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Self Exciting Threshold Interest Rates Models


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    (K. U. Leuven, FETEW, Naamsestraat 69, B-3000 Leuven, Belgium)


    (K. U. Leuven and U. v. Amsterdam, FETEW, Naamsestraat 69, B-3000 Leuven, Belgium)


    (K. U. Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium)


In this paper, we study a new class of tractable diffusions suitable for model's 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 [18], we obtain semi-analytical 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 shifted-lognormal LIBOR market models. Finally, the models are calibrated to the US market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 09 (2006)
Issue (Month): 07 ()
Pages: 1093-1122

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Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:07:p:1093-1122

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Keywords: SETAR; state-price density; skew Brownian motion; eigenfunction expansions; interest rates; market models;


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Cited by:
  1. Rossello, Damiano, 2012. "Arbitrage in skew Brownian motion models," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 50-56.
  2. Alexander Gairat & Vadim Shcherbakov, 2014. "Density of Skew Brownian motion and its functionals with application in finance," Papers 1407.1715,, revised Jul 2014.
  3. Yury Kutoyants, 2012. "On identification of the threshold diffusion processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(2), pages 383-413, April.
  4. Trutnau, Gerald, 2011. "Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1845-1863, August.


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