论文标题
Lévy-Copula驱动的SDE的MLMC计划较弱
A weak MLMC scheme for Lévy-copula-driven SDEs with applications to the pricing of credit, equity and interest rate derivatives
论文作者
论文摘要
本文为莱维驱动的随机微分方程（SDES）开发了一种新型的弱多层蒙特卡洛（MLMC）近似方案。该方案基于驾驶Lévy过程的纯跳跃组件的状态空间离散（通过连续的马尔可夫链近似），如果多维驱动程序由LévyCopula给出，则特别适合。该算法的多级版本需要在该方案的连续级别中近似Lévy驱动程序的新耦合，该耦合通过相应的泊松点过程的耦合来定义。多级方案是薄弱的，因为在级别方差上的界限是基于耦合而无需强大收敛的。此外，耦合对于提出的跳跃离散是很自然的，并且很容易模拟。近似方案及其多级类似物应用于从数学金融中获取的示例，包括信贷，公平和利率衍生品的定价。
This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for Lévy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain approximation) of the pure-jump component of the driving Lévy process and is particularly suited if the multidimensional driver is given by a Lévy copula. The multilevel version of the algorithm requires a new coupling of the approximate Lévy drivers in the consecutive levels of the scheme, which is defined via a coupling of the corresponding Poisson point processes. The multilevel scheme is weak in the sense that the bound on the level variances is based on the coupling alone without requiring strong convergence. Moreover, the coupling is natural for the proposed discretization of jumps and is easy to simulate. The approximation scheme and its multilevel analogous are applied to examples taken from mathematical finance, including the pricing of credit, equity and interest rate derivatives.
