022 - 22 Answers to Questions and Problems Swaps:...

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232 Answers to Questions and Problems 1. At present, you observe the following rates: FRA 0,1 5 5.25 percent and FRA 1,2 5 5.70 percent, where the subscripts refer to years. You also observe prices on calls and puts on one-year LIBOR that expire in one year, with payment the following year. For a call on LIBOR with a strike rate of 5.70 percent, the price is 150 basis points. The corresponding put has a strike rate of 5.70 percent, and a cost of 143 basis points. A. Explain how these prices represent an arbitrage opportunity. Draw a diagram illustrating the arbitrage opportunity. From the forward put-call parity relationship, we know that a long FRA position is equivalent to a long call/short put portfolio with matching quantities and dates. Therefore, the cost of a long call/short put portfolio with a common strike rate equal to the FRA rate should be zero. In our situation, the long call/short put portfolio costs 7 basis points, the difference between the call cost and the put cost. Therefore, we can sell the option portfolio (sell the call and buy the put) and take a long position in the FRA. As the diagram shows, at expiration, the short call/long put portfolio and the long FRA will have exactly offsetting payoffs, for a net zero payoff. 22 Swaps: Applications Short option portfolio payoffs at expiration Long FRA payoffs at expiration One-year LIBOR at expiration 0 5.70% Basis points
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ANSWERS TO QUESTIONS AND PROBLEMS 233 B. Assuming a notional principal of $100 million, state the transactions that you would enter to secure the arbi- trage profit. t 5 0 Sell 1 call for 150 basis points 5 0.0150 3 $100,000,000 51 $1,500,000. Buy 1 put for 143 basis points 5 0.0143 3 $100,000,000 52 $1,430,000. Enter a pay-fixed position in the FRA on one-year LIBOR with a one-year maturity at a contract rate of 5.70 percent. Net Cash Flow: 1 $70,000 t 5 1 There will be a net zero obligation no matter what the one-year spot rate for LIBOR is. Consider two examples, with one-year LIBOR at 5.60 and 5.80 percent: LIBOR 5 5.60 percent Call expires worthless. Long put is worth (0.0570 2 0.0560) 3 $100,000,000 51 $100,000. FRA obligation is ( 2 0.057 1 0.056) 3 $100,000,000 52 $100,000. Net Obligation: 0 LIBOR 5 5.80 percent Short call is exercised against arbitrageur: (0.0580 2 0.0570) 3 $100,000,000 52 $100,000. Put expires worthless. Pay-fixed FRA pays (0.0580 2 0.0570) 3 $100,000,000 51 $100,000. Net Obligation: 0 C. Compute the present value of the arbitrage profit. The present value of the arbitrage profit is $70,000, because it is received immediately at the time of contracting and no other cash flows are incurred. 2. An inverse floating rate note, or inverse floater, is a debt instrument with a floating rate that moves inversely with market rates. Generally, an inverse floater pays a fixed rate minus LIBOR. Consider an FRN with a principal amount of $50 million paying LIBOR with a five-year maturity. Consider also a plain vanilla interest rate swap with a fixed rate of 7 percent, a floating rate equal to LIBOR, a notional principal of $100 million,
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This homework help was uploaded on 04/07/2008 for the course BA 4825 taught by Professor Danısoglu during the Spring '08 term at Middle East Technical University.

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022 - 22 Answers to Questions and Problems Swaps:...

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