European Option Under Jump-Diffusion and Stochastic Interest Rate
affiliation not provided to SSRN
June 1, 2012
A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition probability density is a also developed to value the options for various strikes at a given maturity time.The mathematical formulation of those equations is verified numerically by comparing their finite difference computation results with those of the Monte Carlo simulations. For the Kolmogorov equation, an alternate numerical method called the redistribution method is also developed. The redistribution method is based on the moments of the transition probability density and avoids some of the difficulties of a finite difference method.
Number of Pages in PDF File: 63
Keywords: European option, Black-Scholes equation, Kolmogorov equation, Fokker-Planck equation, Green's function, Partial differential-difference equation, Stochastic interest rate, Local volatility, Jump-Diffusion, Redistribution method
JEL Classification: C00, C60, C63, G12working papers series
Date posted: June 2, 2012 ; Last revised: June 15, 2012
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo8 in 1.281 seconds