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Compute the lower and upper no-arbitrage bounds

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You are working on the trading desk at an investment bank. You have the following prices available to you:

Spot dollar/pound Exchange Rate: 1.5943 $/£ (1£=1.5943$)

6-month Forward dollar/pound Rate 1.5857 $/£

The 6-month US (dollar) risk-free rate is 1.25%.

(Interest rates are quoted in annualized, continuously-compounded form.)

a. If there are no transaction costs, and you can either buy or sell at these exchange rates and borrow or lend at these interest rates, what must the 6-month British (pound) interest rate (annualized, c.c.) be for there to be no arbitrage?

b. Under the same assumptions, suppose that the annualized, continuously-compounded 6-month sterling interest rate is 3.5%. Describe exactly what transactions you would undertake at these prices/rates to lock in an arbitrage profit.

c. Now suppose the British rate is the one you calculated in (a) and that there is a 10 basis point (0.1%) bid/ask spread around both that rate and the U.S. rate (e.g. You can borrow at 1.30% and lend at 1.20%). The spot exchange rate is 1.5940-1.5947. Compute the lower and upper no-arbitrage bounds for the 6-month forward.

(e.g. You can borrow at 1.30% and lend at 1.20%). The spot exchange rate is 1.5940-1.5947. Compute the lower and upper no-arbitrage bounds for the 6-month forward.

Reference no: EM133076324

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