One of the four types of compound options, this is a call option on an underlying put option. If the option owner exercises the call option, he or she receives a put option, which is an option that gives the owner the right but not the obligation to sell a specific asset at a set price within a defined time period. The value of a call on a put changes in inverse proportion to the stock price, i.e. it decreases as the stock price increases, and increases as the stock price decreases. Also known as a split-fee option.

A call on a put will have therefore two strike prices and two expiration dates, one for the call option and the other for the underlying put option. As well, there are two option premiums involved; the initial premium is paid upfront for the call option; the additional premium is only paid if the call option is exercised and the option owner receives the put option. The premium in this case would generally be higher than if the option owner had only purchased the underlying put option to begin with.

For example, consider a U.S. company that is bidding on a contract for a European project; if the company's bid is successful, it would receive say 10 million euros upon project completion in one year's time. The company is concerned about the exchange risk posed to it by the weaker euro if it wins the project. Buying a put option on 10 million euros expiring in one year would involve significant expense for a risk that is as yet uncertain (since the company is not sure that it would be awarded the bid). Therefore, one hedging strategy the company could use would be to buy, for example, a two-month call on a one-year put on the euro (contract amount of 10 million euros). The premium in this case would be significantly lower than it would be if it had instead purchased the one-year put option on the 10 million euros outright.

On the two-month expiry date of the call option, the company has two alternatives to consider. If it has won the project contract or is in a winning position, and still desires to hedge its currency risk, it can exercise the call option and obtain the put option on 10 million euros. Note that the put option will now have ten months (i.e. 12 - 2 months) left to expiry. On the other hand, if the company does not win the contract, or no longer wishes to hedge currency risk, it can let the call option expire unexercised and walk away.