A Vasicek-type short rate model with memory effect

Abstract

We introduce a Vasicek-type short rate model which has two additional parameters representing memory effect. This model presents better results in yield curve fitting than the classical Vasicek model. We derive closed-form expressions for the prices of bonds and bond options. Though the model is non-Markov, there exists an associated Markov process which allows one to apply usual numerical methods to the model. We derive analogs of an affine term structure and term structure equations for the model, and, using them, we present a numerical method to evaluate contingent claims.