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Graphical Representation of Option Price and Sensitivities

Compound option may be described simply as an option on an option.

There are four types of compound options: a call on a call, a put on a call, a put on a put, and a call on a put.

Compound options have two strikes and two exercise dates.

Let us consider an example a call on a call.

Let T_{1} be the time at which we can, if we wish, exercise the compound option to purchase the underlying vanilla option for an amount X_{1}.

This underlying option may be exercised at time T_{2} for an amount X_{2}

in return for an asset with price S.

Hence the payoff function is max(C(S,T_{1})-X_{1},0).

Four types of compound option:

*a Call on a Call*, the payoff is max(C(S,T_{1})-X_{1},0).*a Put on a Call*, the payoff is max(P(S,T_{1})-X_{1},0).*a Put on a Put*, the payoff is max(X_{1}-P(S,T_{1}),0).*a Call on a Put*, the payoff is max(X_{1}-C(S,T_{1}),0).

The first Option on Option model was published by Geske (1977)

Other research has been by Hodges and Selby (1987) and Rubinstein (1991)

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.