Pricing American Interest Rate Options Under the Jump-Extended CIR and CEV Short Rate Models

73 Pages Posted: 16 May 2007

See all articles by Natalia Beliaeva

Natalia Beliaeva

Suffolk University - Department of Finance

Sanjay K. Nawalkha

University of Massachusetts Amherst - Isenberg School of Management

Gloria M. Soto

University of Murcia - Faculty of Business and Economics

Date Written: May 2007

Abstract

This paper presents jump extensions to the Cox, Ingersoll, and Ross (CIR) and the constant-elasticity-of-variance (CEV) models of the short rate, with analytical solutions for the case of exponential jumps, and efficient lattice-based solutions for both exponential jumps and lognormal jumps. We demonstrate how to superimpose a recombining multinomial jump tree on the diffusion tree, creating the mixed jump-diffusion trees for CIR and CEV models extended with jumps. Finally we also present the preference-free versions of these models that allow these models to be fully calibrated to an initially observed forward rate curve, making them consistent with the HJM [1992] paradigm. Our simulations show fast convergence of the trees to the respective analytical solutions.

Keywords: Interest rate models, Term structure models, Jumps, CIR, CEV, Trees

JEL Classification: G11, G12, G13, G21, G22, G23

Suggested Citation

Beliaeva, Natalia and Nawalkha, Sanjay K. and Soto, Gloria M., Pricing American Interest Rate Options Under the Jump-Extended CIR and CEV Short Rate Models (May 2007). Available at SSRN: https://ssrn.com/abstract=985839 or http://dx.doi.org/10.2139/ssrn.985839

Natalia Beliaeva

Suffolk University - Department of Finance ( email )

8 Ashburton Place-Beacon Hill
Boston, MA 02108-2770
United States

Sanjay K. Nawalkha (Contact Author)

University of Massachusetts Amherst - Isenberg School of Management ( email )

Amherst, MA 01003-4910
United States
413-687-2561 (Phone)

Gloria M. Soto

University of Murcia - Faculty of Business and Economics ( email )

Spain

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