Pricing derivatives with fractional volatility

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

International Journal of Financial Engineering (IJFE), 2017, vol. 04, issue 01, 1-28

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.

Keywords: Asian option; fractional Brownian motion; stochastic volatility model; mean-reverting process; hurst index; volatility persistence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S2424786317500141

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