随机局部波动率模型与Wei-Norman分解方法
Stochastic Local Volatility models and the Wei-Norman factorization method
摘要：
本文利用Wei-Norman分解方法和李代数技巧，证明了一个依赖于时间的局部随机波动率（SLV）模型可以归结为一个自治偏微分方程系统，该系统可以用Heat核求解.然后，我们比较了传统的蒙特卡罗模拟的结果与显式的解决方案所获得的技术。这种方法在文献中是新的，除了减少一个非自治的问题到一个自治的，允许减少时间的数值计算。
英文摘要：
In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the Heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional Monte Carlo simulations with the explicit solutions obtained by said techniques. This approach is new in the literature and, in addition to reducing a non-autonomous problem into an autonomous one, allows for reduced time in numerical computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
