固定收益市场利率期限结构建模及其应用研究
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摘要
固定收益市场利率期限结构建模及其应用,主要包括传统利率期限结构理论、利率期限结构建模的均衡方法、利率期限结构建模的无套利方法和利率风险测度与管理四个方面的研究内容。
代表性的传统利率期限结构理论为预期理论、市场分割理论和流动性偏好理论,其中,对基于流动性偏好溢价的预期假说,分别采用单位根、协整分析、向量误差修正模型、因子分解技术进行实证检验,结果表明由各个国债回购利率所构成的利率系统仅由一个共同的随机趋势驱动,利率价差的预测能力与利率的波动程度相关,对去除长期记忆成分后未来利率变化的短暂成分的预测能力显著增强,而对于短期利率序列的纯长期记忆成分的预测能力则很差。
在利率期限结构建模的广义均衡框架下,一方面将传统的息票剥离法和样条估计方法有效结合,提出了扩展的息票剥离法,并通过直接对利率期限结构模型的函数形式进行设定,避免了在使用扩展息票剥离法时必须引入附加方程的问题;另一方面,在CKLS的扩展框架下,采用广义矩估计和极大似然估计方法,对五个短期利率模型进行了最优估计、模型选择和参数偏差校正,并将估计得到的最优模型的参数结果用于随机利率变动情形下的认股权证定价。
在利率期限结构建模的HJM框架下,推导得到了远期利率动力学过程的无套利漂移限制,并采用分解技术将其分解成两个成分函数,以简化HJM类模型的参数估计过程。根据此方法进行的实证研究表明,三因子HJM模型具有相对平稳的指数衰减结构,可以准确地表示取样期间内的国债远期利率期限结构。在分析远期利率波动结构与期限结构动力学过程内在联系的基础上,给出了HJM类模型的马尔可夫化框架,重点研究了在HJM框架下的纯扩散过程中引入随机跳跃成分以及不同波动设定下的马尔可夫系统转换问题,并采用基于控制变量技术的蒙特卡罗方法分别对确定性和状态依赖性远期利率波动结构下的初始债券和初始债券期权价格进行了仿真实现。
在HJM框架下,将传统久期和凸度扩展到广义随机久期和凸度,分析了单因子和双因子HJM模型下的债券投资组合免疫,并对传统久期和凸度以及HJM框架下的三种不同远期利率波动设定下的广义随机久期和凸度进行了实证计算。
Modeling term structure of interest rate with applications mainly include research on traditional theory of term structure of interest rate, generalized equilibrium models of term structure of interest rate, no-arbitrage models of term structure of interest rate and interest rate risk measuring and management.
There are expectation theory, market segmentation theory and liquidity preference theory in classical traditional theory of term structure of interest rate. According to China’s government bond repo rate data, the dissertation individually utilizes unit root method, co-integration analysis method, vector error correction model and factor decomposition procedure to empirically examine expectation hypothesis based on liquidity preference premium. And the result shows that there is only a common stochastic trend which drives interest rate system composed of each bond repo rate, the forecast ability of interest rate spread is correlated with degree of volatility of interest rate and is significantly strengthened for transitory component of future short term interest rate when the permanent component is removed from short term interest rate series, but gets weak predictive power for the permanent component.
Under generalized equilibrium framework of term structure of interest rate models, the dissertation, on the one hand, proposes extended bootstrap method by integrating traditional bootstrap method and cubic spline method and avoids introducing additional equations when utilizing extended bootstrap method by directly designing the function form of term structure of interest rate model. In the meanwhile, the empirical results indicate that the proposed model can capture complicated shape of yield curve and predict future interest rate change. On the other hand, following general CKLS’modeling ideas, the dissertation optimally estimate five different short term interest rate models by adopting GMM and MLE methods, compares these models’descriptive power for the interest rate change behavior by utilizing the log likelihood ratio and Vuong test statistics, corrects the bias of initial parameter values of model by indirect inference method and applies the parameter value of optimal model to the Changjiang River Power Corporation’s warrant (CWB1) assuming interest rate’s stochastic behavior.
Under Heath-Jarrow-Morton framework of term structure of interest rate models, the dissertation derives the no-arbitrage drift term restriction of dynamics of forward interest rate and decomposes forward interest rate term structure into two component functions by a new decomposition technique. According to the procedure, the dissertation also empirically investigates the ability for the model to fit the forward interest rate term structure with the sample of 58 weekly bond price data of Shanghai Stock Exchange. The results show that the three-factor HJM specification has stable exponential decay structure and is a consistent representation of the term structure of interest rate during the sampling period.
Based on analyzing the inherent relation between the volatility structure and the dynamics of forward interest rate, the dissertation presents Markovian framework for HJM class models, investigates the topics for introducing stochastic jump component into pure diffusion process under HJM and Markovian system transformation and reduction for different forward rate volatility specification, and simulates the initial bond and bond option price for deterministic and state dependent volatility structure by utilizing Monte Carlo method based on control variate technique.
Under HJM framework, the dissertation generalizes traditional duration and convexity measure to generalized stochastic duration and convexity for accurately measuring interest rate risk by choosing a zero-coupon bond yield for an arbitrary maturity as state variable, and analyzes interest risk immunization of bonds portfolio for single and two factor HJM models. Finally, the dissertation empirically computes traditional duration and convexity as well as generalized stochastic duration and convexity based on three different forward rate volatility specifications.
