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A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models

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Author Info

  • Damiano Brigo

    (Product and Business Development Group, Banca IMI, SanPaolo IMI Group, Corso Matteotti 6, 20121 Milano, Italy Manuscript)

  • Fabio Mercurio

    (Product and Business Development Group, Banca IMI, SanPaolo IMI Group, Corso Matteotti 6, 20121 Milano, Italy Manuscript)

Abstract

In the present paper we show how to extend any time-homogeneous short-rate model to a model that can reproduce any observed yield curve, through a procedure that preserves the possible analytical tractability of the original model. In the case of the Vasicek (1977) model, our extension is equivalent to that of Hull and White (1990), whereas in the case of the Cox-Ingersoll-Ross (1985) (CIR) model, our extension is more analytically tractable and avoids problems concerning the use of numerical solutions. We also consider the extension of time-homogeneous models without analytical formulas. We then explain why the CIR model is the most interesting model to be extended through our procedure, analyzing it in detail. We also consider an example of calibration to the cap market for two of the presented models. We finally hint at the same extension for multifactor models and explain its advantages for applications.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 5 (2001)
Issue (Month): 3 ()
Pages: 369-387

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Handle: RePEc:spr:finsto:v:5:y:2001:i:3:p:369-387

Note: received: October 1998; final version received: August 2000
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Related research

Keywords: Short-rate models; Analytical tractability; Exponential Vasicek model; Cox-Ingersoll-Ross' model; Calibration to market data;

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Cited by:
  1. Hans-Peter Bermin, 2012. "Bonds and Options in Exponentially Affine Bond Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(6), pages 513-534, December.
  2. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 107-133, March.
  3. Oh Kwon, 2009. "On the equivalence of a class of affine term structure models," Annals of Finance, Springer, vol. 5(2), pages 263-279, March.
  4. Damiano Brigo & Mirela Predescu & Agostino Capponi, 2010. "Credit Default Swaps Liquidity modeling: A survey," Papers 1003.0889, arXiv.org, revised Mar 2010.
  5. Antonio Mannolini & Carlo Mari & Roberto Ren�, 2008. "Pricing caps and floors with the extended CIR model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(4), pages 386-400.

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  1. Cox–Ingersoll–Ross model in Wikipedia (English)

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