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Option pricing and perfect hedging on correlated stocks

Josep Perello·Jaume Masoliver
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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.

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Josep Perello, Jaume Masoliver. 2001-12-04. Option pricing and perfect hedging on correlated stocks. https://doi.org/10.1016/s0378-4371(03)00619-8

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