfolio consists of one (long) $100M asset and a default protection contract on this asset The probability of default over the next year is 10% for the asset, 20% for the counterparty that wrote the default protection The joint probability of default is 3% Estimate the expected loss on this portfolio due to credit defaults over the next year assuming 40% recovery rate on the asset and 0% recovery rate for the counterparty A $3.0M B $2.2M C $1.8M D None of the above Ch 22, Handbook Zvi Wiener slide 22 FRM 2000-39 Credit Risk A portfolio consists of one (long) $100M asset and a default protection contract on this asset The probability of default over the next year is 10% for the asset, 20% for the counterparty that wrote the default protection The joint probability of default is 3% Estimate the expected loss on this portfolio due to credit defaults over the next year assuming 40% recovery rate on the asset and 0% recovery rate for the counterparty A $3.0M B $2.2M C $1.8M = $100*0.03*(1– 40%) only joint default leads to a loss D None of the above Ch 22, Handbook Zvi Wiener slide 23 FRM 2000-62 Credit Risk (22-11) Bank made a $200M loan at 12% The bank wants to hedge the exposure by entering a TRS with a counterparty The bank promises to pay the interest on the loan plus the change in market value in exchange for LIBOR+40bp If after one year the market value of the loan decreased by 3% and LIBOR is 11% what is the net obligation of the bank? A Net receipt of $4.8M B Net payment of $4.8M C Net receipt of $5.2M D Net payment of $5.2M Ch 22, Handbook Zvi Wiener slide 24 FRM 2000-62 Credit Risk (22-11) Bank made a $200M loan at 12% The bank wants to hedge the exposure by entering a TRS with a counterparty The bank promises to pay the interest on the loan plus the change in market value in exchange for LIBOR+40bp If after one year the market value of the loan decreased by 3% and LIBOR is 11% what is the net obligation of the bank? A Net receipt of $4.8M = [(12%-3%) –(11%+0.4%)]*$200M B Net payment of $4.8M C Net receipt of $5.2M D Net payment of $5.2M Ch 22, Handbook Zvi Wiener slide 25 Pricing and Hedging Credit Derivatives Actuarial approach – historic default rates relies on actual, not risk-neutral probabilities Bond credit spread Equity prices – Merton’s model Ch 22, Handbook Zvi Wiener slide 26 Example: Credit Default Swap CDS on a $10M two-year agreement A – protection buyer agrees to pay to B – protection seller a fixed annual fee in exchange for protection against default of 2year bond XYZ The payout will be Notional*(100-B) where B is the price of the bond at expiration, if the credit event occurs XYZ is now A rated with YTM=6.6%, while T-note trades at 6% Ch 22, Handbook Zvi Wiener slide 27 Actuarial Method Starting State A B C D Ending state A B C 0.90 0.07 0.02 0.05 0.90 0.03 0.10 0.85 0 Total D 0.01 0.02 0.05 1.00 1.00 1.00 1.00 1.00 1Y 1% probability of default 2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14% Ch 22, Handbook Zvi Wiener slide 28 Actuarial Method 1Y 1% probability of default 2Y: 0.01*0.90+0.02*0.07+0.05*0.02=1.14% If the recovery rate is 60%, the expected costs are 1Y: 1%*(100%-60%) = 0.4% 2Y: 1.14%*(100%-60%) = 0.456% Annual cost (no discounting): 1% + 1.14% $10M (100% − 60%) = $42,800 Ch 22, Handbook Zvi Wiener slide 29 Credit Spread Method Compare the yield of XYZ with the yield of default-free asset The annual protection cost is Annual Cost = $10M (6.60%-6%) = $60,000 Ch 22, Handbook Zvi Wiener slide 30 Equity Price Method Following the Merton’s model (see chapter 21) the fair value of the Put is Put = −V ⋅ N (− d1 ) + Ke − rT ⋅ N (d ) The annual protection fee will be the cost of Put divided by the number of years To hedge the protection seller would go short the following amount of stocks Ch 22, Handbook Zvi Wiener ∂Put ∂V = 1− ∂V ∂S N (d1 ) slide 31