Find the value of a one-year put option on $15,000 with a strike price of €10,000. In one year the exchange rate (currently S₀($/€) = $1.50/€) can increase by 60% or decrease by 37.5% . The current one-year interest rate in the U.S. is i_$ = 4% and the current one-year interest rate in the euro zone is i_€ = 4%. A)€1,525.52 B)$3,328.40 C)$4,992.60 D)€2,218.94 E)None of the above

Question

Quizplus · Accepted Answer

To find the value of the put option, we need to compare the two possibilities of exchange rate movements.

If the exchange rate increases by 60%, the value of the put option is:
max(0, 10000/1.50 - 15000/1.50) = max(0, 3333.33) = 3333.33

If the exchange rate decreases by 37.5%, the value of the put option is:
max(0, 10000/0.9375 - 15000/1.50) = max(0, 2218.94) = 2218.94

Then we calculate the expected value of the put option:

EV = 0.5 * 3333.33 + 0.5 * 2218.94 = 2776.14

Finally, we discount the expected value by the risk-free rate in the U.S. (where the option is denominated) to get the present value:

PV = 2776.14 / (1 + 0.04) = €2,218.94

Therefore, the correct answer is D, €2,218.94.

Find the Value of a One-Year Put Option on $15,000