Option Pricing Under Discrete Shifts in Stock Returns

Abstract

In this paper we introduce a pricing model for a European call option when the price of the underlying stock (asset) follows a random walk with Markov Chain type of shifts in the drift and volatility parameters according to the regime that the stock market lies in, at a given period of time. We show that the model can explain the main stylised facts of the option pricing literature and substantially reduce the BS option pricing biases which allows for time-varying transition probabilities between the regimes of the stock market version preferences, based on traded option prices data.

Keywords: Markov regime switching, Option pricing, Volatility smile.

JEL Classification: G10, G13, C22