Heston随机波动率模型的Multilevel Monte Carlo方法

在市场并非完全有效的前提下,波动率为常数的Black-Scholes模型已不能准确刻画现实世界中的金融市场,提出了用波动率不为常数的Heston随机波动率模型来刻画资产收益的运动过程,进而研究一种路径依赖形衍生产品,亚氏期权和回望期权;在模型下,通过Milstein离散和Multilevel Monte Carlo法对奇异期权中这两种期权的期权价格进行模拟,最后与普通Monte Carlo法模拟的结果进行比较,数值实验从方差、期望、样本数及计算成本方面验证了Multilevel Monte Carlo方法的高效性。

Multilevel Monte Carlo Method for Heston Stochastic Volatility Model

Under the premise that the market is not completely efficient, the Black Scholes model with constant volatility can no longer accurately describe the financial market in the real world. In view of this situation, this paper proposes a Heston stochastic volatility model with non-constant volatility to describe the motion process of asset returns, and then studies a kind of path-dependent derivatives, Asian options and look-back options. Under this model, the option prices of these two kinds of options in exotic options are simulated by Milstein discrete method and Multilevel Monte Carlo method. Finally, the results of numerical experiments are compared with those of ordinary Monte Carlo method. Numerical experiments verify the efficiency of Multilevel Monte Carlo method from the aspects of variance, expectation, sample number and calculation cost.