Solution 5

Solution 5 - Fin 448 Fixed-Income Securities Homework...

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Homework Solution 5 Wei Yang 1 FRA and Eurodollar futures (1.1) We will deposit or lend, so we will sell FRA. (1.2) (1 + l 6 2 )(1 + f 6 v 12 2 ) = 1 + l 12 f 6 v 12 = 2 . 443% (1.3) The contract gives the seller an equivalent payoff at t = 12 months f 6 v 12 2 - l 6 v 12 2 = ± 1 + f 6 v 12 2 ² - ± 1 + l 6 v 12 2 ² The present value of this payoff at t = 0 is 1 + f 6 v 12 2 1 + l 12 - 1 1 + l 6 2 Hence, the DV 01 of the FRA is the DV 01 of a 1-year zero-coupon bond minus that of a 6-month zero-coupon bond. A rought estimate would put DV 01 at 50. More precisely, for $1M notional DV 01 = 1 1 + l 12 × 1 + f 6 v 12 2 1 + l 12 × 10 6 10 4 - 1 2 1 + l 6 2 × 1 1 + l 6 2 × 10 6 10 4 The answer is $47.73. When interest rates increase, the FRA value decreases. (1.4) We will buy Eurodollar futures. Using the FRA notation, the two Eurodol- lar futures contracts are 6v9 and 9v12. 1
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Solution 5 - Fin 448 Fixed-Income Securities Homework...

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