An arbitrage-free model of the yield gap

In this paper I adapt the perpetual bond valuation model of Cox, Ingersoll and Ross (Journal of Finance, Vol. 35, No. 2 (1980), pp. 389-404) to allow for non-linear mean reversion in the short-term interest rate. In their model, the consol price is inversely proportional to the short-term interest rate. Allowing appropriately for mean reversion has the effect of adding a positive intercept constant to this elementary valuation formula. This modification also gives the short-term rate a Gamma distribution in steady state. The model is used to develop a coherent econometric model of the relationship between short- and long-term rates in the USA and Japan. In contrast, the Cox, Ingersoll and Ross 1985 model (Econometrica, Vol. 53, No. 2 (1985), pp. 385-407) fails to satisfy the relevant cross-equation restrictions.