多因子欧式期权定价的主成分蒙特卡罗加速方法

针对多个随机因子的欧式期权定价问题,提出了一种基于主成分分析的多元控制变量的蒙特卡罗加速框架.其核心思想是,使用单个主成分替换收益函数中的原始随机变量以便更易获得定价问题的精确值,从而可将近似的收益函数作为控制变量.由于主成分的独立性,使用多元控制变量的蒙特卡罗模拟方法比单个控制变量具有更好的加速效果.对多资产期权和亚式期权的数值实验验证了本文算法的高效性和稳定性.

An Efficient Principal Component Monte Carlo Method for Pricing European Options with Multi-Factors

This paper constructs a framework of accelerating Monte Caro simulation for pricing European options with multiple stochastic factors. The underlying principle of the technique is that if all stochastic factors in the payoff function are replaced by some important principal components (PCs), the resulting integral can easily be evaluated in a closed form, and thus the approximated payoff can be used as a control variate. Due to the independence of the PCs, Monte Carlo simulations with multiple control variates are always more effective than the ones with a univariate control. Numerical tests designed for portfolio options and Asian options verify the efficiency and stability of our method.