庭开娟, 罗贤兵, 刘琳芳.Heston随机波动率模型的Multilevel Monte Carlo方法[J].重庆工商大学学报(自然科学版),2020,37(1):65-70
TING Kai-juan, LUO Xian-bing, LIU Lin-fang.Multilevel Monte Carlo Method for Heston Stochastic Volatility Model[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2020,37(1):65-70
Heston随机波动率模型的Multilevel Monte Carlo方法
Multilevel Monte Carlo Method for Heston Stochastic Volatility Model
  
DOI:
中文关键词:  Heston随机波动率模型  Multilevel Monte Carlo法  亚氏期权  回望期权
英文关键词:Heston Stochastic Volatility Model  Multilevel Monte Carlo method  Asian option  lookback option
基金项目:
作者单位
庭开娟, 罗贤兵, 刘琳芳 贵州大学 数学与统计学院贵阳 550025 
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中文摘要:
      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。
英文摘要:
      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.
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