Pde Pricing for Bgm
19 Pages Posted: 11 Mar 2002
Date Written: February 28, 2002
This paper presents a novel method of pricing interest rate derivatives in the context of BGM using a partial differential equation (PDE) approach. PDE methods have the advantage of being computationally faster than Monte Carlo simulation.
The key idea in obtaining the BGM PDEs lies in the Feynman-Kac Theorem that provides a link between expectations of functionals of stochastic differential equations (SDEs) and PDEs. Feynman-Kac may be used as a tool to derive the PDE pricing equations from the fundamental arbitrage-free pricing formula. As an illustration, this tool is applied to the classical Black Scholes case. Subsequently, the 1- and 2-dimensional PDEs for BGM are derived. For illustrative purposes, these PDEs are then applied to the pricing of caps and ratchets, respectively. Finally, some interesting and promising future applications are discussed.
JEL Classification: G13
Suggested Citation: Suggested Citation