时变风险厌恶下的期权定价——基于上证50ETF期权的实证研究

doi:10.16381/j.cnki.issn1003-207x.2019.11.002

摘要/Abstract

摘要： 传统的随机波动率（SV）期权定价是在投资者具有常数风险偏好假设下进行的.但近年来越来越多的研究表明，市场参与者具有时变风险厌恶特征.基于此，本文对时变风险厌恶条件下的期权定价问题进行深入研究.首先，对传统的（非仿射）常数风险厌恶SV（CRA-SV）期权定价模型进行扩展，构建时变风险厌恶SV（TVRA-SV）期权定价模型对期权进行定价，并分析时变风险厌恶对期权价格的影响；其次，采用标的资产与期权数据信息，建立基于连续粒子滤波的极大似然估计方法，对定价模型的客观与风险中性参数进行联合估计；最后，采用我国期权市场上的上证50ETF期权数据，对构建的定价模型进行实证检验.结果表明：TVRA-SV期权定价模型相比传统的CRA-SV期权定价模型具有更好的数据拟合效果，能够更充分地刻画标的上证50ETF收益率在客观与风险中性测度下的波动性；TVRA-SV期权定价模型相比传统的Black-Scholes（B-S）期权定价模型和CRA-SV期权定价模型都具有明显更高的定价精确性。

关键词: 期权定价, 时变风险厌恶, 双因子非仿射随机波动率, 上证50ETF期权, 连续粒子滤波

Abstract: In the past decades, with the rapid development of China's financial markets, more and more derivative products, such as warrants, currency options and covertible bonds have been introduced into the markets. Specially, the SSE 50ETF option, the first stock option in China, was introduced in February 2015. The introduction of the SSE 50ETF options makes the China's equity market more complete. The purpose of this paper is to develop reasonable model for the pricing of the options. It is of great importance for investors and risk managers.
Traditionally, the pricing of options is based on the classical Black-Scholes (B-S) option pricing model. However, an extensive empirical literature has documented the empirical biases of the B-S option pricing model. Most prominently among these biases, observed market prices for out-of-the-money puts and in-the-money calls are higher than the B-S prices. This stylized fact is known as the "volatility smirk". To modeling the smirk, stochastic volatility (SV) models have been introduced. The SV models are popular in the option pricing literature, which have been proved to be helpful in modeling the smirk.
However, in the conventional SV option pricing, investors are supposed to have constant risk preferences. Numerous recent studies have found that the market participants' risk preferences exhibit time-varying characteristics. In contrast to conventional SV option pricing with constant risk aversion, this paper concentrates on the issue of option pricing under time-varying risk aversion. Firstly, by extending the conventional (non-affine) SV option pricing model with constant risk aversion (hereafter CRA-SV option pricing model), a SV option pricing model with time-varying risk aversion (hereafter TVRA-SV option pricing model) is developed to price options, and further the effect of time-varying risk aversion on option prices is examined. Secondly, an estimation approach, the continuous particle filter-based maximum likelihood estimation method, is presented for joint estimation of the objective and risk-neutral parameters of the pricing model, using information provided by the underlying asset and options data. Finally, using the actual financial market data on the SSE 50ETF options, empirically the performance of the developed pricing model is investigated. The results show that the TVRA-SV option pricing model leads to substantial improvements in the empirical fit over the conventional CRA-SV option pricing model, and can describe the volatility dynamics of the underlying SSE 50ETF returns more adequately under both the objective and risk-neutral measures. Moreover, the TVRA-SV option pricing model produces much more accurate option prices than the conventional B-S option pricing model and CRA-SV option pricing model.

Key words: option pricing, time-varying risk aversion, two-factor non-affine stochastic volatility, SSE 50ETF options, continuous particle filters

中图分类号:

F830.9

吴鑫育, 赵凯, 李心丹, 马超群. 时变风险厌恶下的期权定价——基于上证50ETF期权的实证研究[J]. 中国管理科学, 2019, 27(11): 11-22.

WU Xin-yu, ZHAO Kai, LI Xin-dan, MA Chao-qun. Option Pricing Under Time-Varying Risk Aversion: An Empirical Study Based on SSE 50ETF Options[J]. Chinese Journal of Management Science, 2019, 27(11): 11-22.

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