在半个世纪的发展历程中,期权定价领域涌现出大量模型,这些模型在Black-Scholes模型(BS)提出的定价框架下放松了部分假设,细化了对标的资产价格过程的假设,主要成果包括随机波动率模型、随机跳跃模型和随机利率模型。但是,更加细化的模型意味着复杂度的增加,随着参数的增加,如果模型不能从本质上改进BS模型的假设,使其更加贴合市场规律,复杂度的增加反而会影响模型的定价准确度和稳定性。在中国市场上,由于期权品种较少,对期权定价模型的研究也相对较少,现有的研究没有给出这些推广模型能够稳定降低BS模型定价误差的充分证据,现有研究往往在对比各模型的样本外定价误差后就得出结论,缺乏对模型稳定性的探索,也缺乏对实证结果的深入分析。因此,本文将基于上证50ETF期权的数据,选取高波动市场样本和平稳市场样本,对多个经典期权定价模型在中国市场上的实证表现做系统性的深入研究。本文的研究对象包括随机波动率模型(SV)、随机波动率和随机利率的组合模型(SVSI)以及带随机跳跃的随机波动率模型(SVJ),比较基准是BS模型。本文从各个模型的样本内拟合情况、样本外定价误差和对冲误差三个方面研究对比了各个模型的实证表现,探讨了推广模型相较BS模型定价精确度的提升程度,并深入分析了原因。本文的实证研究发现,SV、SVSI和SVJ模型在样本内拟合和在样本外定价多期期权合约价格时,都具有比BS模型更低的定价误差,在高波动市场样本下,SVJ模型的定价误差会进一步低于SV模型,在平稳市场样本下,只有定价短期期权时,SVJ模型的定价误差才会低于SV模型;在进行风险对冲时,SV模型有最低的对冲误差。但是,SV、SVSI和SVJ模型的参数估计结果波动性很大,并且随着定价日逐渐远离参数估计日,三个波动率模型的定价误差以远远快于BS模型的速度上涨,推广模型与BS模型的对冲误差比也远高于定价误差比,推广模型的稳定性差于BS模型。分析模型假设和市场实际,本文得到结论,随机波动率模型虽然引入了波动率风险,定价和对冲误差低于BS模型,但模型关于波动率过程的假设与市场存在不符之处,在模型稳定性上不如BS模型。
In the course of half a century of development, numerous option pricing models have emerged, which relax some assumptions under the pricing framework proposed by Black-Scholes model (BS) and refine assumptions about the price process of the underlying asset. The main achievements include stochastic volatility model, stochastic jump model and stochastic interest rate model. However, a more refined model means an increase in complexity. As the number of parameters increases, if the model cannot essentially improve the assumptions of the BS model and make it more consistent with the market law, the increase in complexity will affect the pricing accuracy and stability of the model. In the Chinese market, due to the small number of options, there are relatively few studies on option pricing models. Existing studies have not provided sufficient evidence that these extension models can stably reduce the pricing errors of BS model. Existing studies often draw conclusions after comparing the out-of-sample pricing errors of various models, lacking exploration of model stability and in-depth analysis of empirical results. Therefore, based on the data of SSE 50ETF options, this paper will select high-volatility market sample and stable market sample, and conduct a systematic and in-depth study on the empirical performance of several classic option pricing models in the Chinese market.The research objects of this paper include the stochastic volatility model (SV), the combination model of stochastic volatility and stochastic interest rate (SVSI) and the stochastic volatility model with stochastic jump (SVJ), and the comparison base is BS model. This paper compares the empirical performance of each model from three aspects: in-sample fitting, out-of-sample pricing error and hedging error, discusses the degree of improvement of the pricing accuracy of the generalized model compared with the BS model, and analyzes the reasons in depth.The empirical study conducted in this paper reveals that, when fitting the sample data and pricing multi-period options out of sample, the SV, SVSI, and SVJ models exhibit lower pricing errors compared to the BS model. In highly volatile market conditions, the SVJ model demonstrates even lower pricing errors compared to the SV model. In a stable market environment, however, the SVJ model only outperforms the SV model in pricing short-term options. When it comes to risk hedging, the SV model exhibits the lowest hedging error. Nevertheless, the parameter estimation of the SV, SVSI, and SVJ models is highly volatile. As the pricing date diverges from the parameter estimation date, the pricing errors of these three volatility models increase significantly faster than those of the BS model. Additionally, the hedging error ratio between the extended models and the BS model is also notably higher than the pricing error ratio, indicating inferior stability in the extended models compared to the BS model. By analyzing model assumptions and market realities, this paper arrives at the conclusion that although the stochastic volatility models introduce volatility risk and achieve lower pricing and hedging errors than the BS model, they fail to accurately capture the essence of volatility risk, resulting in inferior stability compared to the BS model.