The Affine Stochastic Volatility Interest Rate Model With Jump Process And Its Application

As one of the fundamental economic variables, interest rate has always been focus of study in the field of finance. The quantitative description of the characteristics of the short-term interest rate, which directly affects the pricing of financial products and the effective risk management, is one of the most rapidly evolving and dynamic area in finance. But in China little research has been done on this subject, and most of the exiting literatures concentrate on the qualitative instead of quantitative analysis. Therefore, based on a comparative study of the existing literatures, the author constructs the affine stochastic volatility interest rate model with jump process by quantitative methods, and estimates parameters of the model.Firstly, the author analyzes the traditional term structure models of interest rate and reviews the latest development in this field. The author analyzes and compares many exiting term structure models of interest rate, for example, CKLS models, ARCH models, stochastic volatility model, stochastic drift, mean-reversion and level effect of interest rate. As a result, the author finds that CKLS model is the optimal one of the various single-factor models, which describes the behavior of interest rate in financial market more effectively than other single-factor models. Among the multi-factor models, the stochastic volatility model effectively catches the leptokurtosis and volatility clustering characters of the behavior of short-term interest rate relative to ARCH model. Though theoretically the stochastic drift model is a more generalized model, in reality it cannot effectively describe the behavior of short-term interest rate.Secondly, the author takes into account the effect of the jump process on short-term interest rate. Based on the Geometric Brownian Motion plus Jump model, and taking into account the drift coefficient of CKLS model and the diffusion coefficient of affine stochastic volatility model, the author constructs the affine stochastic volatility term structure of interest rate with jump-diffusion process, which is called ASVJD model in this paper.Lastly, the author introduces a new method to estimate multi-factor models, Efficient Method of Moments, which is based on the "moment". The author then estimates the parameters of the models by the data of CHIBOR. The author further compares the ASVJD model with the Geometric Brownian model, CKLS model, Geometric Brownian with Jump model and the Affine Stochastic Volatility model in demonstration. And as a result, the author finds that the ASVJD model is the optimal...