A Vasicek-type short rate model with memory effect

TL;DR

This paper introduces a modified Vasicek short rate model incorporating memory effects, resulting in improved yield curve fitting and providing closed-form bond pricing formulas, despite its non-Markovian nature.

Contribution

The paper presents a Vasicek-type model with memory parameters, deriving closed-form bond prices and numerical methods for contingent claim valuation.

Findings

Better yield curve fitting than classical Vasicek model

Closed-form bond and option pricing formulas

Numerical methods applicable despite non-Markovian structure

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.