考虑跳跃波动与符号跳跃的50ETF期权定价研究

›› 2019, Vol. 31 ›› Issue (9): 28-36.

考虑跳跃波动与符号跳跃的50ETF期权定价研究

瞿慧, 陈静雯

南京大学工程管理学院, 南京 210093

收稿日期:2018-07-10 出版日期:2019-09-28 发布日期:2019-09-29
通讯作者: 瞿慧(通讯作者),南京大学工程管理学院副教授,美国康奈尔大学博士
作者简介:陈静雯,南京大学工程管理学院硕士研究生。
基金资助:
国家自然科学基金项目（71671084）。

Pricing 50ETF Options Considering Jump Volatility and Signed Jumps

Qu Hui, Chen Jingwen

School of Management and Engineering, Nanjing University, Nanjing 210093

Received:2018-07-10 Online:2019-09-28 Published:2019-09-29

摘要/Abstract

摘要：

标的资产的波动率是期权定价的核心参数。利用高频数据计算已实现波动并进一步区分为连续波动和跳跃波动。对连续波动构建带抛物型杠杆的异质自回归伽马模型，并进一步引入符号跳跃以改进波动预测。用复合泊松过程建模跳跃波动，其中随机跳跃大小服从伽马分布。对参数估计值进行从真实测度到风险中性测度的转换，进而实现蒙特卡洛模拟法的期权定价。采用50ETF期权上市起至2017年6月30日合约数据的实证表明，在期权价格均方根误差和隐含波动率均方根误差指标下，基于高频数据的模型较GARCH模型的定价误差更小，考虑跳跃波动可以提升期权定价能力。进一步地，同时考虑跳跃波动和符号跳跃则可以获得最佳的期权定价表现。

关键词: 期权定价, 高频数据, 跳跃波动, 符号跳跃, 蒙特卡洛模拟

Abstract:

The volatility of the underlying asset is key for option pricing. We use high-frequency prices to calculate realized volatility and separate it into jump and continuous volatilities. Heterogeneous autoregressive gamma with parabolic leverages model is constructed for the continuous volatility, which is then augmented by including the signed jumps. Compound Poisson process is used to model the jump volatility, with the random jump sizes Gamma distributed. The parameter estimates are mapped from physical measure to risk-neutral measure, which are then used in the Monte Carlo simulations for option pricing. Experiments with the 50ETF option data from February 9, 2015 to June 30, 2017 show that, under the option price root mean square error and the implied volatility root mean square error, the high-frequency based models all have better option pricing performance than the GARCH model, modeling the jump volatility can improve option pricing, and the best option pricing performance is obtained by further including the singed jumps.

Key words: option pricing, high-frequency data, jump volatility, signed jump, Monte Carlo simulation

瞿慧, 陈静雯. 考虑跳跃波动与符号跳跃的50ETF期权定价研究[J]. , 2019, 31(9): 28-36.

Qu Hui, Chen Jingwen. Pricing 50ETF Options Considering Jump Volatility and Signed Jumps[J]. , 2019, 31(9): 28-36.

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