ar X iv : c on d - m at / 0 01 20 14 v 3 4 D ec 2 00 1 Option pricing and perfect hedging on correlated stocks

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 τ ≥ 0. 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.