Question

A speculator is considering the purchase of one three-month put option on USD with a strike price of 97 yen per U.S. dollar. The premium is 0.24 yen per U.S. dollar. The current spot price is 107.81 yen per U.S. dollar and the 90-day forward rate is 71.46 yen/USD. The speculator believes the USD will depreciate to $1.00 versus 93 yen over the next three months. As the speculator’s assistant, you have been asked to prepare the followings: 1. Graph the profit/loss diagram of the put option in an Excel spreadsheet. 2. Determine the speculator’s profit if the USD depreciates to 93 yen/USD. 3. Determine the speculator’s profit/loss if the USD depreciates to the forward rate. 4. Determine the future spot price at which the speculator will only break even.

Answer 1

K = 97; P = 0.24; F = 71.46; F_exp = 93

Profit / (Loss) from Put option = max (K - S, 0) - P = max (97 - S, 0) - 0.24

Part (1)

The profit/loss table is as shown below:

S	Profit / (Loss) = max (97 - S, 0) - 0.24
0	96.76
10	86.76
20	76.76
30	66.76
40	56.76
50	46.76
60	36.76
70	26.76
80	16.76
90	6.76
100	-0.24
110	-0.24
120	-0.24
130	-0.24
140	-0.24
150	-0.24

And the diagram is:

Part (2)

Profit / (Loss) when S = 93 will be = max (97 - S, 0) - 0.24 = max (97 - 93, 0) - 0.24 = $ 3.76

Part (3)

Profit / (Loss) when S = 71.46 will be = max (97 - S, 0) - 0.24 = max (97 - 71.46, 0) - 0.24 = $ 25.30

Part (4)

Break even rate will be given by S such that max (97 - S, 0) - 0.24 = 0 Or, 97 - S - 0.24 = 0

Hence, S = 97 - 0.24 = $ 96.76