Long memory stochastic volatility in option pricing

Sergei Fedotov, Abby Tan

    Research output: Contribution to journalArticlepeer-review

    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.

    Original languageEnglish
    Pages (from-to)381-392
    Number of pages12
    JournalInternational Journal of Theoretical and Applied Finance
    Volume8
    Issue number3
    DOIs
    Publication statusPublished - 1 May 2005

    Keywords

    • Long memory
    • Option pricing
    • Stochastic volatility

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