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Pricing derivatives with fractional volatility

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  • Hideharu Funahashi

    (Mizuho Securities Co. Ltd., Otemachi First Square 1-5-1, Otemachi, Chiyoda-ku, Tokyo 100-0004, Japan)

Abstract

This paper studies the effect of fractional volatility on path-dependent options, which are highly sensitive to the volatility structure of a targeted underlying asset process. To this end, we propose an approximation formula for average and barrier options when volatility follows a fractional Brownian motion. Furthermore, using the analytical formula, we investigate the impact of the Hurst index on option prices. Overall, our important finding is that when the maturity is short and speed of mean-reversion is slow, the impact of the Hurst index strongly influences the option prices and that is non-negligible. This is an important lesson for practitioners who uses standard Brownian motion.

Suggested Citation

  • Hideharu Funahashi, 2017. "Pricing derivatives with fractional volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-28, March.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500141
    DOI: 10.1142/S2424786317500141
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    References listed on IDEAS

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    Cited by:

    1. Hideharu Funahashi & Tomohide Higuchi, 2018. "An analytical approximation for single barrier options under stochastic volatility models," Annals of Operations Research, Springer, vol. 266(1), pages 129-157, July.

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