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The CARMA Interest Rate Model

33 Pages Posted: 30 May 2008 Last revised: 1 Feb 2013

Arne Andresen

Norwegian University of Science and Technology (NTNU) - Department of Industrial Economics and Technology

Fred Espen Benth

University of Oslo

Steen Koekebakker

School of Business and Law at the University of Agder

Valeriy Zakamulin

University of Agder - School of Business and Law

Date Written: December 20, 2012

Abstract

In this paper we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This models is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provide closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Keywords: interest rate model, short rate, forward rate, term structure, CARMA process, bond pricing, bond option pricing, yield curve, volatility curve, calibration

JEL Classification: C50, E43, G13

Suggested Citation

Andresen, Arne and Benth, Fred Espen and Koekebakker, Steen and Zakamulin, Valeriy, The CARMA Interest Rate Model (December 20, 2012). Available at SSRN: https://ssrn.com/abstract=1138632 or http://dx.doi.org/10.2139/ssrn.1138632

Arne Andresen

Norwegian University of Science and Technology (NTNU) - Department of Industrial Economics and Technology ( email )

NO-7491 Trondheim
Norway

Fred Espen Benth

University of Oslo ( email )

Center of Mathematics for Applications
Oslo, N-0317
Norway

Steen Koekebakker (Contact Author)

School of Business and Law at the University of Agder ( email )

Servicebox 422
Kristiansand, N-4604
Norway
+47 38 14 15 31 (Phone)

Valeriy Zakamulin

University of Agder - School of Business and Law ( email )

Service Box 422
Kristiansand, N-4604
Norway
+47 38141039 (Phone)

HOME PAGE: http://vzakamulin.weebly.com/

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