A compound option contains two options in a certain manner across a Put and a Call. Such options can be created by choosing a Put on a Put, Call on a Put, Put on a Call or a Call on a Call. So if an investor buys a Put on a Put option, it means he has an option to sell a Put option which is an option to sell the underlying asset. The person buying the Compound option has to pay a Front Fee or the premium for the first option. Premium on second option is paid only when that option (second) is exercised. So in short, the Front Fee becomes the fees paid for having an option for an option (compound option). There are various advantages and disadvantages of buying a compound option.
Advantage: If the buyer of the normal option is not sure of the usage/need of the normal option, he can exercise the option above the normal option, which will reduce his premium over the normal option.
Disadvantage: If the second underlying option is also exercised, there will be two premiums paid and overall cost will increase.
For Example: If a person buys a compound option of put on a Call. He has to pay a premium for buying that Compound option which is the Front Fee. He will then have the option to sell, the option to buy the underlying asset. Suppose there is an option to buy a stock @ $30 i.e. Call option. The cost of this option is $5 premium. Now suppose the investors who owns this option wants to have an option to sell this Call Option. The investor will ask for the compound option by which, paying a Premium Fee or the Front Fee suppose $3, he can create his Option to sell that Call Option. So until the Call option is exercised he doesn’t have to pay the premium of $5 of the Call option. He only has to pay $3 premium over the first option i.e. Option to sell the call option.