统计与数据科学学院知识库

  贸易摩擦、自然灾害、军事冲突和经济周期等因素导致大宗商品、股票和原油等价格频繁波动，严重影响了实体企业、金融机构及国家经济的安全与稳定。因此，规避商品和金融资产价格波动的研究变得尤为重要。期权作为一种重要的金融衍生工具，通过支付一定费用获得未来某一价格的买卖权力，能够提前锁定资产价格，常被用作规避价格波动风险的重要手段。此外，期权在企业经营中也有广泛应用，如代理人激励、企业兼并和融资管理等。因此，研究期权的定价理论对于企业和金融投资者规避价格波动风险、促进金融体系和经济的稳定增长具有重要意义。

梳理现有文献，发现期权的参数和非参数定价模型因其定价原理不同，各具优劣，且仍有进一步提升的空间。基于此，本文旨在有效结合参数和非参数定价模型的优势，优化和改善现有期权参数和非参数定价模型，并考虑最优集成信息会随时间变化的特征建立结合期权参数和非参数定价模型的动态集成框架。

  为了改善参数定价模型，本文提出了时变隐含波动率参数定价模型算法、时变参数定价模型算法和基于物理信息（PINN）网络的CIR-3/4随机波动率跳扩散模型，分别从参数优化和期权假设条件放宽两个方面进行了改善。一方面，针对参数定价模型的参数优化，提出了时变隐含波动率参数定价模型算法和时变参数定价模型算法。考虑波动率参数对于期权定价模型、投资组合、风险管理等领域的重要性以及本身存在的波动“从聚性”，建立了时变隐含波动率参数定价模型算法。运用上证50ETF期权交易数据验证了该算法能够有效提升含有波动率参数的定价模型，并通过局部累积效应算法发现时变隐含波动率相比历史波动率和GARCH波动率更贴近现实市场。此外，考虑更多的参数并不存在“自相关性”和“从聚性”等特征，加之期权参数定价模型会随时间的迁移而变化，本文使用滚动窗口的方法提出了时变参数定价模型算法。实证表明期权的参数的确会随时间变化而改变，而且该算法能够提升参数定价模型定价精度的50%。另一方面，针对期权参数定价模型假设条件的放宽，提出了基于物理信息网络的随机利率CIR-3/4随机波动率跳扩散模型。该模型由于采用更加符合市场信息的非仿射随机波动率结构，得不到闭式解，难以参数校准，因此本文提出了基于SLSQP的最小二乘蒙特卡洛模拟参数估计算法。实证表明，通过提出的参数估计算法和PINN网络数值求解的方法，可以在不获得期权显示解的情况下快速地获得期权价格，并且优于已有的Merton和Heston模型。

  为了改善非参数定价模型，本文提出了新的投资者情绪指数和特征融合的时空频预测模型，分别从特征变量引入和模型的改进两个方面改善了期权非参数定价模型。一方面，运用网络股评文本提出了新的投资者情绪指数算法。该投资者情绪指数能够囊括文本差异性，是通过建立专业的金融词典，运用深度神经网络学习金融资产价格变化和文本信息之间的关系提出的新投资者情绪指数算法。通过计量经济学和期权价格预测两个视角验证了该投资者情绪指数的有效性。比较发现，与使用词典法的投资者情绪指数相比，新的指数能够促进期权价格的预测。另一方面，提出了频域增强的混合图循环卷积Transfromer（FHGRCT）时空预测模型。该模型针对期权交易数据利用Copula相关系数建立期权合约之间的先验图，融合多种空间信息和时空信息，使用频域增强和特征融合的方式构建了时空预测模型。实证表明，提出的模型具有更高的定价精确度而且更加稳定，并使用可解释性算法分析发现FHGRCT更加依赖于期权的交易指标数据。

  在集成期权参数和非参数定价模型方面，提出了动态残差优化集成算法，该算法考虑了集成特征随时间变化，有效结合了两类定价模型的优势。实证结果表明，动态残差优化集成算法相比静态集成方法，进一步提升了定价模型的准确度和稳定性。期权参数和非参数定价模型各有优劣：非参数定价模型在定价精度和稳定性上优于参数定价模型，但依赖于期权交易数据；而参数定价模型虽然牺牲了部分定价精度，但具备更高的可解性且不依赖于数据。为此，本文提出了在分解集成框架下结合参数和非参数定价模型的动态残差优化集成算法。该算法使用序列分解方法将期权交易数据分解为参数定价模型的趋势项和其他高频模态分量，并考虑模态分量与长期趋势项之间的动态集成关系。实证结果表明，该算法优于单一的期权参数和非参数定价模型以及其他分解集成类混合模型，充分发挥了两者的优势，为风险管理和资产定价提供了新的思路。

      Trade frictions, natural disasters, military conflicts, and economic cycles have led to frequent fluctuations in the prices of commodities, stocks, and crude oil, significantly impacting the safety and stability of real enterprises, financial institutions, and national economies. Therefore, research on avoiding price fluctuations in commodities and financial assets has become particularly important. Options, as an important financial derivative, provide the right to buy or sell an asset at a certain price in the future by paying a certain fee, allowing for the locking in of asset prices in advance. They are often used as a key means to mitigate the risks of price fluctuations. Additionally, options have widespread applications in business operations, such as agent incentives, corporate mergers, and financing management. Thus, researching the pricing theory of options is of great significance for enterprises and financial investors to avoid price fluctuation risks and promote the stable growth of the financial system and economy.

