Option pricing during post-crash relaxation times

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices are then estimated using Monte Carlo and finite difference methods. Results of the model show that call option prices after the crash are systematically less than those predicted by the Black-Scholes model. This is a result of the effect of non-constant volatility of the model that causes a volatility skew.