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The purpose of this paper is to study the generalized Fong--Vasicektwo-factor interest rate model with stochastic volatility. In this model thedispersion of the stochastic short rate (square of volatility) is assumed to bestochastic as well and it follows a non-negative process with volatilityproportional to the square root of dispersion. The drift of the stochasticprocess for the dispersion is assumed to be in a rather general form including,in particular, linear function having one root (yielding the originalFong--Vasicek model or a cubic like function having three roots (yielding ageneralized Fong--Vasicek model for description of the volatility clustering).We consider averaged bond prices with respect to the limiting distribution ofstochastic dispersion. The averaged bond prices depend on time and currentlevel of the short rate like it is the case in many popular one-factor interestrate model including in particular the Vasicek and Cox--Ingersoll-Ross model.However, as a main result of this paper we show that there is no suchone-factor model yielding the same bond prices as the averaged values describedabove.

On non-existence of a one factor interest rate model for volatility averaged generalized Fong-Vasicek term structures