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# Problem Set III for Futures &amp; Options Roy Zuckerman Rutgers Business School Note: This homework is designed to understand pricing and hedging...

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Problem Set III for Futures & Options Roy Zuckerman Rutgers Business School Note: This homework is designed to understand pricing and hedging using swaps. 1. Swap spreads : Assume the following term structure of risky and riskless interest rates (all rates are annually compounded, annual rates): Year Riskless (%) Risky (%) 1 6.91 7.33 2 7.00 7.40 3 7.15 7.59 4 7.22 7.63 5 7.29 7.70 6 7.33 7.75 7 7.35 7.79 8 7.38 7.85 9 7.40 7.90 10 7.40 7.93 Further assume that securities (zero-coupon bonds) for both types exist and can be bought or sold short at these rates. (a) Compute the 1–year forward rates between each maturity for both term-structures. (b) Swap 1 is a 10–year ﬁxed-for-ﬂoating swap for riskless counterparties using the riskless 1–year ﬂoating rate, and swap 2 is a 10-year ﬁxed–for–ﬂoating swap for risky counterparties using the risky 1–year ﬂoating rate. Compute the swap spread for swap 2. Note that The swap spread for a swap contract is its swap rate minus the riskless swap rate. So you need to compute the fair (par)rates for both swaps. Hint : the swap rate can be expressed as a weighted average of current forward rates as discussed in the lecture notes. 1
2. Currency swap pricing : The interest rate term structures in both the US and Europe are ﬂat, and continuously compounded risk–free rates are r EU = 4% in Europe and r US = 5 . 5% in the US. You are interested in entering into a three–year currency swap in which each year you pay 6%/year in dollars. The principal amounts in the two currencies are \$100 million and Euro 120 million. The current exchange rate is 0.92 \$/Euro. (a) What is the fair Euro coupon rate for this swap if you exchange principal at the beginning and at the end? (b) What if you do not swap principal at initiation? Compare the results in (a) and (b). (c) Six months after entering into the swap in (a), the market exchange rate becomes 0.74 (\$/Euro) and the term structures are unchanged. What is the value of the swap to you? What is the value of the swap to the counterparty? 3. Compound swaps. You work for the trading desk of a large oil company and are facing the forward prices and interest rates shown in the table below. (The interest rates are zero-coupon continuously-compounded riskless rates.) You can trade on these prices without cost. Date Euro Forwards Crude Forwards EUR rate USD rate T i (dollars/euro) (dollars/barrel) (c.c.) (c.c.) 0 (spot) 1.1788 30.96 0.5 1.1735 29.06 2.00 1.10 1.0 1.1694 27.17 2.20 1.40 1.5 1.1647 26.05 2.35 1.55 2.0 1.1601 25.51 2.50 1.70 2.5 1.1555 25.42 2.70 1.90 3.0 1.1508 25.33 2.90 2.10 3.5 1.1503 25.49 3.00 2.30 4.0 1.1531 25.66 3.15 2.60 4.5 1.1578 25.91 3.30 2.90 5.0 1.1642 26.15 3.45 3.20 You are asked by a client to quote a fair price for a ﬁve-year semi-annual oil swap denominated in euros . (a) What is the no-arbitrage swap price (assuming perfect markets)? 2
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