论文标题
多级理查森·罗姆伯格（Richardson-Romberg）和衍生定价中的重要性抽样
Multilevel Richardson-Romberg and Importance Sampling in Derivative Pricing
论文作者
论文摘要
在本文中，我们提出和分析了多级Richardson-Romberg（ML2R）和重要性采样算法的新型组合，以减少整体计算时间，同时在定价同时实现所需的根平方误差。我们开发了一个想法来构建处理量度变化的蒙特卡洛估计器。我们依靠带有投影的Robbins-Monro算法，以近似于度量参数的最佳更改，以在我们的多级算法中的各种分辨率。此外，我们建议将离散化方案纳入具有高阶强收敛性，以模拟潜在的随机微分方程（SDE），从而实现更好的准确性。为此，我们研究了一般多级算法的中心极限定理。此外，我们研究了估计量的渐近行为，从而证明了大量的强大定律。最后，我们提出了数值结果，以证实我们开发算法的功效。
In this paper, we propose and analyze a novel combination of multilevel Richardson-Romberg (ML2R) and importance sampling algorithm, with the aim of reducing the overall computational time, while achieving desired root-mean-squared error while pricing. We develop an idea to construct the Monte-Carlo estimator that deals with the parametric change of measure. We rely on the Robbins-Monro algorithm with projection, in order to approximate optimal change of measure parameter, for various levels of resolution in our multilevel algorithm. Furthermore, we propose incorporating discretization schemes with higher-order strong convergence, in order to simulate the underlying stochastic differential equations (SDEs) thereby achieving better accuracy. In order to do so, we study the Central Limit Theorem for the general multilevel algorithm. Further, we study the asymptotic behavior of our estimator, thereby proving the Strong Law of Large Numbers. Finally, we present numerical results to substantiate the efficacy of our developed algorithm.
