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Option pricing and perfect hedging on correlated stocks

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  • Perelló, Josep
  • Masoliver, Jaume

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.

Suggested Citation

  • Perelló, Josep & Masoliver, Jaume, 2003. "Option pricing and perfect hedging on correlated stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 622-652.
    • Handle: RePEc:eee:phsmap:v:330:y:2003:i:3:p:622-652
    DOI: 10.1016/S0378-4371(03)00619-8
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    Cited by:

    1. Piotrowski, Edward W. & Schroeder, Małgorzata & Zambrzycka, Anna, 2006. "Quantum extension of European option pricing based on the Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 176-182.

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