You have written a call option on £10,000 with a strike price of $20,000.The current exchange rate is $2.00/£1.00 and in the next period the exchange rate can increase to $4.00/£1.00 or decrease to $1.00/€1.00 .The current interest rates are i_$ = 3% and are i_£ = 2%.Find the hedge ratio and use it to create a position in the underlying asset that will hedge your option position. A)Enter into a short position in a futures contract on £6,666.67 B)Lend the present value of £6,666.67 today at i_£ = 2% C)Enter into a long position in a futures contract on £6,666.67 D)Lending the present value of £6,666.67 today at i_£ = 2% or entering into a long position in a futures contract on £6,666.67 would both work.

Question

Quizplus · Accepted Answer

The hedge ratio is calculated as the option's delta, which is the change in the option price for a one-unit change in the underlying asset price. The delta in this case is (20,000-10,000)/(2.00*10,000) = 0.5. This means that for every pound in the underlying asset, we need to hedge with 0.5 pounds in the futures contract or by lending at the risk-free rate. Both options (lending or entering into a long futures position) achieve the same result, so either D could be chosen. Since lending at the risk-free rate is less risky (no market price risk), it might be the better choice.

You Have Written a Call Option on £10,000 with a Strike