狀態相依利率模型－結合GARCH（1,1）與變異性參數模型

Abstract

Abstract The interest rate model could be divided into two categories: equilibrium models and no-arbitrage models. The foundation of this paper is the theory of equilibrium model. The state-dependent variables are introduced to both the Vasicek model and the CIR model. The interest rate fluctuations influenced by the foresighted information of the equity and bond market are also taken into consideration. Coefficients of the state-dependent interest rate model vary with time and reflect the future changes in the market. In reducing the heteroscedasticity of interest rates, GARCH(1,1) is used for coefficients estimating and expected to improve the model forecasting potency on yield curves. Finally, we use the state-dependent interest model to simulate the term structure under real measure which can be used on pricing the product of non-traded target asset. The main objectives of our research are as follows: (1)Verify the improvement of the forecasting potency of the state-dependent interest rate model by comparing it to original Vasicek model. (2)Make certain the superior forecasting abilities of sate-dependent interest rate model by different simulated yield curves. (3)Pricing the product of non-traded target asset by Monte Carlo simulated term structures The empirical result shows the term structure produced by state-dependent interest rate model are better than simulated by the Vasicek model. In different shape of simulated term structures, the state-dependent interest model always exhibits lower prediction errors in contrast to the Vasicek model. We successfully introduce state variables to the equilibrium model. Indeed, the state-dependent interest rate model with varying coefficients improves the capibility of forecasting.