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

Chapter 17 in Finance at Fields, 2012, pp 389-406 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn 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: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
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