Option pricing and perfect 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 tau. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed expression for the European call price which is always lower than Black-Scholes price. We also obtain a partial differential equation for the option price and study the sensitivity to several parameters and the risk of the dynamics of the call price.