Self Exciting Threshold Interest Rates Models

International Journal of Theoretical and Applied Finance, Vol. 9, No. 7, pp. 1093-1122, 2006

36 Pages Posted: 7 Jan 2005 Last revised: 15 Mar 2009

See all articles by Marc Decamps

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: February 28, 2005

Abstract

In this paper, we study a new class of tractable diffusions suitable for model primitives of interest rates. We consider scalar diffusions with scale s'(x) and speed m(x) densities discontinuous at the level x*. We call that family of processes Self Exciting Threshold (SET) diffusions. Following Gorovoi and Linetsky (2004), we obtain semianalytical expressions for the transition density of SET (killed) diffusions. We propose several applications to interest rates modeling. We show that SET short rate processes do not generate arbitrage possibilities and we adapt the HJM procedure to forward rates with discontinuous scale density. We also extend the CEV and the shiftedlognormal Libor market models. Finally, the models are calibrated to the U.S. market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.

Keywords: SETAR, State-price density, Skew Brownian motion, Eigenfunction expansions, Interest rates, Market models

Suggested Citation

Decamps, Marc and Goovaerts, Marc and Schoutens, Wim, Self Exciting Threshold Interest Rates Models (February 28, 2005). International Journal of Theoretical and Applied Finance, Vol. 9, No. 7, pp. 1093-1122, 2006, Available at SSRN: https://ssrn.com/abstract=642961 or http://dx.doi.org/10.2139/ssrn.642961

Marc Decamps (Contact Author)

Katholieke Universiteit Leuven (KUL) ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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