THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION

Jim Gatheral () and Tai-Ho Wang ()
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Jim Gatheral: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA
Tai-Ho Wang: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2012, vol. 15, issue 01, 1-18

Abstract: In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.

Keywords: Most-likely-path; heat kernel expansion; implied volatility; local volatility model; asymptotic expansion (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (10)

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DOI: 10.1142/S021902491250001X

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