Continuous time Ehrenfest process in term structure modelling

TL;DR

This paper introduces a finite-state mean-reverting short-rate model using the continuous time Ehrenfest process, deriving explicit bond pricing formulas and exploring its connection to the Vasicek model through numerical analysis.

Contribution

It presents a novel application of the Ehrenfest process in term structure modeling and derives explicit formulas for bond prices, linking it to established models.

Findings

Explicit zero-coupon bond pricing formulas derived

Model's limiting behavior related to Vasicek model

Numerical results illustrate model properties

Abstract

In this paper, a finite-state mean-reverting model for the short-rate, based on the continuous time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and the special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.