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中国管理科学

中国管理科学 ›› 2024, Vol. 32 ›› Issue (3): 105-115.doi: 10.16381/j.cnki.issn1003-207x.2020.0615

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基于已实现EGARCH-FHS模型的上证50ETF期权定价研究

吴鑫育1(),姜晓晴1,李心丹2,马超群3   

  1. 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
  • 收稿日期:2020-04-07 修回日期:2022-10-23 出版日期:2024-03-25 发布日期:2024-03-25
  • 通讯作者: 吴鑫育 E-mail:xywu@aufe.edu.cn
  • 基金资助:
    国家自然科学基金项目(71971001);安徽省自然科学基金项目(2208085Y21);安徽省高校杰出青年科研项目(2022AH020047);安徽省高校学科（专业）拔尖人才学术项目(gxbjZD2022019);安徽省高校优秀科研创新团队项目(2022AH010045);安徽高校协同创新项目(GXXT-2021-078)

The Pricing of SSE 50 ETF Options with Realized EGARCH-FHS Model

Xinyu Wu1(),Xiaoqing Jiang1,Xindan Li2,Chaoqun Ma3   

  1. 1.School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China
    2.School of Management and Engineering, Nanjing University, Nanjing 210093, China
    3.Business School, Hunan University, Changsha 410082, China
  • Received:2020-04-07 Revised:2022-10-23 Online:2024-03-25 Published:2024-03-25
  • Contact: Xinyu Wu E-mail:xywu@aufe.edu.cn

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摘要：

本文基于已实现EGARCH（REGARCH）模型，结合滤波历史模拟（FHS）方法，构建了REGARCH-FHS模型对期权定价。采用上证50ETF期权数据进行的实证研究结果表明，不论是在样本内还是样本外，REGARCH-FHS模型均相比Black-Scholes模型和GJR-GARCH-FHS模型具有更好的期权定价表现。具体地，在样本内，REGARCH-FHS模型相比Black-Scholes模型和GJR-GARCH-FHS模型在均方根定价误差（RMSE）方面分别改进了77.70%和15.64%；在样本外，分别改进了64.16%和5.40%。REGARCH-FHS模型对于GJR-GARCH-FHS模型的样本内改进主要体现在对短期（剩余期限少于60天）期权的定价，样本外改进主要体现在对短期（剩余期限为30~60天）期权的定价。上述结论对不同的定价表现评价指标是稳健的。研究结果凸显了引入已实现测度（价格极差）与灵活的FHS方法对于期权定价的重要性。

关键词: 期权定价, 已实现EGARCH, GJR-GARCH, FHS, 价格极差

Abstract:

On February 9， 2015， the Shanghai Stock Exchange （SSE） launched its first exchange-traded option， the SSE 50 ETF option. The SSE 50 ETF option is an European-style option written on the 50 ETF. The SSE 50 ETF option provides an effective hedging instrument for the investors in China's stock market. One of the important issues for the development of derivatives markets is to address the question on how derivatives can be valued correctly. It aims to develop an appropriate model for pricing the SSE 50 ETF option in this paper.Classical option pricing theory （such as the Black-Scholes model） is based on the assumption that the underlying asset returns are normally distributed with constant volatility. However， the assumptions are inconsistent with empirical findings， resulting in option pricing biases. It is well recognized that asset returns exhibit characteristics such as skewness and heavy tails， which cannot be captured by using a normal distribution. Moreover， asset returns exhibit the volatility clustering property： the volatility changes over time and its degree shows a tendency to persist. To overcome the drawbacks of the conventional option pricing approach， the GARCH option pricing models have been developed. In particular， the GJR-GARCH-FHS option pricing model has been proved to be useful in fitting the option prices.However， the GJR-GARCH-FHS option pricing model does not exploit the high-frequency information for pricing options. The usefulness of high-frequency information to price options has been well established in the literature. In light of this， this paper proposes the REGARCH-FHS model which combines the realized EGARCH （REGARCH） model with the filtered historical simulation （FHS） method for pricing option. The model extends the conventional GJR-GARCH-FHS option pricing model by incorporating the rich high-frequency intraday information from the realized measure to price options. The model is easy to implement， allows for flexible change of measure and is able to capture volatility asymmetry （leverage effect） as well as non-Gaussian innovation distribution.Empirical analysis based on SSE 50 ETF options shows that our proposed REGARCH-FHS model outperforms the Black-Scholes and GJR-GARCH-FHS models in both in-sample and out-of-sample option pricing. Specifically， the root-mean-square error （RMSE） of the REGARCH-FHS model is 77.70% and 15.64% lower than the RMSE of the Black-Scholes and GJR-GARCH-FHS models in in-sample option pricing， while it is 64.16% and 5.40% lower than the RMSE of the Black-Scholes and GJR-GARCH-FHS models in out-of-sample option pricing. Moreover， the REGARCH-FHS model improves the GJR-GARCH-FHS model most significantly for the pricing of the short-term （days to maturity less than 60 days） in-sample and for the pricing of the short-term （days to maturity： 30-60 days） out-of-sample. Our results are robust to alternative criteria for pricing performance evaluation. In summary， our study highlights the value of incorporating the realized measure （price range） and the flexible FHS method for option pricing.

Key words: option pricing, realized EGARCH, GJR-GARCH, FHS, price range

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