The relationship between put and call option prices: a remark

The put call parity is based on a static portfolio argument that requires no distributional assumptions. Risk-neutral valuation gives a further way to specify the relationship between put and call prices. The two expressions coincide when the discounted asset price is a martingale. However, the martingale property must not hold in empirically relevant CEV and stochastic volatility models and this causes the two parities to differ. We argue that the familiar put call parity then is to be discarded. This finding implies that the familiar put call parity should only be used when it is ascertained beforehand that the
underlying is a martingale.