状态空间模型理论与算法及其在金融计量中的应用
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摘要
金融时间序列的非线性、非高斯等特征，以及潜变量和参数时变性等问题，使得标准计量分析模型在实践中面临重大挑战。建立在递推贝叶斯滤波理论基础上，融合了现代统计计算方法的状态空间模型，以其独特的模型结构为处理更广泛的时间序列分析问题提供一致的分析框架。
本文深入研究了状态空间建模理论与算法，通过仿真实验进行了比较检验。在此基础上，讨论其在金融中的若干应用，并进行了实证研究。具体包括以下四个方面：
1．针对金融时间序列建模中的非线性、非高斯问题，以及金融市场的时变性特征和潜变量问题，本文确定了基于状态空间模型的研究分析框架，以递推贝叶斯滤波理论为出发点，对状态空间建模理论及算法进行了系统研究。本文讨论了关于状态估计算法的优缺点和改进策略，设计了仿真实验进行性能检验。进一步，本文将递推贝叶斯滤波算法、平滑算法与EM原理相结合，推导了关于参数估计的方法，从而为处理具有复杂数据生成过程的金融时间序列，构建了一个一致且完整的分析框架。
2．在状态空间模型框架下对经典的CAPM模型进行了重建。一是用于研究我国行业股票组合风险系数的时变性，克服了过去利用递归回归和移动窗口回归方法估计时变Beta的缺点；二是和夏普的对角线模型相结合，用于估计投资组合的时变风险价值(VaR)，该方法适合于对大型投资组合进行风险度量。
3．在状态空间模型框架下，对经典的BS期权定价模型进行了重建。本文把波动率看作是一个不可观测的随机变量，提出了一个可以同时处理时变波动率估计和权证序贯定价的非线性状态空间模型。实证结果表明，与常用的方法相比，该方法提高了权证定价的精确性。
4．在状态空间模型框架下对经典的基金收益风格分析模型进行了重建。本文把传统的静态风格分析推广到动态风格分析，同时解决了线性约束和不等式约束给建模带来的困难，拓展了模型的应用范围，并对虚拟投资组合和我国证券投资基金分别进行了分析和实证。结果表明，新模型具有良好的估计效果，与传统模型相比，更具实用价值。
The stylized facts of financial time series and the problem about unobserved component and time varying model parameters made the classical econometric model meet greate challenge in practice. The state space model, which is based on recursive bayesian filtering and combined with modern statistical methods, with its special model structure, provides a consistent analysis frame for an extensive issue of time series analysis.
The dissertation investigates the theory and algorithms on state space modeling and tests their performance through simulation.Then discuss the applications in financial by empirical research. The researches are organized as following:
1. Aiming at the problem about nonlinear, non-Gaussian, latent variable and time varying parameters in financial market, this dissertation sets up a research frame basen on the state space model.The advantage and disadvantage about those algorithms are discussed and some mothed to improve the performance are pointed out. Combining the recursive bayesian filtering with the EM algorithm, deduces the parameter estimation method, and form a consistent analysis frame for the problem in financial time series.
2. The CAPM was rebuilt. (l)The time-varying betas of Chinese industrial stock returns were estimated using Kalman Filter, which overcomes the shortcoming of recursive regressions and rolling regressions. (2)VaR of the portfolio was estimated via combining the Sharpe diagonal model with Time-Varying beta.The result shows significant results.
3.The Black-Scholes option pricing model was rebuilt. The variance rate was estimated taken as unobserved component and a nonlinear state-space model for warrant pricing was provided.Comparing the performance of the particle filter approach with the EWMA model and the implied volatilities model, the result suggests that the new approach is preferred.
4. The classical return-based style analysis model was rebuilt and extended to a dynamic style analysis model. New model can consider the condition of linear and inequation restriction and was applied to an artificial portfolio and to return series of funds, the result suggests that the new approach is preferred.
本文深入研究了状态空间建模理论与算法，通过仿真实验进行了比较检验。在此基础上，讨论其在金融中的若干应用，并进行了实证研究。具体包括以下四个方面：
1．针对金融时间序列建模中的非线性、非高斯问题，以及金融市场的时变性特征和潜变量问题，本文确定了基于状态空间模型的研究分析框架，以递推贝叶斯滤波理论为出发点，对状态空间建模理论及算法进行了系统研究。本文讨论了关于状态估计算法的优缺点和改进策略，设计了仿真实验进行性能检验。进一步，本文将递推贝叶斯滤波算法、平滑算法与EM原理相结合，推导了关于参数估计的方法，从而为处理具有复杂数据生成过程的金融时间序列，构建了一个一致且完整的分析框架。
2．在状态空间模型框架下对经典的CAPM模型进行了重建。一是用于研究我国行业股票组合风险系数的时变性，克服了过去利用递归回归和移动窗口回归方法估计时变Beta的缺点；二是和夏普的对角线模型相结合，用于估计投资组合的时变风险价值(VaR)，该方法适合于对大型投资组合进行风险度量。
3．在状态空间模型框架下，对经典的BS期权定价模型进行了重建。本文把波动率看作是一个不可观测的随机变量，提出了一个可以同时处理时变波动率估计和权证序贯定价的非线性状态空间模型。实证结果表明，与常用的方法相比，该方法提高了权证定价的精确性。
4．在状态空间模型框架下对经典的基金收益风格分析模型进行了重建。本文把传统的静态风格分析推广到动态风格分析，同时解决了线性约束和不等式约束给建模带来的困难，拓展了模型的应用范围，并对虚拟投资组合和我国证券投资基金分别进行了分析和实证。结果表明，新模型具有良好的估计效果，与传统模型相比，更具实用价值。
The stylized facts of financial time series and the problem about unobserved component and time varying model parameters made the classical econometric model meet greate challenge in practice. The state space model, which is based on recursive bayesian filtering and combined with modern statistical methods, with its special model structure, provides a consistent analysis frame for an extensive issue of time series analysis.
The dissertation investigates the theory and algorithms on state space modeling and tests their performance through simulation.Then discuss the applications in financial by empirical research. The researches are organized as following:
1. Aiming at the problem about nonlinear, non-Gaussian, latent variable and time varying parameters in financial market, this dissertation sets up a research frame basen on the state space model.The advantage and disadvantage about those algorithms are discussed and some mothed to improve the performance are pointed out. Combining the recursive bayesian filtering with the EM algorithm, deduces the parameter estimation method, and form a consistent analysis frame for the problem in financial time series.
2. The CAPM was rebuilt. (l)The time-varying betas of Chinese industrial stock returns were estimated using Kalman Filter, which overcomes the shortcoming of recursive regressions and rolling regressions. (2)VaR of the portfolio was estimated via combining the Sharpe diagonal model with Time-Varying beta.The result shows significant results.
3.The Black-Scholes option pricing model was rebuilt. The variance rate was estimated taken as unobserved component and a nonlinear state-space model for warrant pricing was provided.Comparing the performance of the particle filter approach with the EWMA model and the implied volatilities model, the result suggests that the new approach is preferred.
4. The classical return-based style analysis model was rebuilt and extended to a dynamic style analysis model. New model can consider the condition of linear and inequation restriction and was applied to an artificial portfolio and to return series of funds, the result suggests that the new approach is preferred.
引文
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