Monte Carlo Euler approximations of HJM term structure financial models

TL;DR

This paper develops Monte Carlo Euler methods for approximating the HJM term structure model, providing error estimates and efficient computation techniques, with numerical validation demonstrating their effectiveness.

Contribution

It introduces novel Monte Carlo Euler approximation techniques with error analysis for infinite-dimensional HJM models, enhancing computational efficiency and accuracy.

Findings

Error estimates effectively distinguish discretization and statistical errors

Numerical examples confirm the accuracy of the error bounds

Computational effort for error estimation is low compared to model simulation

Abstract

We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on \Ito stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates.