2.1 Swaps Lecture 2

2.2 Types of Rates Treasury rates LIBOR rates Euribor rates

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2.4

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2.6

2.7 Zero Rates A zero rate (or spot rate), for maturity T, is the rate of interest earned on an investment that provides a payoff only at time T

2.8 Example

2.9 Bond Pricing To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate In our example, the theoretical price of a two- year bond providing a 6% coupon semiannually is

2.10 Bond Yield The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond Suppose that the market price of the bond in our example equals its theoretical price of The bond yield is given by solving to get y = or 6.76%.

2.11 Forward Rates The forward rate is the future zero rate implied by today’s term structure of interest rates

2.12 Calculation of Forward Rates Zero Rate forForward Rate an n -year Investmentfor n th Year Year ( n )(% per annum)

2.13 Formula for Forward Rates Suppose that the zero rates for time periods T 1 and T 2 are R 1 and R 2 with both rates continuously compounded. The forward rate for the period between times T 1 and T 2 is

2.14 Duration of a bond that provides cash flow c i at time t i is where B is its price & y is its yield (continuously compounded) This leads to Duration

2.15 Duration Matching This involves hedging against interest rate risk by matching the durations of assets and liabilities It provides protection against small parallel shifts in the zero curve

2.16 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

2.17 An Example of a “Plain Vanilla” Interest Rate Swap An agreement by “Company B” to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows

Millions of Dollars LIBORFLOATINGFIXEDNet DateRateCash Flow Mar.1, % Sept. 1, %+2.10–2.50–0.40 Mar.1, %+2.40–2.50–0.10 Sept. 1, %+2.65– Mar.1, %+2.75– Sept. 1, %+2.80– Mar.1, %+2.95– Cash Flows to Company B

2.19 Typical Uses of an Interest Rate Swap Converting a liability from –fixed rate to floating rate –floating rate to fixed rate Converting an investment from –fixed rate to floating rate –floating rate to fixed rate

2.20 A and B Transform a Liability A B LIBOR 5% LIBOR+0.8% 5.2% A: from 5.2 fixed to floating ---> pays Libor+0.2% B: from floating Libor+0.8% to fixed ---> pays 5%+0.8%

2.21 A and B Transform an Asset A B LIBOR 5% LIBOR-0.25% 4.7%

2.22 The Comparative Advantage Argument Company A wants to borrow floating Company B wants to borrow fixed FixedFloating Company A10.00%6-month LIBOR % Company B11.20%6-month LIBOR %

2.23 The Swap A B LIBOR LIBOR+1% 9.95% 10% A: from 10% fixed to floating ---> pays Libor+0.05% B: from floating Libor+1% to fixed ---> pays 9.95%+1%

2.24 Valuation of an Interest Rate Swap Interest rate swaps can be valued as the difference between the value of a fixed- rate bond & the value of a floating-rate bond

2.25 Valuation in Terms of Bonds The fixed rate bond is valued in the usual way The floating rate bond is valued by noting that it is worth par immediately after the next payment date

2.26 Swapping a BTP

2.27 Credit Risk A swap is worth zero to a company initially At a future time its value is liable to be either positive or negative The company has credit risk exposure only when its value is positive

2.28 Examples of Other Types of Swaps Amortizing & step-up swaps Extendible & puttable swaps Index amortizing swaps Equity swaps Commodity swaps Differential swaps