ON A VOLATILITY AVERAGING IN A TWO-FACTOR INTEREST RATE MODEL

In this paper we deal with the Fong-Va s cek two-factor interest rate model for valuing term structures. The volatility of the short rate process is assumed to be stochastic and it satises a stochastic dieren tial equation of the mean reversion type. The equation for the zero coupon bond price is a linear parabolic equation in two space dimensions. These spatial dimensions correspond to the short rate and volatility. It is shown that this equation possesses an explicit solution giving rise to study further properties of the two-factor model analytically. Knowing the density distribution of the stochastic volatility we are yet able to perform averaging of the bond price and the term structure with respect to stochastic volatility. Unlike the short rate known from the market date on daily basis the volatility of the short rate process is unknown and can be hardly estimated from historical data. Therefore such a volatility averaging is of special importance when applying two-factor interest rate models to market data analysis.