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To Exercise or Not to Exercise Put Options

A foreign exchange put option gives you the right to sell foreign currency. As in the case of call options, put options can be used by MNCs and speculators alike. An American exporter may have account receivables in a foreign currency. In this case, the exchange rate risk is a possible depreciation of the foreign currency and the MNC would like to hedge against this risk.

If you are a speculator, you plan to buy foreign currency at a cheaper price at the future spot market and sell it at a higher price on the put option. In this case, you’d like to take advantage of a possible depreciation of the foreign currency.

As an MNC or a speculator, a put option locks you in a minimum exchange rate to be received in the future. As in the case of the call option, your benchmark for exercising the put option or not is the future spot market.

If the spot exchange rate is lower than the exercise price, the holder of the put option exercises the option to sell currency on the put option. If the future spot rate is higher than the exercise price, the holder of the put option lets the option expire without exercising it.

For example, a U.S. firm exports backpacks to Germany and expects to be paid €100,000 upon delivery in March. The American exporter has future receivables in euros and faces the risk of depreciation in the euro.

The American firm buys a put option with a premium of $0.021 per euro and the exercise price of $1.31. Therefore, the American exporter pays a total premium of $2,100 upfront ($0.021 x 100,000). If the firm decides to exercise the option, it will sell €100,000 for $131,000 (€100,000 x $1.31).

The exchange rate risk faced by the American exporter is depreciation of the euro. If in fact the euro depreciates in the future spot market, the American firm will exercise the put option and sell the euros at a higher rate on the put option. Suppose the future spot rate is $1.29.

In this case, the American exporters exercises the put option and sells €100,000 for $131,000 (€100,000 x $1.31) instead of the spot market, which would give the firm only $129,000 (€100,000 x $1.29).

What if the future spot rate is $1.36? This time the American exporter has the opportunity to sell its euros for $136,000 (€100,000 x $1.36) at the spot market. Compared to the revenue from the put option ($131,000), using the spot market provides more dollars. Therefore, the firm lets the put option to expire.

In terms of speculating with put options, your goal is the same: you want to buy currency at a lower price and sell it at a higher price. Using a put option, you are planning to buy currency cheaper at the future spot market and sell it at a higher price on the put option. You must have an expectation of depreciation of the foreign currency.

Suppose you expect depreciation of the euro in a month. You buy a put option for €100,000 with a premium of $0.021 per unit and a strike price of $1.32. Again, you pay a total premium of $2,100 upfront ($0.021 x 100,000). The expiration date is a month from now.

The dollar–euro exchange rate that you’ll observe in the future spot market is the benchmark for your decision for exercising or not exercising the put option. When the future spot rate is lower than the exercise price, you’ll exercise the put option.

Suppose the spot rate one month from now is $1.31. In this case, your per-unit revenue is $0.01 ($1.32 – $1.31) because you’ll buy euros at the spot market for $1.31 and sell them on the put option for $1.32. Your total revenue from this transaction is $1,000 (€100,000 x $0.01).

If the future spot rate is higher than the exercise price, you wouldn’t exercise the put option. Suppose the future spot rate is $1.33. In this case, your per-unit revenue from buying euros at the spot market and selling them on a put option is negative ($1.32 – $1.33 = –$0.01). Now you let the put option expire.

In terms of your payoff or profit, in a put option, your profit/loss is indicated by:

profit/loss = selling price – buying price

Your selling price corresponds to the exercise price at which you sell currency on the put option. The premium that you paid upfront and the spot exchange rate at which you buy currency are subtracted from the exercise price. In other words:

profit/loss = exercise price – (spot exchange rate + premium)

Consider the case when you buy a put option for €100,000 with a premium of $0.021 per unit and a strike price of $1.32. You exercise your option to sell euros when the spot rate is $1.31. In this case, your per-unit loss is:

profit/loss = $1.32 – $1.31 – $0.021 = –$0.011

Considering the fact that you sell €100,000, your total loss is $1,100 (€100,000 x $0.011).

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