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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 T1 be the time at which we can, if we wish, exercise the compound option to purchase the underlying vanilla option for an amount X1.
This underlying option may be exercised at time T2 for an amount X2
in return for an asset with price S.
Hence the payoff function is max(C(S,T1)-X1,0).

Four types of compound option:

  1. a Call on a Call, the payoff is max(C(S,T1)-X1,0).
  2. a Put on a Call, the payoff is max(P(S,T1)-X1,0).
  3. a Put on a Put , the payoff is max(X1-P(S,T1),0).
  4. a Call on a Put , the payoff is max(X1-C(S,T1),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.