基于SVJD动态扩展模型的中国固定收益证券定价研究

【作者】 周茂彬；

【导师】 张金清；

【作者基本信息】 复旦大学 ， 金融管理与金融工程， 2008， 博士

【摘要】 自上世纪九十年代以来,中国的市场利率以及固定收益证券市场发生了以下几个显著的变化:第一,中国的利率市场化改革已经取得了显著的成效,市场利率的动态行为特征发生了显著的变化;第二,利率成为央行调节宏观经济的重要工具变量之一,宏观经济状况对利率的影响越来越重要;第三,中国固定收益证券市场取得了长足的发展;第四,投资者和金融机构所面临的利率风险加剧了。上述变化引出了以下既有理论意义、又有现实应用价值、且紧密联系的三个问题。第一,中国市场利率的动态行为特征及宏观经济状况对利率行为的影响;第二,固定收益证券的定价,尤其是宏观经济变量对固定收益证券价格的影响;第三,收益率曲线的形状及其变动特征,即利率期限结构问题。论文在分析关于这三个问题现有研究不足的基础上,进一步对它们进行了深入的研究,得到以下主要结果:1.中国市场利率的动态行为特征中国市场利率不仅具有均值回复和时变波动率特征,还具有跳跃行为。通货膨胀率以及利率水平偏离其长期趋势水平的幅度是决定利率跳跃强度的重要因素,偏离幅度越大,利率发生跳跃的可能性越大。2.固定收益证券定价以中国市场利率动态行为特征为依据,论文构建了扩展SVJD动态利率期限结构模型,并给出了扩展模型下零息债券及其欧式看涨期权的封闭定价公式,以及抵押贷款支持证券的蒙特卡罗模拟数值定价方法。在研究这些固定收益证券价格的性质时,论文尤其关注通货膨胀率以及利率的跳跃行为对证券价格的影响。零息债券价格具有如下性质:第一,零息债券价格关于通货膨胀率z的单调性随着短期利率跳跃幅度均值μ_J符号的变化而变化,μ_J为负(正)数时,零息债券价格是z的增(减)函数;第二,零息债券价格关于z长期趋势水平(?)的单调性也取决于μ_J的符号,μ_J小(大)于零时,零息债券价格是(?)的减(增)函数;第三,零息债券价格是宏观经济波动率σ_z的增函数,而它关于z均值回复速度κ_z的单调性不仅取决于z与(?)的相对大小关系,还取决于μ_J的符号;第四,当σ_z比较小时,零息债券价格是μ_J的减函数;但当σ_z比较大时,随着μ_J的增加,零息债券价格先下降后上升;零息债券价格总是短期利率跳跃幅度标准差σ_J的增函数、凸函数;第五,零息债券价格波动率是z、σ_z以及σ_J的增函数。零息债券欧式看涨期权价格具有如下性质:第一,μ_J大(小)于零时,期权价格是z的减(增)函数;第二,期权价格是σ_z的增函数;第三,期权价格是μ_J的减函数,是σ_J的增函数。抵押贷款支持证券价格具有如下性质:第一,抵押贷款支持证券价格是z的减函数,当μ_J小于零(足够大)时,它是宏观经济波动率σ_z的增(先增后减)函数;第二,抵押贷款支持证券价格是房产价格h的增函数,是h波动率σ_h的减函数;第三,σ_z较小(大)时,抵押贷款支持证券的价格是μ_J的增(减)函数;抵押贷款支持证券价格是σ_J的减函数。3.收益率曲线的形状及其变动特征基于零息债券的定价公式,论文推导了扩展模型生成的收益率曲线,研究了收益率曲线的形状及其变动特征。就收益率曲线形状而言,扩展模型能够生成递增、递减、先递增后递减以及先递减后递增等多种复杂形状的收益率曲线。当短期利率r与其长期趋势水平(?)比较接近时,收益率曲线的单调性与μ_J的符号密切相关,μ_J大于零时,收益率曲线往往会先递增、后递减;反之,收益率曲线就递减。就收益率曲线的变动特征而言,扩展模型能够生成向上移动、向下移动以及扭曲变动等多种形式的收益率曲线变动方式。但是,只有通货膨胀率状态变量z的增加能够使得收益率曲线发生扭曲变动。z主要对收益率曲线的前端部分产生影响,而利率的跳跃行为对收益率曲线前端部分的影响强于其对收益率曲线尾端部分的影响。z、z的波动率σ_z以及σ_J增加时,收益率的波动率也增加。更多还原

