THE STOCHASTIC VOLATILITY IN INTEREST RATE MODELS OF DIFFUSION PROCESSES

In this paper, we consider two interest rate models, a one factor interest rate model and a two-factor interest rate with stochastic volatility and we propose that the interest rate follows diffusion process. An application to US Treasury Bill data is illustrated and a comparison with a one-factor model is shown. We prove some results that show that the two factor diffusion process is more suitable for the pricing of the American Treasury bond than the one factor model. We make a simulation of the two factors and the one factor diffusion model and we see which of them is more suitable for catching the variation of the stochastic interest rates. To achieve that goal we compare the two curves obtained by the both diffusion process and the real curve observed in the interest rate market.