瞿慧,何佳诺.基于已实现波动率的50ETF期权定价研究[J].管理科学,2019,32(3):148-160
基于已实现波动率的50ETF期权定价研究
Pricing 50 ETF Options Using Realized Volatility
投稿时间:2017-07-31  修订日期:2018-02-23
DOI:10.3969/j.issn.1672-0334.2019.03.012
中文关键词:  期权定价  已实现波动率  异质自回归伽马模型  异质杠杆  已实现半差  50ETF
英文关键词:option pricing  realized volatility  heterogeneous autoregressive gamma model  heterogeneous leverage  realized semivariance  50ETF
基金项目:国家自然科学基金(71671084,71201075)
作者单位E-mail
瞿慧 南京大学 工程管理学院南京 210093 linda59qu@nju.edu.cn 
何佳诺 南京大学 工程管理学院南京 210093 jianuohe@163.com 
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中文摘要:
        2015年2月9日上证50ETF期权正式上市交易,标志着中国开始进入期权时代,也对期权的准确定价提出了迫切要求。波动率是期权定价模型的核心参数,准确估计和有效预测波动率对期权定价性能至关重要。
        利用50ETF的日内高频价格计算已实现波动率,使不可观测的波动率可以直接估计和建模。对已实现波动率构建带杠杆的异质自回归伽马(HARGL)模型,以及带异质杠杆的异质自回归伽马(HARGHL)模型。提出进一步区分日内价格上行、下行风险对已实现波动率预测的贡献,引入利用日内正、负高频收益率计算的已实现正、负半差,将上述模型分别改进为HARGL-S模型和HARGHL-S模型,以更好地刻画波动的日内杠杆效应。通过对参数估计从真实测量到风险中性测量的转换,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4月18日的42 406条期权合约收盘价数据,通过模拟在期权价格和隐含波动率上的均方根误差,比较4种模型的定价性能。
        研究结果表明,①50ETF看涨期权和看跌期权均表现出明显的波动率“微笑”特征;②中国股市波动的风险溢酬显著为正,有必要对波动率模型参数估计进行从真实测量到风险中性测度的转换;③已实现正、负半差和异质杠杆的引入都能够显著提高模型的期权定价能力,同时引入则模型定价能力总体最优;④引入已实现正、负半差对非深度实值超短期、短期看涨期权的定价性能改善最为明显,引入异质杠杆对非深度实值超短期、短期看跌期权的定价性能改善最为明显。
        研究结论拓展了对50ETF期权定价的方法,肯定了在已实现波动率异质自回归伽马模型中引入已实现正、负半差和异质杠杆的重要价值,对于投资者进行有效的期权定价和交易以及监管机构进行有效的决策具有实际指导意义。
英文摘要:
        The official release of 50ETF options on February 9, 2015 indicates the start of China′s option era, and calls for accurate option pricing methods. As a kernel parameter of the option pricing models,volatility′s accurate estimation and forecasting is critical for option pricing performance.
        Intraday high-frequency prices of 50ETF are used to calculate realized volatility, which transforms the unobservable volatility into a variable that can be directly measured and modeled. The realized volatility is then modeled with the heterogeneous autoregressive gamma with leverage(HARGL) model, and the heterogeneous autoregressive gamma with heterogeneous leverage(HARGHL) model. In addition, we propose to separate the contribution to volatility forecasting of intraday upside and downside price movements. Thus, we calculate realized positive and negative semivariances with intraday positive and negative returns respectively, and introduce semivariances into the above two models, so as to better characterize the intraday leverage effect. The new models are named as the HARGL-S model and the HARGHL-S model, respectively. The estimated model parameters are mapped from the physical measure to the risk-neutral measure, which are then used in the Monte Carlo simulations for option pricing. The 42406 close prices of 50ETF options between February 9, 2015 and April 18, 2017 are used for the option pricing experiments. The root mean square error on option prices and the root mean square error on implied volatility are used for performance analysis.
        Empirical results indicate that: ①50ETF call and put options both have obvious volatility smiles. ②The market price of volatility risk is significantly positive in China′s stock market, which necessitates the mapping of the model parameter estimates from the physical measure to the risk-neutral measure. ③The introduction of realized positive and negative semivariances as well as the introduction of heterogeneous leverage effects can both largely improve the option pricing capability of the HARGL model; while the introduction of both leads to the highest pricing capability. ④The introduction of realized positive and negative semivariances improves the pricing capability of extreme short to short maturity non-deep-in-the-money call options most significantly. The introduction of heterogeneous leverage effects improves the pricing capability of extreme short to short maturity non-deep-in-the-money put options most significantly.
        The above results extend the pricing methods for 50ETF options, and confirm the important value of introducing realized positive and negative semivariances as well as heterogeneous leverage effects into the HARGL model. This study provides practical guidance for investors in their option pricing and trading practices, as well as for regulators in their decision-making processes.
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