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

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 conditions on the interpolation functions and some regularity conditions on the volatility functionals.