Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions

16 Pages Posted: 2 Apr 2011

Date Written: March 31, 2011

Abstract

Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local volatility processes. In particular, we compute all the heat kernel coefficients for the CEV and quadratic local volatility models; in the later case, we are able to use these to construct an exact explicit formula for the processes' transition density. We then derive low order approximation formulas for the cubic local volatility model, an affine-affine short rate model, and a generalized mean reverting CEV model. We finally demonstrate that the approximation formulas are accurate in certain model parameter regimes via comparison to Monte Carlo simulations.

Suggested Citation

Taylor, Stephen Michael, Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions (March 31, 2011). Available at SSRN: https://ssrn.com/abstract=1800415 or http://dx.doi.org/10.2139/ssrn.1800415

Stephen Michael Taylor (Contact Author)

New Jersey Institute of Technology ( email )

University Heights
Newark, NJ 07102
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
222
Abstract Views
822
rank
137,656
PlumX Metrics