When you sell a foreign exchange put option, you are selling the right to sell currency. Therefore, you become the buyer of currency and have no option. The buyer of the put option has the right to sell currency to you. You collect the premium and need to accommodate the decision of the buyer regarding exercising his option.

Suppose that you sell a put option with a premium of \$0.019 per euro and an exercise price of \$1.32. If the transaction amount is €100,000, you collect a premium of \$1,900. Suppose the expiration date is a month from now.

If the future spot rate is \$1.30, the buyer exercises the put option, because he buys euros at the spot market for \$1.30 and sells them on the put option to you for \$1.32, making \$0.02 per euro (\$1.32 – \$1.30). But his gain is your loss. You have to buy euros from him at a higher rate (\$1.32) and sell them at a lower rate at the spot market (\$1.30).

Consider your payoff. The premium that you collect and the spot exchange rate at which you sell euros are your total selling price or what you receive in these transactions. The exercise price on the put option is the exchange rate at which you buy euros. Therefore:

profit/loss = selling price – buying price
profit/loss = (spot exchange rate + premium) - exercise price
profit/loss = \$1.30 + \$0.019 – \$1.32 = –\$0.001

Your per-unit loss is \$-0.001 and your total loss is \$100. In the case of selling the put option, the buyer of the put option can limit his loss to the premium, while his profits have no limits. You, the seller of the put option, can make a maximum per-unit profit that equals the premium; however, your loss has no limits.