THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION

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...

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Published in:International journal of theoretical and applied finance 2012-02, Vol.15 (1), p.1250001-125000118
Main Authors: GATHERAL, JIM, WANG, TAI-HO
Format: Article
Language:English
Subjects:
Applied economics
Heat kernel
Mathematical analysis
Most likely path approximation
Probability
Statistical models
Volatility
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description 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.
doi_str_mv 10.1142/S021902491250001X
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subjects Applied economics
Heat kernel
Mathematical analysis
Most likely path approximation
Probability
Statistical models
Volatility
title THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION
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