September 2023 Interest rate modeling with generalized Langevin equations
Markus Hess
Author Affiliations +
Braz. J. Probab. Stat. 37(3): 513-533 (September 2023). DOI: 10.1214/23-BJPS579


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.

Funding Statement

No funding was received.


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Markus Hess. "Interest rate modeling with generalized Langevin equations." Braz. J. Probab. Stat. 37 (3) 513 - 533, September 2023.


Received: 1 December 2022; Accepted: 1 August 2023; Published: September 2023
First available in Project Euclid: 22 November 2023

Digital Object Identifier: 10.1214/23-BJPS579

Keywords: forward measure , forward rate , generalized/retarded Langevin equation , market-consistent calibration , option pricing , short rate , zero-coupon bond price

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 3 • September 2023
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