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An Arbitrage‐free Model of the Yield Gap
Author(s) -
Spencer Peter D.
Publication year - 1999
Publication title -
the manchester school
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.361
H-Index - 42
eISSN - 1467-9957
pISSN - 1463-6786
DOI - 10.1111/1467-9957.67.s1.6
Subject(s) - mean reversion , economics , econometrics , yield curve , valuation (finance) , interest rate , arbitrage , term (time) , short rate model , mathematical economics , rendleman–bartter model , financial economics , monetary economics , physics , finance , volatility (finance) , quantum mechanics
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.