An Arbitrage‐free Model of the Yield Gap

Peter Spencer

Manchester School, 1999, vol. 67, issue s1, 116-133

Abstract: 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 Γ 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.

Date: 1999
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