Interest rate modeling with generalized Langevin equations

Abstract

In this paper, we present an arithmetic short rate model based on generalized Langevin equations. The innovative feature of the model is that it accounts for memory effects in interest rate markets via the involved Langevin processes. In this setup, we provide a representation for the related zero-coupon bond price and infer its risk-neutral time dynamics. We also deduce the associated forward rate dynamics, the latter being of Heath–Jarrow–Morton type. We further establish a measure change to the risk-adjusted forward measure and propose a market-consistent calibration procedure. We finally derive a pricing formula for a European call option written on the zero-coupon bond by Fourier transform methods.