Options for the Beginner and Beyond: Unlock the Opportunities and Minimize the Risks

Applications of Put-Call Parity

1. An important application of [4] is the notion of “synthetic stock.” As an alternative to buying 100 shares of stock at the strike price K, it is possible to create a synthetic replica of the stock by buying one call contract and selling one put contract with the same strike price K and the same expiration month. How well does this synthetic stock track the real thing? At expiration, when t = T, [4] implies the following:

   C(T) - P(T) = S(T) - K. [6]

   That is, the synthetic stock, which has a value of C(T) – P(T) is exactly equal to the profit or loss that results from buying the stock at the strike price K.

   This notion of synthetic stock was presented in Chapter 21, “Stock Substitutes.” it is particularly appealing ...