Implied Volatility from Local Volatility: A Path Integral Approach

Large Deviations and Asymptotic Methods in Finance, Peter K. Friz, Jim Gatheral, Archil Gulisashvili, Antoine Jacquier, Josef Teichmann eds., pp. 247-271, Springer, 2015

25 Pages Posted: 23 Jun 2014 Last revised: 10 Jul 2015

See all articles by Tai-Ho Wang

Tai-Ho Wang

Baruch College, CUNY

Jim Gatheral

CUNY Baruch College

Date Written: June 22, 2014

Abstract

Assuming local volatility, we derive an exact Brownian bridge representation for the transition density; an exact expression for the transition density in terms of a path integral then follows. By Taylor-expanding around a certain path, we obtain a generalization of the heat kernel expansion of the density which coincides with the classical one in the time-homogeneous case, but is more accurate and natural in the time inhomogeneous case. As a further application of our path integral representation, we obtain an improved most-likely-path approximation for implied volatility in terms of local volatility.

Keywords: Small time asymptotic expansion, heat kernels expansion, implied volatility, local volatility model, most likely path, path integral

Suggested Citation

Wang, Tai-Ho and Gatheral, Jim, Implied Volatility from Local Volatility: A Path Integral Approach (June 22, 2014). Large Deviations and Asymptotic Methods in Finance, Peter K. Friz, Jim Gatheral, Archil Gulisashvili, Antoine Jacquier, Josef Teichmann eds., pp. 247-271, Springer, 2015 . Available at SSRN: https://ssrn.com/abstract=2457618 or http://dx.doi.org/10.2139/ssrn.2457618

Tai-Ho Wang

Baruch College, CUNY ( email )

1 Bernard Baruch Way
New York, NY 10010
United States
+1-646-312-4130 (Phone)

Jim Gatheral (Contact Author)

CUNY Baruch College ( email )

Department of Mathematics
One Bernard Baruch Way
New York, NY 10010
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
783
rank
30,020
Abstract Views
2,783
PlumX Metrics