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

arXiv:1809.05643v5 Announce Type: replace-cross Abstract: We study kernel-based collocation methods for numerical solutions of Heath-Jarrow-Morton models in Musiela parametrization. The methods are Euler-Maruyama approximations of finite-dimensional stochastic differential equations and can be used with standard Monte Carlo procedures for derivative pricing. We give a conditional mean-square error estimate under explicit stability assumptions on the differentiated cardinal basis over the full evaluation region required by the volatility functional. The estimate uses the spatial-radius exponent dictated by the squared-error calculation. Two finite-resolution examples illustrate the method for a Vasicek model and for caplet pricing.