Question

You have the following market data.

- A British pound futures contract expires in 12 months.
- The annualized, continuously compounded risk-free interest rates in Britain and the U.S. are 1.55% and 1.01%, respectively, from today until expiration.
- The spot exchange rate between the British pound and the U.S. dollar is $1.645 per British pound.

What is the no-arbitrage futures price (expressed in U.S. dollars)?

*Do not round values at intermediate steps in your
calculations. Enter your answer in dollars and cents to
four decimal places, but omit the $ symbol and commas. For
example, enter $1,234.5678 as 1234.5678 as your answer.*

Answer #1

Spot rate for $ per British Pound = S($/£) = $1.645 , Period = 12 months = 1 years,

Risk free rate in Britain = R_{B} = 1.55% p.a
continuously compounded. and Risk free rate in US=R_{U}
=1.01% p.a continuously compounded, T= years to expiry = 1

No Arbitrage Future Price in $ = F($/£) = S($/£) x
(e^{RU}^{-
RB})^{T}

F($/£) =1.645 x (e^{1.01% - 1.55%})^{1} = 1.645
x (e^{1.01% - 1.55%}) = 1.645 x
e^{-0.54% } =1.645 x e^{-0.0054}

We can find e^{-0.0054} by using exp function in
excel

Formula to be used in excel: =exp(-0.0054)

we get e^{-0.0054} = 0.9946

Hence F($/£) = 1.645 x 0.9946 = 1.636117 = $1.6361

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