Does the Hurst index matter for option prices under fractional volatility?

Hideharu Funahashi () and Masaaki Kijima ()
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Hideharu Funahashi: Mizuho Securities Co. Ltd.
Masaaki Kijima: Tokyo Metropolitan University

Annals of Finance, 2017, vol. 13, issue 1, No 3, 55-74

Abstract: Abstract This study examines the effect of fractional volatility on option prices. To this end, we develop an approximation method for the pricing of European-style contingent claims when volatility follows a fractional Brownian motion. Through extensive numerical experiments, we confirm that the decrease in the smile amplitude under fractional volatility is much slower than that under the standard stochastic volatility model. We also show that the Hurst index under fractional volatility has a crucial impact on option prices when the maturity is short and speed of mean reversion is slow. On the contrary, the impact of the Hurst index on option prices reduces for long-dated options.

Keywords: Fractional Brownian motion; Hurst index; Stochastic volatility; Mean-reverting process; Implied volatility (search for similar items in EconPapers)
JEL-codes: G12 G13 G17 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10436-016-0289-1

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