A compound option or split-fee option is an option on an option. A compound option then has two expiration dates and two strike prices. Another common business application that compound options are used for is to hedge bids for business projects that may or may not be accepted.

Compound options provide their owners with the right to buy or sell another option. These options create positions with greater leverage than do traditional options. There are four basic types of compound options: The formulas for compound option parity can be derived using the principle that two portfolios with identical payoffs should have the same price.

Suppose that you purchase a CoC and sell a PoC on the same underlying call option and with the same strike price and time to maturity. The payoff of this portfolio is always the same: If the underlying call's price at the time of maturity is greater than the strike price, you will exercise your CoC and purchase the underlying call at its strike price.

If the underlying call's price at the time of maturity is less than the strike price, the counterparty will exercise its PoC and you will need to purchase the underlying call at its strike price.

Dynamic Hedging: Managing Vanilla and Exotic Options - Nassim Taleb - Google Livres

Thus, there will always be a cash outflow equal to the strike price and you will come into possession of a call option.

The payoff of this portfolio is identical to the first portfolio. You will own a call that is identical to the underlying call above and you also will have to repay the loan balance, which will be equal to the strike price above.

Therefore, these two portfolios must have the same price. Where P indicates price of what's inside the parentheses and PV indicates present value. Similar logic leads to the following:.

From Wikipedia, the free encyclopedia. Credit spread Debit spread Exercise Expiration Moneyness Open interest Pin risk Risk-free interest rate Strike price the Greeks Volatility.

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Put–call parity - Wikipedia

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MFE Put Call Parity for Compound options : actuary

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