代表性的传统利率期限结构理论为预期理论、市场分割理论和流动性偏好理论,其中,对基于流动性偏好溢价的预期假说,分别采用单位根、协整分析、向量误差修正模型、因子分解技术进行实证检验,结果表明由各个国债回购利率所构成的利率系统仅由一个共同的随机趋势驱动,利率价差的预测能力与利率的波动程度相关,对去除长期记忆成分后未来利率变化的短暂成分的预测能力显著增强,而对于短期利率序列的纯长期记忆成分的预测能力则很差。
在利率期限结构建模的广义均衡框架下,一方面将传统的息票剥离法和样条估计方法有效结合,提出了扩展的息票剥离法,并通过直接对利率期限结构模型的函数形式进行设定,避免了在使用扩展息票剥离法时必须引入附加方程的问题;另一方面,在CKLS的扩展框架下,采用广义矩估计和极大似然估计方法,对五个短期利率模型进行了最优估计、模型选择和参数偏差校正,并将估计得到的最优模型的参数结果用于随机利率变动情形下的认股权证定价。
在利率期限结构建模的HJM框架下,推导得到了远期利率动力学过程的无套利漂移限制,并采用分解技术将其分解成两个成分函数,以简化HJM类模型的参数估计过程。根据此方法进行的实证研究表明,三因子HJM模型具有相对平稳的指数衰减结构,可以准确地表示取样期间内的国债远期利率期限结构。在分析远期利率波动结构与期限结构动力学过程内在联系的基础上,给出了HJM类模型的马尔可夫化框架,重点研究了在HJM框架下的纯扩散过程中引入随机跳跃成分以及不同波动设定下的马尔可夫系统转换问题,并采用基于控制变量技术的蒙特卡罗方法分别对确定性和状态依赖性远期利率波动结构下的初始债券和初始债券期权价格进行了仿真实现。
在HJM框架下,将传统久期和凸度扩展到广义随机久期和凸度,分析了单因子和双因子HJM模型下的债券投资组合免疫,并对传统久期和凸度以及HJM框架下的三种不同远期利率波动设定下的广义随机久期和凸度进行了实证计算。
Modeling term structure of interest rate with applications mainly include research on traditional theory of term structure of interest rate, generalized equilibrium models of term structure of interest rate, no-arbitrage models of term structure of interest rate and interest rate risk measuring and management.
There are expectation theory, market segmentation theory and liquidity preference theory in classical traditional theory of term structure of interest rate. According to China’s government bond repo rate data, the dissertation individually utilizes unit root method, co-integration analysis method, vector error correction model and factor decomposition procedure to empirically examine expectation hypothesis based on liquidity preference premium. And the result shows that there is only a common stochastic trend which drives interest rate system composed of each bond repo rate, the forecast ability of interest rate spread is correlated with degree of volatility of interest rate and is significantly strengthened for transitory component of future short term interest rate when the permanent component is removed from short term interest rate series, but gets weak predictive power for the permanent component.
Under generalized equilibrium framework of term structure of interest rate models, the dissertation, on the one hand, proposes extended bootstrap method by integrating traditional bootstrap method and cubic spline method and avoids introducing additional equations when utilizing extended bootstrap method by directly designing the function form of term structure of interest rate model. In the meanwhile, the empirical results indicate that the proposed model can capture complicated shape of yield curve and predict future interest rate change. On the other hand, following general CKLS’modeling ideas, the dissertation optimally estimate five different short term interest rate models by adopting GMM and MLE methods, compares these models’descriptive power for the interest rate change behavior by utilizing the log likelihood ratio and Vuong test statistics, corrects the bias of initial parameter values of model by indirect inference method and applies the parameter value of optimal model to the Changjiang River Power Corporation’s warrant (CWB1) assuming interest rate’s stochastic behavior.
Under Heath-Jarrow-Morton framework of term structure of interest rate models, the dissertation derives the no-arbitrage drift term restriction of dynamics of forward interest rate and decomposes forward interest rate term structure into two component functions by a new decomposition technique. According to the procedure, the dissertation also empirically investigates the ability for the model to fit the forward interest rate term structure with the sample of 58 weekly bond price data of Shanghai Stock Exchange. The results show that the three-factor HJM specification has stable exponential decay structure and is a consistent representation of the term structure of interest rate during the sampling period.
Based on analyzing the inherent relation between the volatility structure and the dynamics of forward interest rate, the dissertation presents Markovian framework for HJM class models, investigates the topics for introducing stochastic jump component into pure diffusion process under HJM and Markovian system transformation and reduction for different forward rate volatility specification, and simulates the initial bond and bond option price for deterministic and state dependent volatility structure by utilizing Monte Carlo method based on control variate technique.
Under HJM framework, the dissertation generalizes traditional duration and convexity measure to generalized stochastic duration and convexity for accurately measuring interest rate risk by choosing a zero-coupon bond yield for an arbitrary maturity as state variable, and analyzes interest risk immunization of bonds portfolio for single and two factor HJM models. Finally, the dissertation empirically computes traditional duration and convexity as well as generalized stochastic duration and convexity based on three different forward rate volatility specifications.
引文
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