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^{R_U- R_B})^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