Investopedia explains 'Put On A Put'
A put on a put has two strike prices and two expiration dates, one for the initial compound put option and the other for the underlying vanilla put option. Note that compound options are generally European-style exercise, which means that they can only be exercised on the expiration date.
Since one of the variables that determines the cost of an option is the price of the underlying asset, the cost of a put on a put option will generally be lower than the cost of a put on the corresponding asset. It can therefore provide a great deal of leverage to the options trader.
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