Swaps Zvi Wiener 02 588 3049 http pluto

Swaps Zvi Wiener 02 -588 -3049 http: //pluto. mscc. huji. ac. il/~mswiener/zvi. html http: //pluto. huji. ac. il/~mswiener/zvi. html FRM 972 -2 -588 -3049

Interest Rate Swaps: Concept • An agreement between 2 parties to exchange periodic payments calculated on the basis of specified interest rates and a notional amount. • Plain Vanilla Swap Fixed rate B A Floating rate Based on a presentation of Global Risk Strategy Group of Deutsche Bank Credit Derivatives Zvi Wiener 2

IRS • In a standard IRS, one leg consists of fixed rate payments and the other depends on the evolution of a floating rate. • Typically long dated contracts: 2 -30 years • Sometimes includes options, amortization, etc. • Interest compounded according to different conventions (eg 30/360, Act/Act. Act/360, etc. ) Credit Derivatives Zvi Wiener 3

IRS Origins AAA wants to borrow in floating and BBB wants to borrow in fixed. Fixed Floating AAA 7. 00% LIBOR+5 bps BBB 8. 50% LIBOR+85 bps difference 1. 5% 0. 8% Net differential 70 bps = 0. 7% Credit Derivatives Zvi Wiener 4

Comparative Advantage 7. 0% 7. 4% AAA Libor BBB Libor+85 bp Cost of funds for AAA=Libor - 40 bp (45 bps saved) Cost of funds for BBB=8. 25% (25 bps saved) Swap rate = 7. 40% Swap rate is the fixed rate which is paid against receiving Libor. Credit Derivatives Zvi Wiener 5

Basic terms of IRS • Notional amount • Fixed rate leg • Floating rate leg • Calculated period • Day count fraction Credit Derivatives Zvi Wiener 6

Basic terms of IRS • Payer and receiver - quoted relative to fixed interest (i. e. payer = payer of fixed rate) • buyer = payer, seller =receiver • Short party = payer of fixed, (buyer) • Long party = receiver of fixed, (seller) • Valuation = net value NOT notional!! Credit Derivatives Zvi Wiener 7

Various swaps • Coupon swaps - fixed against floating. • Basis or Index swaps - exchange of two streams both are computed using floating IR. • Currency swap - interest payments are denominated in different currencies. • Asset swap - to exchange interest received on specific assets. • Term swap maturity more then 2 years. • Money Market swap - less then 2 years. Credit Derivatives Zvi Wiener 8

Payments Fixed payment = (notional)(Fixed rate)(fixed rate day count convention) Floating payment = (notional)(Float. rate)(float. rate day count convention) Credit Derivatives Zvi Wiener 9

Time Value of Money • present value PV = CFt/(1+r)t • Future value FV = CFt(1+r)t • Net present value NPV = sum of all PV -PV Credit Derivatives 5 5 5 Zvi Wiener 5 10

Credit Derivatives Zvi Wiener 11

Swap Pricing A swap is a series of cash flows. An on-market swap has a Net Present Value of zero! PV(Fixed leg) + PV(Floating leg) = 0 Credit Derivatives Zvi Wiener 12

Pricing • Floating leg is equal to notional amount at each day of interest rate settlement (by definition of LIBOR). • Fixed leg can be valued by standard NPV, since the paid amount is known. Credit Derivatives Zvi Wiener 13

Credit Derivatives Zvi Wiener 14

Credit Derivatives Zvi Wiener 15

Forward starting swaps • interest starts accruing at some date in the future. • Valuation is similar to a long swap long and a short swap short. Credit Derivatives Zvi Wiener 16

• Zero coupon swap (reinvested payments) • Amortizing swap (decreasing notional) • Accreting swap (increasing notional) • Rollercoaster (variable notional) Credit Derivatives Zvi Wiener 17

Amortizing swap Decreasing notional affects coupon payments Credit Derivatives Zvi Wiener 18

Unwinding an existing swap • Enter into an offsetting swap at the prevailing market rate. • If we are between two reset dates the offsetting swap will have a short first period to account for accrued interest. • It is important that floating payment dates match!! Credit Derivatives Zvi Wiener 19

Unwinding 8% A LIBOR B 6% A LIBOR C Net of the two offsetting swaps is 2% for the life of the contract. (sometimes novation) Credit Derivatives Zvi Wiener 20

Risks of Swaps • Interest rate risk - value of fixed side may change • Credit risk - default or change of rating of counterparty • Mismatch risk - payment dates of fixed and floating side are not necessarily the same • Basis risk and Settlement risk Credit Derivatives Zvi Wiener 21

Credit risk of a swap contract Default of counterparty (change of rating). Exists when the value of swap is positive Frequency of payments reduces the credit risk, similar to market. Netting agreements. Credit exposure changes during the life of a swap. Credit Derivatives Zvi Wiener 22

