Higher-order volatility: dynamics and sensitivities

Alexander Carey

MPRA Paper from University Library of Munich, Germany

Abstract: In this addendum to Carey (2005), we draw several more analogies with the Black-Scholes model. We derive the characteristic function of the underlying log process as a function of the volatilities of all orders. Option prices are shown to satisfy an infinite-order version of the Black-Scholes partial differential equation. We find that in the same way that the option sensitivity to the cost of carry is related to delta and vega to gamma in the Black-Scholes model, the option sensitivity to j-th order volatility is related to the j-th order sensitivity to the underlying. Finally, we argue that third-order volatility provides a possible basis for the introduction of a "skew swap" product.

Keywords: higher-order volatility; higher-order moments; characteristic function; Black-Scholes; infinite-order PDE (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2006-08-24
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Citations: View citations in EconPapers (1)

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