Approximation and application of the Musiela stochastic PDE in forward rate models

Abstract

In this article, we consider the Musiela equation of forward rates, which is a hyperbolic stochastic partial differential equation. A weak formulation of the problem using the streamline upwind Petrov–Galerkin method is analysed. Error analysis of the method yields estimates for the convergence rates. Computational examples are provided that illustrate not only the discretization methods used, but the type of results relevant to bond pricing that can be obtained from the equation.

Keywords:

• Musiela equation
• stochastic PDE
• forward rate
• error analysis
• SUPG finite element methods

2010 AMS Subject Classification :

• 62P05
• 60H15
• 65N30

Acknowledgement

M.G. was supported in part by the US Air Force of Office Research under grant FA9550-08-1-0415.

Notes

This is due to the HJM drift condition 3.