Draw the tree for a put 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

The tree diagram shows that if the exchange rate doubles, the option will not be exercised as the dollar value of £10,000 will be $40,000, higher than the current dollar value of $20,000. If the exchange rate is cut in half, the option will be exercised as the dollar value of £10,000 will be $10,000, lower than the current $20,000 strike price. Therefore, the option has a value of $10,000 in one period, and using the discounted cash flow formula, the present value of the option is $9,803.29 (computed as $10,000/(1+3%) = $9,708.74 in the U.S., and then converted to pounds using the exchange rate of £1.00 = $2.00, giving a value of £4,854.37, which is then discounted at the U.K. risk-free rate of 2% to the present, giving a value of $9,803.29). The other options are incorrect because they either assume that the option will always be exercised or never be exercised, which is not realistic given the two possible outcomes of the exchange rate.

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