Option Pricing and Hedging on Correlated Stocks

Abstract

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. After obtaining an effective one-dimensional market model, we achieve a closed expression for the European call price within the Black-Scholes framework and find that our price is always lower than the Black-Scholes price. We obtain the same price if we start from a modified portfolio although now we get a different hedging strategy than that of Black-Scholes. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation effects are also observed.

Keywords: Option pricing, Ornstein-Uhlenbeck, Market model, inefficient market, Black-Scholes

JEL Classification: G12, C50, C41, G10, C6