CAJ | 학술논문

本文在扩展的卡尔曼滤波法及拟极大似然估计法的基础上,首次把离散时间下三因子二次方形式的动态利率期限结构模型应用于上交所国债期限的研究,并在二次方利率期限结构框架内比较了常数型、仿射型和二次方型市场风险函数对不同利率期限结构的拟合效果。我们发现二次方市场风险对1年期利率拟合的最好;对2年期利率的拟合,常数型和仿射型市场风险比二次方市场风险表现更佳;而对3、4、5年期利率的拟合,仿射型市场风险表现最好。
본문재확전적잡이만려파법급의겁대사연고계법적기출상,수차파리산시간하삼인자이차방형식적동태리솔기한결구모형응용우상교소국채기한적연구,병재이차방리솔기한결구광가내비교료상수형、방사형화이차방형시장풍험함수대불동리솔기한결구적의합효과。아문발현이차방시장풍험대1년기리솔의합적최호;대2년기리솔적의합,상수형화방사형시장풍험비이차방시장풍험표현경가;이대3、4、5년기리솔적의합,방사형시장풍험표현최호。
Term structure of interest rates has become a major research topic in the financial and economics fields.The rapid development of financial derivatives modeling and econometric estimation methods has primarily contributed to the growing importance of this research topic.Modeling methods used to manage the term structure of interest rates are more mature in the developed countries.In contrast,the bond market in China is at the inception stage,and is often susceptible to the influence of national policies and high market volatility.After being through a series of financially institutional reforms,Chinese bond market has made great progress in bond issue scales and types in the primary market,as well as in trading rules in the secondary market.These distinct market characteristics call for special attention to the term structure of interest rates in Chinese bond market.This study examines well-established econometric theories and methods on term structure of interest rates.We apply these theories and methods to understanding Chinese bond market.A model is proposed to better assess Chinese bond market.This proposed model can help uncover the existing term structure of interest rates in Chinese bond market.Knowledge about Chinese bond market can provide a theoretical basis to help understand Chinese derivative pricing and hedging practices.More importantly,investors can understand how the central government in China conducts its monetary policy and its potential influence on the derivative market.Affine term structure models（ATSMs） accommodate stochastic volatility,jumps and correlations among all risk factors and provide analytical tractability for investors.Virtually all of the empirical implications of multifactor term structure models have utilized ATSMs because they use time series data on long-and short-term bond yields simultaneously.However,empirical evidence shows that this model has tension between delivering empirical performance of fitting interest rates and denying positive probabilities of negative interest rates.ATSMs also have the inherent drawback of making a trade-off between the structure of bond price volatility and admissible nonzero conditional correlations of variables.Another drawback is that there exists the possibility of omitting nonlinearity in the ATSMs.These weaknesses may create issues when trying to applying ATSMs to analyzing Chinese bond market.Chinese bond market is susceptible to the influence of macroeconomic policies and politics,which can exert nonlinearity influence.In order to minimize the potential influence,this study adopts quadratic term structure models（QTSMs）,one kind of nonaffine term structure models.QTSMs can not only overcome the drawbacks of single-factor or multi-factor affine models,but also relax the assumption conditions.QTSMs can better model the nonlinearity nature of the term structure of interest rates in Chinese bond market.This study employs three-factor QTSMs in discrete time to study bond yields in Shanghai Exchange.The analysis includes the term structure of 1,2,3,4,and 5 years from January 7,2005 to September 9,2008.We add a quadratic form of three factors to the affine form of ATSMs.As such,QTSMs used in this study can capture the dynamic feature of risk-free instantaneous rate.The three factors are unobserved independent components and follow Gaussian auto-regressive processes,where the noise terms are normally distributed with vector＇s mean values and constant variances.Three different risks of market price are used to compare their fitted performance of bonds with different maturities,including constant market price of risk（CMPR）,affine market price of risk（AMPR） and quadratic market price of risk（QMPR）.Due to the latent nature of the state variables and the non-linear relationship between the instantaneous interest rate or yields,the underlying state variables cannot be inverted from the observable yields even in unique factor models.Hence we use Extended Kalman Filter（EKF）,a recursive dynamic process,to estimate the state variables and Quasi-Maximum-Likelihood（QML）.This method enables us to obtain not only the unknown parameters but also the extracted state variables,which are important in interest rate derivatives pricing.In addition,to ensure the identification and uniqueness of the estimated parameters,some restrictions,such as instantaneous rate,auto-regressive vector and matrix of three factors,are incorporated into the models.The research finds these three factors have significant autoregressive effects.For the model with CMPR,the market price risk is mainly from the exterior shocks caused by the first and the second factors.For the model with AMPR,the market price risk is mainly from the exterior shocks caused by the second and the third factors.For the model with QMPR,the market price risk is equally caused by the three factors.From the perspective of mean squared errors（MSE）,QMPR is best fitted in the bond yield with one year to maturity.QMPR can capture the nonlinearity from sudden change in the one-year-maturity bond.Constant MPR and affine MPR are equally fitted as QMPR in the yield with 2 years to maturity.The plots reveal that QMPR can perform well as CMPR and AMPR,but worsen in sudden change points.For the yield with 3,4,and 5 years to maturity,affine MPR has the best performance.The longer the maturity the smoother the interest rate curve is.The affine MPR model can outperform QMPR in capturing linearity in market pricerisk.In summary,this paper employs a new term structure of interest rate model to study Chinese bond yield.Our study shows that QTSMs with different market price risks can capture Chinese bonds with different maturities.Modeling Chinese bond yields is a big challenge.However,with the continuous development of more complex econometric models and methods,future models of understanding the term structure of interest rates will become more accurate and can better capture the reality.