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Long Memory Stochastic Volatility In Option Pricing

Author

Listed:
  • SERGEI FEDOTOV

    (School of Mathematics, The University of Manchester, M60 1QD, UK)

  • ABBY TAN

    (School of Mathematics, The University of Manchester, M60 1QD, UK)

Abstract

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black–Scholes equation involving volatility with long-range dependence. We define the stochastic option price as a sum of classical Black–Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we derive the asymptotic equation for this deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

Suggested Citation

  • Sergei Fedotov & Abby Tan, 2005. "Long Memory Stochastic Volatility In Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 381-392.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:03:n:s0219024905003013
    DOI: 10.1142/S0219024905003013
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, November.
    2. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
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    Cited by:

    1. Sergei Fedotov & Stephanos Panayides, 2004. "An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility," Papers cond-mat/0410294, arXiv.org, revised Jan 2006.

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