A Wall Street trading firm is using the Merton (1976) jump-diffusion model to price their index options. They are pricing European calls and then using put-call parity to compute the prices of puts. The problem with this is
A) Put-call parity is not valid for models with jumps.
B) Put-call parity works only if jumps are symmetric.
C) Put-call parity works with jumps only if there are no dividends.
D) Nothing---there is no problem with using put-call parity even if there are jumps in the stock price.

Question

Quizplus · Accepted Answer

Put-call parity is a fundamental principle in options pricing that relates the price of a European call option to a European put option with the same strike price and expiration date. The presence of jumps in the stock price, as modeled by the Merton jump-diffusion model, does not invalidate the use of put-call parity. This principle is based on arbitrage arguments and holds as long as the options are European and no arbitrage opportunities exist, regardless of the specific dynamics of the underlying asset's price.

A Wall Street Trading Firm Is Using the Merton (1976)