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## Swaps

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**Swaps**Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FRM**Fixed rate**B A Floating rate 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 Based on a presentation of Global Risk Strategy Group of Deutsche Bank Zvi Wiener**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.) Zvi Wiener**IRS Origins**AAA wants to borrow in floating and BBB wants to borrow in fixed. Fixed Floating AAA 7.00% LIBOR+5bps BBB 8.50% LIBOR+85bps difference 1.5% 0.8% Net differential 70bps = 0.7% Zvi Wiener**7.4%**Libor Comparative Advantage Cost of funds for AAA=Libor - 40bp (45bps saved) Cost of funds for BBB=8.25% (25bps saved) Swap rate = 7.40% Swap rate is the fixed rate which is paid against receiving Libor. 7.0% Libor+85bp BBB AAA Zvi Wiener**Basic terms of IRS**• Notional amount • Fixed rate leg • Floating rate leg • Calculated period • Day count fraction Zvi Wiener**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!! Zvi Wiener**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. Zvi Wiener**Payments**Fixed payment = (notional)(Fixed rate)(fixed rate day count convention) Floating payment = (notional)(Float. rate)(float. rate day count convention) Zvi Wiener**-PV 5 5 5 5 105**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 Zvi Wiener**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 Zvi Wiener**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. Zvi Wiener**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. Zvi Wiener**Zero coupon swap (reinvested payments)**• Amortizing swap (decreasing notional) • Accreting swap (increasing notional) • Rollercoaster (variable notional) Zvi Wiener**Amortizing swap**Decreasing notional affects coupon payments Zvi Wiener**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!! Zvi Wiener**8%**6% A B A C LIBOR LIBOR Unwinding Net of the two offsetting swaps is 2% for the life of the contract. (sometimes novation) Zvi Wiener**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 Zvi Wiener**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 mark to market. Netting agreements. Credit exposure changes during the life of a swap. Zvi Wiener**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). Zvi Wiener**IRS Markets**Daily average volume of trade (notional) 1995 1998 2001 $63B $155B $331B Zvi Wiener**Mark to market**• daily repricing • collateral • adjustments • reduces credit exposure Zvi Wiener**Reasons to use swaps by firms**• Lower cost of funds • Home market effects • Comparative advantage of highly rated firms Zvi Wiener**FRM-GARP 00:47**Which one of the following deals has the largest credit exposure for a $1,000,000 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 Zvi Wiener**FRM-GARP 00:47**Which one of the following deals has the largest credit exposure for a $1,000,000 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 Zvi Wiener**Global Derivatives Markets 1999**OTC Instruments $88T Exchange traded $13.5T 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 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 World GDP in 99 = 30,000B All stocks and bonds = 70,000 Liquidation value = 2,800B Zvi Wiener Source BIS**Global Derivatives Markets 2001**OTC Instruments $111T Exchange traded $23.5T 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 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 Zvi Wiener Source BIS**Chapter 22Credit Derivatives**Following P. Jorion 2001 Financial Risk Manager Handbook FRM**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. Zvi Wiener**Credit Derivatives**Bond insurance Letter of credit Credit derivatives on organized exchanges: TED spread = Treasury-Eurodollar spread (Futures are driven by AA type rates). Zvi Wiener**Types of Credit Derivatives**Underlying credit (single or a group of entities) Exercise conditions (credit event, rating, spread) Payoff function (fixed, linear, non-linear) Zvi Wiener**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% Zvi Wiener**premium**Contingent payment 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. B - seller A - buyer Reference asset Zvi Wiener**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. Zvi Wiener**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 Zvi Wiener**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). Zvi Wiener**Payment tied to reference asset**Payment tied to reference rate Total Return Swap (TRS) B - seller A - buyer Reference asset Zvi Wiener**Example TRS**• Bank A made a $100M 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 $95M. • The bank has to pay $10M-$5M=5M and will receive in exchange $9+$0.5M=9.5M Zvi Wiener**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 Zvi Wiener**Credit Spread Option**Put type Payment = Max(S-K, 0)*Duration*Notional Call type Payment = Max(K-S, 0)*Duration*Notional Zvi Wiener**Example**A credit spread option has a notional of $100M with a maturity of one year. The underlying security is a 8% 10-year bond issued by corporation XYZ. The current spread is 150bp against 10-year Treasuries. The option is European type with a strike of 160bp. Assume that at expiration Treasury yield has moved from 6.5% to 6% and the credit spread widened to 180bp. 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*$100M = $1,297,237 Zvi Wiener**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. Zvi Wiener**CLN**A buys a CLN, B invests the money in a high-rated 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. Zvi Wiener**par**Xbp L+X+Y Contingent payment Contingent payment par LIBOR+Y Credit Linked Note CLN = AAA note + Credit swap Credit swap buyer investor AAA asset Asset backed securities can be very dangerous! Zvi Wiener