基于核函数的配置法求解带有Musiela参数化的Heath-Jarrow-Morton模型
Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrization
AI总结：
该研究提出基于核函数的配置法，结合Euler-Maruyama近似与标准蒙特卡洛程序，用于求解带Musiela参数化的Heath-Jarrow-Morton模型，通过误差估计与实例验证其在Vasicek模型及上限期权定价中的有效性。
摘要：
我们研究了用于求解带有Musiela参数化的Heath-Jarrow-Morton模型数值解的基于核函数的配置法。该方法是有限维随机微分方程的Euler-Maruyama近似，可与标准蒙特卡洛程序结合用于衍生品定价。我们在波动率泛函所需的整个评估区域上，对微分基数基施加显式稳定性假设，给出了条件均方误差估计，该估计使用了由平方误差计算确定的空间半径指数。两个有限分辨率示例说明了该方法在Vasicek模型和上限期权（caplet）定价中的应用。
英文摘要：
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.
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