Duration of a swap • Fixed leg has a long duration )approximately. ( • Short leg has duration about time to reset. Duration is a measure of price sencitivity to interest rate changes )approximately is equal to average time to payment. ( Credit Derivatives Zvi Wiener 23

IRS Markets Daily average volume of trade (notional) 1995 1998 2001 $63 B $155 B $331 B Credit Derivatives Zvi Wiener 24

Mark to market • daily repricing • collateral • adjustments • reduces credit exposure Credit Derivatives Zvi Wiener 25

Reasons to use swaps by firms • Lower cost of funds • Home market effects • Comparative advantage of highly rated firms Credit Derivatives Zvi Wiener 26

Credit Derivatives Zvi Wiener 27

Credit Derivatives Zvi Wiener 28

Credit Derivatives Zvi Wiener 29

FRM-GARP 00: 47 Which one of the following deals has the largest credit exposure for a $1, 000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk. A. Pay fixed in an interest rate swap for 1 year B. Sell USD against DEM in a 1 year forward contract. C. Sell a 1 -year DEM Cap D. Purchase a 1 -year Certificate of Deposit Credit Derivatives Zvi Wiener 30

FRM-GARP 00: 47 Which one of the following deals has the largest credit exposure for a $1, 000 deal size. Assume that the counterparty in each deal is a AAA-rated bank and there is no settlement risk. A. Pay fixed in an interest rate swap for 1 year B. Sell USD against DEM in a 1 year forward contract. C. Sell a 1 -year DEM Cap D. Purchase a 1 -year Certificate of Deposit Credit Derivatives Zvi Wiener 31

Global Derivatives Markets 1999 Exchange traded $13. 5 T IR contracts 11, 669 Futures 7, 914 Options 3, 756 FX contracts 59 Futures 37 Options 22 Stock-index contr. 1, 793 Futures 334 Options 1, 459 World GDP in 99 = 30, 000 B All stocks and bonds = 70, 000 Liquidation value = 2, 800 B Credit Derivatives Zvi Wiener Source BIS OTC Instruments $88 T IR contracts 60, 091 FRAs 6, 775 Swaps 43, 936 Options 9, 380 FX contracts 14, 344 Forwards 9, 593 Swaps 2, 444 Options 2, 307 Equity-linked contr. 1, 809 Forw. and swaps 283 Options 1, 527 Commodity contr. 548 Others 11, 408 32

Global Derivatives Markets 2001 Exchange traded $23. 5 T IR contracts 21, 614 Futures 9, 137 Options 12, 477 FX contracts 89 Futures 66 Options 23 Stock-index contr. 1, 838 Futures 295 Options 1, 543 Credit Derivatives Zvi Wiener Source BIS OTC Instruments $111 T IR contracts 77, 513 FRAs 7, 737 Swaps 58, 897 Options 10, 879 FX contracts 16, 748 Forwards 10, 336 Swaps 3, 942 Options 2, 470 Equity-linked contr. 1, 881 Forw. and swaps 320 Options 1, 561 Commodity contr. 598 Others 14, 375 33

Chapter 22 Credit Derivatives Following P. Jorion 2001 Financial Risk Manager Handbook http: //pluto. huji. ac. il/~mswiener/zvi. html FRM 972 -2 -588 -3049

Credit Derivatives From 1996 to 2000 the market has grown from $40 B to $810 B Contracts that pass credit risk from one counterparty to another. Allow separation of credit from other exposures. Credit Derivatives Zvi Wiener 35

Credit Derivatives Bond insurance Letter of credit Credit derivatives on organized exchanges: TED spread = Treasury-Eurodollar spread (Futures are driven by AA type rates). Credit Derivatives Zvi Wiener 36

Types of Credit Derivatives Underlying credit (single or a group of entities) Exercise conditions (credit event, rating, spread) Payoff function (fixed, linear, non-linear) Credit Derivatives Zvi Wiener 37

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% Credit Derivatives Zvi Wiener 38

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 Credit Derivatives Zvi Wiener 39

Example • The protection buyer (A) enters a 1 -year credit default swap on a notional of $100 M 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 $60 M. Credit Derivatives Zvi Wiener 40

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 Credit Derivatives Zvi Wiener 41

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). Credit Derivatives Zvi Wiener 42

Total Return Swap (TRS) Payment tied to reference asset B - seller A - buyer Payment tied to reference rate Reference asset Credit Derivatives Zvi Wiener 43

