Draw the tree for a call option on $20,000 with a strike price of £10,000. The current exchange rate is £1.00 = $2.00 and in one period the dollar value of the pound will either double or be cut in half. The current interest rates are i_$ = 3% and are i_£ = 2%. C)None of the above

Question

Quizplus · Accepted Answer

In the first branch of the tree, the exchange rate doubles, meaning £1.00 = $4.00. In this scenario, exercising the call option is profitable as the buyer can purchase the £10,000 for $40,000 and then sell it in the market for $80,000. The profit would be $80,000 - $20,000 - $2,800 (the cost of the option premium) = $57,200.

In the second branch of the tree, the exchange rate is cut in half, meaning £1.00 = $1.00. In this scenario, the buyer would not exercise the option as they can purchase the £10,000 in the market for $20,000 without using the option. Therefore, the profit would be -$2,800, which is the cost of the option premium.

Calculating the expected value of the option using the risk-neutral probabilities (based on the interest rates) yields:

Expected value = (0.5*$57,200 + 0.5*-$2,800)*e^(-0.03) = $27,308.

Therefore, the option is worth buying and the best choice is B.

Draw the Tree for a Call Option on $20,000 with a Strike