Fixed Income Securities Pricing Svjd Dynamic Extension Model Study

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...