Put-call parity

Put call parity is a relationship between the prices of European call and put options on the same underlying with the same expiry and strike price:

p + s = k + c

p is the price of the put option,
c is the price of the call option,
k is the price of a zero coupon risk free bond that matures on the expiry date with a face value equal to the strike price, and
s is the price of the underlying.

This assumes that there are no dividend payments on the underlying between the date on which the relationship applies and expiry. In this context dividends includes interest and any other payments a holder of a security will receive. If there are dividends, then the present value of the dividends should be subtracted from the price of the underlying.

It can also be deduced from put-call parity that the prices are such that the implied volatility calculated from the put is the same as that calculated from the call. This is, in any case, implied by the no arbitrage requirement.

Put call parity may be used to identify arbitrage opportunities, possibly as part of a more complex model that incorporates many such relationships.

Copyright Graeme Pietersz © 2005-2019