Example TRS • Bank A made a $100 M loan to company XYZ at a fixed rate of 10%. The bank can hedge the exposure to XYZ by entering TRS with counterparty B. The bank promises to pay the interest on the loan plus the change in market value of the loan in exchange for LIBOR + 50 bp. • Assume that LIBOR=9% and by the end of the year the value of the bond drops from $100 to $95 M. • The bank has to pay $10 M-$5 M=5 M and will receive in exchange $9+$0. 5 M=9. 5 M Credit Derivatives Zvi Wiener 44

Credit Spread Forward Payment = (S-F)*Duration*Notional S – actual spread F – agreed upon spread Cash settlement May require credit line of collateral Payment formula in terms of prices Payment =[P(y+F, T)-P(y+S, T)]*Notional Credit Derivatives Zvi Wiener 45

Credit Spread Option Put type Payment = Max(S-K, 0)*Duration*Notional Call type Payment = Max(K-S, 0)*Duration*Notional Credit Derivatives Zvi Wiener 46

Example A credit spread option has a notional of $100 M with a maturity of one year. The underlying security is a 8% 10 -year bond issued by corporation XYZ. The current spread is 150 bp against 10 -year Treasuries. The option is European type with a strike of 160 bp. Assume that at expiration Treasury yield has moved from 6. 5% to 6% and the credit spread widened to 180 bp. The price of an 8% coupon 9 -year semi-annual bond discounted at 6+1. 8=7. 8% is $101. 276. The price of the same bond discounted at 6+1. 6=7. 6% is $102. 574. The payout is (102. 574 -101. 276)/100*$100 M = $1, 297, 237 Credit Derivatives Zvi Wiener 47

Credit Linked Notes (CLN) Combine a regular coupon-paying note with some credit risk feature. The goal is to increase the yield to the investor in exchange for taking some credit risk. Credit Derivatives Zvi Wiener 48

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. Credit Derivatives Zvi Wiener 49

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! Credit Derivatives Zvi Wiener 50

Types of Credit Linked Note Type Asset-backed Compound Credit Principal Protection Enhanced Asset Return Credit Derivatives Maximal Loss Initial investment Amount from the first default Interest Pre-determined Zvi Wiener 51

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 Credit Derivatives Zvi Wiener 52

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 Credit Derivatives Zvi Wiener 53

FRM 2000 -39 Credit Risk (22 -5) A portfolio consists of one (long) $100 M 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. 0 M B. $2. 2 M C. $1. 8 M D. None of the above Credit Derivatives Zvi Wiener 54

FRM 2000 -39 Credit Risk A portfolio consists of one (long) $100 M 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. 0 M B. $2. 2 M C. $1. 8 M = $100*0. 03*(1– 40%) only joint default leads to a loss D. None of the above Credit Derivatives Zvi Wiener 55

FRM 2000 -62 Credit Risk (22 -11) Bank made a $200 M 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+40 bp. 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. 8 M B. Net payment of $4. 8 M C. Net receipt of $5. 2 M D. Net payment of $5. 2 M Credit Derivatives Zvi Wiener 56

FRM 2000 -62 Credit Risk (22 -11) Bank made a $200 M 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+40 bp. 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. 8 M = [(12%-3%) –(11%+0. 4%)]*$200 M B. Net payment of $4. 8 M C. Net receipt of $5. 2 M D. Net payment of $5. 2 M Credit Derivatives Zvi Wiener 57

Pricing and Hedging Credit Derivatives 1. Actuarial approach – historic default rates relies on actual, not risk-neutral probabilities 2. Bond credit spread 3. Equity prices – Merton’s model Credit Derivatives Zvi Wiener 58

Example: Credit Default Swap CDS on a $10 M two-year agreement. A – protection buyer agrees to pay to B – protection seller a fixed annual fee in exchange for protection against default of 2 year 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 Tnote trades at 6%. Credit Derivatives Zvi Wiener 59

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 0. 10 0. 85 0 0 0 Total D 0. 01 0. 02 0. 05 1. 00 1 Y 1% probability of default 2 Y: 0. 01*0. 90+0. 02*0. 07+0. 05*0. 02=1. 14% Credit Derivatives Zvi Wiener 60

Actuarial Method 1 Y 1% probability of default 2 Y: 0. 01*0. 90+0. 02*0. 07+0. 05*0. 02=1. 14% If the recovery rate is 60%, the expected costs are 1 Y: 1%*(100%-60%) = 0. 4% 2 Y: 1. 14%*(100%-60%) = 0. 456% Annual cost (no discounting): Credit Derivatives Zvi Wiener 61

Credit Spread Method Compare the yield of XYZ with the yield of default-free asset. The annual protection cost is Annual Cost = $10 M (6. 60%-6%) = $60, 000 Credit Derivatives Zvi Wiener 62

Equity Price Method Following the Merton’s model (see chapter 21) the fair value of the Put is 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 Credit Derivatives Zvi Wiener 63