一种用于金融工程中高维问题的集成准蒙特卡洛方法
An integrated quasi-Monte Carlo method for handling high dimensional problems with discontinuities in financial engineering
AI总结：
本文提出了一种集成准蒙特卡洛方法，通过平滑方法消除金融工程中典型函数的不连续性，并设计新的路径生成方法以降低目标函数的有效维度，从而提高高维和不连续问题的计算效率。
摘要：
准蒙特卡洛（QMC）方法是一种用于复杂金融衍生品定价和对冲的有用数值工具。这些问题通常具有高维性和不连续性，这两个因素可能会显著降低QMC方法的性能。本文开发了一种集成方法，同时克服高维性和不连续性的挑战。为此，提出了一种平滑方法以消除某些典型函数中的不连续性。为了使平滑方法适用于更一般性的函数，设计了一种新的路径生成方法，用于模拟基础资产的路径，使得生成的函数具有所需形式。新的路径生成方法还具有降低目标函数有效维度的能力。我们提出的方法适用于多种模型规格，包括Black-Scholes、指数正常逆高斯莱维和Heston模型。针对这些模型的数值实验表明，在QMC设置下，所提出的平滑方法结合新的路径生成方法可以显著减少定价具有不连续支付的奇异期权和计算期权希腊字母的方差。对有效维度及其相关特征的调查解释了联合过程的显著增强。
英文摘要：
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the performance of the QMC method. This paper develops an integrated method that overcomes the challenges of the high dimensionality and discontinuities concurrently. For this purpose, a smoothing method is proposed to remove the discontinuities for some typical functions arising from financial engineering. To make the smoothing method applicable for more general functions, a new path generation method is designed for simulating the paths of the underlying assets such that the resulting function has the required form. The new path generation method has an additional power to reduce the effective dimension of the target function. Our proposed method caters for a large variety of model specifications, including the Black-Scholes, exponential normal inverse Gaussian Lévy, and Heston models. Numerical experiments dealing with these models show that in the QMC setting the proposed smoothing method in combination with the new path generation method can lead to a dramatic variance reduction for pricing exotic options with discontinuous payoffs and for calculating options' Greeks. The investigation on the effective dimension and the related characteristics explains the significant enhancement of the combined procedure.
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。
