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9FX_Swaps

# 9FX_Swaps - Review Swaps Slide 8-1 Swap prices We saw that...

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Slide 8-1 Review: Swaps

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Slide 8-2 Swap prices We saw that swap prices are weighted averages of forward prices. Lets review the idea: a swap into a fixed rate. 1st step: view a swap as a strip of forwards. To see this, think about a swap dealer seeking to hedge a swap. (=the good-old hedging approach to derivatives pricing.) Example: interest rate swap 2nd step: argue that a swap is a perfect substitute for the strip of forwards, and should thus be priced s.t. Time Swap payments to dealer CF of FRAs (in arrears) Net cash flows to dealer t 1 R-r 0 R-r 0 t 2 R-r 1 r 1 -r 0 (t 1 ,t 2 ) R-r 0 (t 1 ,t 2 ) t 3 R-r 2 r 2 -r 0 (t 2 ,t 3 ) R-r 0 (t 2 ,t 3 ) 0 )) , ( 1 ( ) , ( )) , ( 1 ( ) , ( ) , ( 1 3 3 0 0 3 2 0 2 2 0 0 2 1 0 1 0 0 0 = + + + + + t t r t t r R t t r t t r R t t r r R
Slide 8-3 Swap prices (ctd.) 3rd step: algebra To use this formula, recall that To avoid the need to compute forward rates before computing the swap rate, use the formula on slide 21 of past week. R r 0 ( t i- 1 , t i ) (1 + r 0 ( t 0 , t i )) i i = 1 n = P 0 ( t 0 , t i ) ( R r 0 ( t i- 1 , t i )) i = 1 n = 0 R = P 0 (t 0 ,t i )r 0 (t i- 1 ,t i ) i = 1 n P 0 (t 0 ,t i ) i = 1 n r 0 (t i- 1 ,t i ) = P 0 ( t 0 , t i 1 ) P 0 ( t 0 , t i ) 1

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Slide 8-4 Example - Table 8.4 - contango in rates Expiration month June spot zero price Spot rate Forward rate Weighted av. forward rate Swap rate p.a. Jun-00 0.0692 Sep-00 0.9830 0.0173 0.0173 0.0173 0.0702 Dec-00 0.9658 0.0176 0.0178 0.0175 0.0711 Mar-01 0.9485 0.0178 0.0182 0.0178 r 0 (t i- 1 ,t i ) = P 0 ( t 0 , t i 1 ) P 0 ( t 0 , t i ) 1 r 0 (t 0 ,t i ) = 1 P 0 ( t 0 , t i ) i 1 > Borrowing at the swap rate is cheaper in the long run than borrowing at the floating rate. BUT THE FLOATING RATE IS CHEAPER IN THE SHORT RUN.
Slide 8-5 The slope of the yield curve and corporate swap use, 1993-2003 Yield spread = 10-year yield minus 1-year yield measures contango in rates! % yield spread % swapped to floating 2% 1% 0 % +10 % -10% 0% Source: Chernenko et al. (2006)

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Slide 8-6 Currency Swaps Chapter 8 Chapter 8
Slide 8-7 Currency Swaps A currency swap is an agreement between two parties to exchange a given amount of one currency for another, and to repay these currencies with interest in the future. A currency swap is equivalent to borrowing in one currency and lending in another. The first currency swap was arranged between the World Bank and IBM in 1981.

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Slide 8-8 Example A U.S. firm has a 3-year 3.5% Euro-denominated bond outstanding (face value = market price = 100). The firm would like to hedge its currency risk.
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9FX_Swaps - Review Swaps Slide 8-1 Swap prices We saw that...

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