Option pricing and perfect hedging on correlated stocks

Josep Perelló and Jaume Masoliver

Physica A: Statistical Mechanics and its Applications, 2003, vol. 330, issue 3, 622-652

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 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. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed and exact expression for the European call price which is always lower than Black-Scholes price. We obtain the same price and a modified delta hedging if we start from an effective one-dimensional market model. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation effects are also observed.

Keywords: Econophysics; Colored noise; Stochastic differential equations; Option pricing (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:330:y:2003:i:3:p:622-652

DOI: 10.1016/S0378-4371(03)00619-8

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