       A review of the existing literature reveals that both parametric and non-parametric pricing models for options have their own advantages and disadvantages due to different pricing principles, and there is still room for further improvement. Based on this, this paper aims to effectively combine the advantages of parametric and non-parametric pricing models, optimizing and improving the existing option pricing models, and establishing a dynamic integrated framework that combines parametric and non-parametric pricing models while considering the characteristics of optimal integrated information that may change over time.

       To improve the parametric pricing model, this paper proposes the time-varying implied volatility parametric pricing model algorithm, the time-varying parametric pricing model algorithm, and the CIR-3/4 stochastic volatility jump diffusion model based on Physics-Informed Neural Networks (PINN). These improvements are made from two aspects: parameter optimization and the relaxation of option assumption conditions.On one hand, regarding the parameter optimization of the parametric pricing model, we propose the time-varying implied volatility parametric pricing model algorithm and the time-varying parametric pricing model algorithm. Considering the importance of the volatility parameter in option pricing models, portfolios, risk management, and the inherent phenomenon of volatility clustering, we establish the time-varying implied volatility parametric pricing model algorithm. Using trading data from the SSE 50 ETF options, we validate that this algorithm effectively enhances the pricing model that includes volatility parameters. Additionally, through the local accumulation effect algorithm, we find that the time-varying implied volatility is closer to the real market compared to historical volatility and GARCH volatility. On the other hand, considering that more parameters do not exhibit characteristics such as "autocorrelation" and "clustering," and that the parametric pricing model will change over time, this paper employs a rolling window method to propose the time-varying parametric pricing model algorithm. Empirical evidence shows that the parameters of options indeed change over time, and this algorithm can improve the pricing accuracy of the parametric pricing model by 50%.                 

      Furthermore, in response to the relaxation of the assumption conditions of the option parametric pricing model, we propose a stochastic interest rate CIR-3/4 stochastic volatility jump diffusion model based on PINN. Due to its use of a non-affine stochastic volatility structure that better aligns with market information, this model does not yield a closed-form solution and is challenging to calibrate. Therefore, this paper introduces a parameter estimation algorithm based on SLSQP for least squares Monte Carlo simulation. Empirical results indicate that the proposed parameter estimation algorithm, combined with the numerical solution methods of the PINN network, can quickly obtain option prices without requiring explicit solutions for options, outperforming existing Merton and Heston models.

      To improve the non-parametric pricing model, this paper proposes a new investor sentiment index and a spatiotemporal frequency prediction model that integrates features, enhancing the option non-parametric pricing model from two aspects: the introduction of feature variables and model improvements. On one hand, a new investor sentiment index algorithm is developed using network stock commentary texts. This investor sentiment index encompasses textual diversity and is formulated by establishing a specialized financial dictionary and employing deep neural networks to learn the relationship between financial asset price changes and textual information. The effectiveness of this investor sentiment index is validated from the perspectives of econometrics and option price forecasting. Comparisons reveal that the new index facilitates better predictions of option prices compared to those using dictionary-based sentiment indices. On the other hand, we propose a frequency-domain enhanced Hybrid Graph Recurrent Convolutional Transformer (FHGRCT) spatiotemporal prediction model. This model utilizes Copula correlation coefficients to establish prior graphs between option contracts based on trading data, integrating various spatial and temporal information. It constructs the spatiotemporal prediction model through frequency-domain enhancement and feature fusion. Empirical evidence indicates that the proposed model achieves higher pricing accuracy and stability, and an analysis using explainability algorithms shows that FHGRCT relies more on trading indicator data of options.

      In the integration of parametric and non-parametric pricing models, we introduce a dynamic residual optimization ensemble algorithm that takes into account the temporal variation of integrated features, effectively combining the advantages of both types of pricing models. Empirical results demonstrate that the dynamic residual optimization ensemble algorithm enhances the accuracy and stability of the pricing model compared to static integration methods.Both option parametric and non-parametric pricing models have their strengths and weaknesses: the non-parametric pricing model excels in pricing accuracy and stability but relies heavily on option trading data, while the parametric pricing model, although sacrificing some pricing accuracy, offers higher solvability and does not depend on data. Therefore, this paper proposes a dynamic residual optimization ensemble algorithm that combines parametric and non-parametric pricing models within a decomposed integration framework. This algorithm employs a sequential decomposition method to break down option trading data into a trend component of the parametric pricing model and other high-frequency modal components, considering the dynamic integration relationship between modal components and long-term trend components. Empirical results indicate that this algorithm outperforms individual parametric and non-parametric pricing models as well as other decomposed integration hybrid models, fully leveraging the strengths of both approaches, thereby providing new insights for risk management and asset pricing.