Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrization

TL;DR

This paper introduces kernel-based collocation methods for numerically solving Heath-Jarrow-Morton models with Musiela parametrization, enabling derivative pricing via Monte Carlo with proven convergence rates.

Contribution

It develops a novel kernel-based collocation approach for Heath-Jarrow-Morton models, providing convergence analysis and practical computation techniques.

Findings

Convergence rate bounds under specific conditions

Method effectively approximates stochastic differential equations

Enables derivative pricing using Monte Carlo methods

Abstract

We propose kernel-based collocation methods for numerical solutions to Heath-Jarrow-Morton models with Musiela parametrization. The methods can be seen as the Euler-Maruyama approximation of some finite dimensional stochastic differential equations, and allow us to compute the derivative prices by the usual Monte Carlo methods. We derive a bound on the rate of convergence under some decay condition on the inverse of the interpolation matrix and some regularity conditions on the volatility functionals.