The Estimation Based On The Maximum Likelihood Estimation And The Pricing Of Zero-Coupon Bond

As a fundamental determinant economic variable, the short-term interest rate directly affects the pricing models of financial products and the effective risk management, so many term structure models of interest rates have been developed and estimated by academic researchers. But the subject is not researched much in China.Since the entering of WTO will hasten the development of China financial market greatly, we need an analysis of term structure models for China. In this paper, I first review the theory and models of term structure of interest rates and the pricing theory of the zero-coupon bond, the CKLS model is greatly examined. Then I review the theory of maximum likelihood estimation and the approaches on how to get the approximation of the transition density of the diffusion models of the interest rate, the approaches included the Euler, SMLE, Crank-Nicolson, Hermite. By making use of the simulated data, we get the optimal approach under the CKLS model. Using the interest rate data of China-inter-bank, we estimate the parameters of CKLS model under the optimal approach and get the price of the zero-coupon bond and the term structure of this market. After reach, I find that under the CKLS model, the Hermite approach is the best and the Crank-Nicolson is the worst.The estimated parameters show that in the studied market, the interest rates show great mean-reversion and level effect. The term structure of the zero-coupon bond is not always upward. In some time the hump shaped and the downward shaped term structure can be got. These finding maybe useful to the policy enact of the monetary authority and the investment and the hedge of the institutional and individual investor.