Study On Dynamics Term Structure Of Interest Rate And Its Applications In The Pricing Of Derivatives

As the disorganization of the Bretton Woods System in the 1970's, many momentous events occurred. The financial market became more and more complex because of the mercerization of interest rate and exchange rate. Recently, China made bigger steps in mercerization of interest rate and construction of the modern financial market and it becomes more and more urgent to establish a comprehensive derivatives market. For these reasons, the pricing of derivatives is one of the important issues in the researches of the modern financial theories and practices.In this dissertation, we will discuss the pricing issues of the derivatives on interest rate, national bonds and commodities under the fundamental researches on dynamic interest rate term structures. We establish connections between the problems of pricing of derivatives and the real economical elements in China. The main contents of the dissertation are as follows:Firstly, we compare interest rate term structures of Chinese bond market fitted by NS model and SNS model using the time serial of national bonds'prices, we find that both NS model and SNS model are suitable to build the interest rate term structure, but NS model is better than SNS model. We also analyzed the three components of the instantaneous future interest rate through the macro-economic variables like industry production rate, M2, inflation rate and inter-bank interest rates, etc. to reveal the causes of interest rate. While testing the Pure Expectation Hypothesis over NS model, we find that the probability of the acceptance of PEH is extremely high. But this highly prominence is the outcome of the actuality of mercerization interest rate in China rather than the effective bond market in China. The PEH of NS model can be applied to the forecast of the term structure of interest rates.Secondly, we establish a well-defined dynamic model that combines the inflation, real interest rate and their central tendencies by the results of analyzing the relations between the macro-economic variables and bond yields. Base on the results of Kalman filter, we decompose the risk premium of the yield curve which partly explains the reason that the yield of long-term bond is larger than the yield of short-term bonds; the risk premium can also explain why yields in Chinese bond market are lower than those in U.S. bond market. We also analyze the implied monetary policy above the dynamic model. The results reveal significance for the implementation of monetary policies, investment activities and pricing of the financial derivatives.Thirdly, we introduce macro-economic variables to establish a dynamics model. Base on the parameters estimation results of Kalman filter, we deduce pricing formula about interest rate swap and interest rate options. Just like other financial derivatives, a fixed-floating interest rate swap contract has its time values. We also adopt Feynman-Kac theory and the Fourier inversion of the conditional characteristic function to calculate the numerical price of interest rate options (interest rate floor, interest rate cap and interest rate collar). Detail numeric analysis is discussed in this section.Fourthly, as a further step of the pricings of interest rate derivatives, we discuss the pricings of bond derivatives. Under an equivalent martingale framework, we deduce the pricing formula about discount bond option, discount bond futures, discount bond futures option, coupon bond, coupon bond option, etc. those whose prices derive from the interest rate level. Numerical calculations are shown in the section.Lastly, futures market is very important to investors and hedgers, prices discovery is one of its basic functions. According to the theory of storage, we characterize a three-factor model of commodity spot prices, convenience yields, and interest rates processes. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time varying risk premium. We deduce the futures price equation under equivalent martingale. Adopting the soybean futures-spot prices serials; we estimate the parameters and solve the ODEs by Kalman filter and Runge-Kutta. We also discuss the commodity option price by Fourier inversion numerically. We apply the results in forecasting and evaluate the futures price; the errors show that our model can capture the dynamics of the futures price.