基于随机波动率模型的上证50ETF期权定价研究  

The Pricing of SSE 50 ETF Options Based on Stochastic Volatility Model

作　　者：吴鑫育[1] 李心丹[2] 马超群[3] WU Xin-yu;LI Xin-dan;MA Chao-qun(School of Finance,Anhui University of Finance and Economics,Anhui Bengbu 233030,China;School of Management and Engineering,Nanjing University,Jiangsu Nanjing 210093,China;Business School,Hunan University,Hunan Changsha 410082,China)

机构地区：[1]安徽财经大学金融学院,安徽蚌埠233030 [2]南京大学工程管理学院,江苏南京210093 [3]湖南大学工商管理学院,湖南长沙410082

出　　处：《数理统计与管理》2019年第1期115-131,共17页Journal of Applied Statistics and Management

基　　金：国家自然科学基金青年基金项目(71501001);教育部人文社会科学青年基金项目(14YJC790133);中国博士后科学基金项目(2015M580416);2017年度高校优秀青年骨干人才国内外访学研修项目(gxfx2017031);苏南资本市场研究中心(2017ZSJD020)

摘　　要：传统上,期权定价主要基于Black-Scholes (B-S)模型。但B-S模型不能描述时变波动率以及解释"波动率微笑"现象,导致期权定价存在较大的误差。随机波动率模型克服了B-S模型的这些缺陷,能够合理地刻画波动率动态性和波动率微笑。基于此,本文考虑随机波动率模型下的期权定价问题,并针对我国上证50ETF期权进行实证分析。为了解决定价模型的参数估计问题,采用上证50ETF及其期权价格数据,建立两步法对定价模型的参数进行估计。该估计方法保证了定价模型在客观与风险中性测度下的一致性。采用2016年1月到2017年10月的上证50ETF期权价格数据为研究样本,对随机波动率模型进行了实证检验。结果表明,无论是在样本内还是样本外,随机波动率模型相比传统的常数波动率B-S模型都能够获得明显更为精确和稳定的定价结果,B-S模型的定价误差总体偏大且呈现较高波动,凸显了随机波动率对于期权定价的重要性。另外,随机波动率模型对于短期实值期权的定价相比对于其它期权的定价要更精确。Traditionally, the pricing of options is mainly based on the Black-Scholes(B-S) model. However, it has been well-documented in the finance literature that the B-S model isn’t able to describe time-varying volatility and to explain volatility smile/smirk, which leads to substantial pricing errors.To overcome the drawbacks of the B-S model, the stochastic volatility model which can account for the volatility dynamics and volatility simle/smirk has been reasonably proposed. This paper concentrates on the pricing of SSE 50 ETF options under the stochastic volatility model. To estimate the model parameters in a way that maintains the internal consistency of the objective and risk-neutral measures,this paper proposes a two-step approach by using SSE 50 ETF and its option prices data. Using the actual market data on the SSE 50 ETF option prices from January 2016 to October 2017, an empirical investigation is carried out. The results show that the stochastic volatility model produces much more accurate and stable option pricing results than the traditional constant volatility of B-S model both inand out-of-sample, and the B-S model performs badly in the pricing of SSE 50 ETF options with high pricing errors, which suggests the importance of stochastic volatility in option pricing. Moreover, the stochastic volatility model provides more accurate pricing results for the short-term and in-the-money options than for the others.

关 键 词：期权定价 随机波动率 非仿射模型 上证50ETF期权 两步估计法 

分 类 号：F830[经济管理—金融学] O212[理学—概率论与数理统计]