Put-Call parity

Put call parity states the price of a call minus a put having the same strike and expiration is equal to the forward of the underlying minus the strike. It is not the case this always holds. For example, if the options are American style exercise then they may have different optimal exercise times.

The relation between the underlying spot price and its forward is called cost-of-carry. For a one-period model of intruments I the initial prices are given by x\in\boldsymbol{R}^I. The terminal prices are given by a bounded functions X\colon S\to\boldsymbol{R}^I where S is the set of possible outcomes.