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.

中文翻译：

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具有 Musiela 参数化的 Heath-Jarrow-Morton 模型的基于核的搭配方法

我们提出了基于内核的搭配方法，用于使用 Musiela 参数化的 Heath-Jarrow-Morton 模型的数值解。这些方法可以看作是一些有限维随机微分方程的 Euler-Maruyama 近似，并允许我们通过通常的 Monte Carlo 方法计算衍生价格。我们在插值矩阵的逆矩阵的一些衰减条件下和波动率函数的一些规律性条件下推导出收敛速度的界限。