【Abstract】 In the last 20 years,several significant changes have taken place in the market interest rate and the fixed income security market of China.First,great progress has been made in the interest rate reform,and the dynamics of the market interest rate has changed significantly.Second,interest rate has been an important policy instrument of the central bank to adjust the macro economy,so the condition of the macro economy has great impact on the behavior of the interest rate.Third,extensive development has achieved in the fixed income security markets.Fourth,interest rate risk that the investors and financial institutions are faced with has been enlarged.Such changes result in the following three theoretically meaningful,practically valuable problems which are related with each other closely.First,the dynamics of Chinese market interest rate and the impact on the behavior of the interest rate imposed by the macro economy.Second,pricing of the fixed income securities and the influence on the prices that the macro economic variables have.Third,shape and shift of the yield curve,that is to say,the problem of the term structure of interest rate.Based on the analysis of the shortcomings of the existing research about the previous three problems,this dissertation studies them to a deeper extent.The results are as follows:1.Dynamics of Chinese market interest rateThere are not only mean reversion and time-varying volatility features in the dynamics of Chinese market rate,but also jump behavior in it.Deviations from the level of the inflation and interest rate to their respective long term level are important determinants of the jump intensity of the interest rate.The bigger of the deviations, the larger of the probability that the interest rate will jump.2.Fixed income securities pricingBased on the dynamics of Chinese market interest rate,the dissertation constructed an extended SVJD dynamic interest rate model.Closed form pricing formulas of zero-coupon bond and its option are derived under the extended model, and the Monte Carlo numerical pricing methods of the mortgage-backed security (MBS) are also performed.When studying the properties of the prices of these securities,the dissertation focuses on the impacts imposed by inflation and the jump behavior of the interest rate.Properties of the zero-coupon bond price are as follows:(1) the monotony of the zero-coupon bond price as a function of inflation z alters according to the sign of the mean of the jump size of the short rateμ_J whenμ_J is negative(positive),the price is an increasing(a decreasing) function of z;(2) whenμ_J is smaller(bigger) than zero, zero-coupon bond price is a decreasing(an increasing) function of the long term level of inflation,(?);(3) zero-coupon bond price is an increasing function of the volatility of the macro economy,σ_z;its monotony as a function ofκ_z,the mean reversion rate of z,depends not only on the relative size between z and(?),but also on the sign ofμ_J;(4) whenσ_z is small,the price is a decreasing function ofμ_J,but whenσ_z is large, zero-coupon bond price is first decreasing then increasing asμ_J increases;the price is a increasing and convex function of the standard deviation of the jump size aσ_J;(5) the volatility of the zero-coupon price is a increasing function of z,σ_z andσ_J.Properties of the price of the European call option on the zero-coupon bond are as follows:(1) asμ_J is bigger(smaller) than zero,option price is a decreasing(an increasing) function of z;(2) option price is an increasing function ofσ_z;(3) option price is a decreasing function ofμ_J,and an increasing function ofσ_J.Properties of the price of MBS are as follows:(1) it is a decreasing function of z; whenμ_J is smaller than zero(large enough),it is an increasing(a first increasing then decreasing) function ofσ_z;(2) the price of MBS is an increasing function of house price,h,a decreasing function of the volatility of house priceσ_h;(3) whenσ_z is small (large),the price of MBS is an increasing(a decreasing) function ofμ_J,it is also a decreasing function ofσ_J.3.Shape and shift of the yield curveFrom the zero-coupon bond pricing formula,the dissertation derives the yield curve generated by the extended model,and then investigates the shape and shift of the yield curve.As to the shape of the yield curve,the extended model can generate decreasing, increasing,first increasing then decreasing and first decreasing then increasing types of shape.When short rate r is close to its long term level(?),the monotony of the yield curve is closely related with the sign ofμ_J,asμ_J is bigger than zero,the yield curve will first increase,and then decrease;conversely,the yield curve will decrease.As to the shift of the yield curve,the extended model can generate upward, downward and twisted shifts.But only the changes of the inflation can generate twisted shift of the yield curve.z mainly impacts the short end of the yield,and the impact that the jump behavior has on the short end is more influential than on the long end of the yield curve. As z,σ_z andσ_J increase respectively,yield volatility increases accordingly更多还原