Lévy过程下金融期权风险对冲参数的模拟仿真估计

A simulation approach to financial options Greeks estimation under Lévy processes

金融期权风险对冲参数的精确估计是衍生品风险管理实践的重要环节,也是金融工程学术界研究的热点之一.模拟仿真方法由于规避了"维度灾难"问题,近年来成为金融工程的主流技术之一.提出了一种基于路径求导的新的模拟仿真方法,来高效地估计Lévy过程下的金融期权风险对冲参数.对于满足Lévy过程的资产价格模型,仅有特征函数是已知的,通过Fourier逆变换并且通过线性插值方法来构造其分布函数和密度函数,从而可以生成随机样本并得到风险对冲参数的模拟仿真估计.数值试验验证了该方法的实际效果,结果显示,与文献中现有的方法相比,提出的估计方法具有更高的计算效率.

Accurate estimation of the Greeks for financial options is an important practical procedure for risk management of financial derivatives. It is also an important topic in financial engineering research. Monte Carlo simulation method, being capable of avoiding the problem of ＂curse of dimensionality＂, is one of the most popular computational tools in financial engineering. Here a new Monte Carlo simulation method was developed to estimate Greeks for financial options under Levy processes. For asset price models following Levy processes, only the characteristic functions are known. By building our method on Fourier transform inversion and linear interpolations, approximations of the cumulative distribution functions and the probability density functions can be obtained, paving the way for generating random samples and constructing Monte Carlo simulation estimates to the Greeks. Numerical experiments were conducted to illustrate the efficiency of the proposed method and the results show that it performs more efficiently than alternatives in the literature.