Using Proxies for the Short Rate: When are Three Months Like an Instant?

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Abstract
The dynamics of the unobservable short rate are frequently estimated directly using a proxy. We examine the biases resulting from this practice (the 'proxy problem'). Analytic results show that the proxy problem is not economically significant for single-factor affine models. In the two-factor affine model of Longstaff and Schwartz (1992), the proxy problem is only economically significant for pricing discount bonds with maturities of more than five years. We also describe two different numerical procedures for assessing the magnitude of the proxy problem in a general interest rate model. When applied to a nonlinear single-factor model, they suggest that the proxy problem can be economically significant.