LONG MEMORY STOCHASTIC VOLATILITY IN OPTION PRICING

Sergei Fedotov () and Abby Tan
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Sergei Fedotov: School of Mathematics, The University of Manchester, M60 1QD, UK
Abby Tan: School of Mathematics, The University of Manchester, M60 1QD, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 03, 381-392

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.

Keywords: Long memory; stochastic volatility; option pricing (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024905003013

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