Profit and Loss Calculation for Put Option on Japanese Yen

How can we calculate Kiko's profit or loss at maturity for the put option on Japanese yen?

Kiko Peleh writes a put option on Japanese yen with a strike price of $0.008000 per yen (yen 125.00 per $) at a premium of 0.0080 cents per yen and with an expiration date six months from now. The option is for ¥12,500,000. What is Kiko's profit or loss at maturity if the ending spot rates are yen 110 per $, yen 115 per $, yen 120 per $, yen 125 per $, yen 130 per $, yen 135 per $, and yen 140 per $?

Profit and Loss Calculation for Put Option on Japanese Yen

To calculate Kiko's profit or loss at maturity, we need to consider the different ending spot rates stated in the question. The put option gives Kiko the right to sell yen at the strike price of $0.008000 per yen. If the ending spot rate is higher than the strike price, Kiko will profit. If the ending spot rate is lower than the strike price, Kiko will have a loss.

Explanation

When selling a put option, the writer receives a premium upfront. The profit or loss at maturity depends on whether the ending spot rate is above or below the strike price of the option.

Let's calculate the profit or loss for each ending spot rate:

• If the ending spot rate is yen 110 per $, Kiko's profit will be calculated as $((0.008000 - 0.008615) x ¥12,500,000) - (0.008000 x ¥12,500,000).
• If the ending spot rate is yen 115 per $, Kiko's profit will be calculated as $((0.008000 - 0.007826) x ¥12,500,000) - (0.008000 x ¥12,500,000).
• If the ending spot rate is yen 120 per $, Kiko's profit will be calculated as $((0.008000 - 0.007692) x ¥12,500,000) - (0.008000 x ¥12,500,000).