The Heat-Kernel Most-Likely-Path Approximation
19 Pages Posted: 23 Aug 2010 Last revised: 22 Jun 2014
Date Written: September 22, 2011
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: implied volatility, local volatility, approximation, heat-kernel expansion
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