系统管理学报

系统管理学报 ›› 2020, Vol. 29 ›› Issue (1): 190-188.DOI: 10.3969/j.issn.1005-2542.2020.01.021

• 金融工程 • 上一篇    

4/2随机波动率模型下的期权定价

王波，朱顺伟，邓亚东，廖昕   

  1. 上海理工大学 管理学院，上海200093
  • 出版日期:2020-01-29 发布日期:2020-05-14
  • 作者简介:王波（1960-），男，博士，教授。研究方向为科技事业管理、社会风险与公共危机管理等。
  • 基金资助:
    国家自然科学基金资助项目（11601330）

Options on S&P 500 Index by Fundamental Transform Approach: 4/2 Stochastic Volatility Model

WANG Bo, ZHU Shunwei, DENG Yadong, LIAO Xin   

  1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Online:2020-01-29 Published:2020-05-14

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摘要： 现有的随机波动率模型存在这样一个问题：给定一组参数，在一定的标的资产波动率水平下，单因子模型只能产生陡峭或平滑的期权隐含波动率曲线，而不能同时存在两种形态，这与实际观察的数据不符。为了更准确地刻画市场隐含波动率曲面，研究一种双因子4/2随机波动率模型，该模型结合了Heston模型和3/2 模型。采用Lewis的基础变换法将期权定价问题转化为求解偏微分方程（PDE）的问题；利用标普500指数期权数据估计模型的参数，比较了不同模型在期权定价上的差异。结果表明，4/2模型的期权价格拟合误差小于另外两种模型，弥补了原模型在这方面的不足。

关键词: 随机波动率, 基础变负, 4/2模型, 李对称, 拉普拉斯变换

Abstract: The existing stochastic volatility models have such a problem: A single-factor volatility model can generate steep curves or flat curves at a given volatility, but it cannot generate both for given parameters, which is inconsistent with the actual observed data. To precisely describe the market implied volatility curve, this paper studied a two-factor 4/2 stochastic volatility model that includes, as special instances, the Heston model and the 3/2 model. Besides, it applied Lewis’s fundamental transform approach to deduce the partial differential equation(PDE). In addition, by adopting the data on S&P 500, it estimated the parameters of the 4/2 model. Furthermore, it investigated the 4/2 model along with the Heston model and the 3/2 model, and compare their different performances. The results indicate that the option price fitting error of the 4/2 model is smaller than that of other two models.

Key words: stochastic volatility, fundamental transform, 4/2 model, Lie's symmetries, Laplace transform

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