Pricing American Interest Rate Options Under the Jump-Extended Vasicek Model

Posted: 1 Mar 2007 Last revised: 15 Aug 2019

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: December 27, 2006

Abstract

This paper shows how to price American interest rate options under the exponential jumps-extended Vasicek model, or the Vasicek-EJ model. We modify the Gaussian jump-diffusion tree of Amin [1993] and apply to the exponential jumps-based short rate process under the Vasicek-EJ model. The tree is truncated at both ends to allow fast computation of option prices. We also consider the time-inhomogeneous version of this model, denoted as the Vasicek-EJ model that allows exact calibration to the initially observable bond prices. We provide an analytical solution to the deterministic shift term used for calibrating the short rate process to the initially observable bond prices, and show how to generate the jump-diffusion tree for the Vasicek-EJ model. Our simulations show fast convergence of European option prices obtained using the jump-diffusion tree, to those obtained using the Fourier inversion method for options on zero-coupon bonds (or caplets), and the cumulant expansion method for options on coupon bonds (or swaptions).

Keywords: Bond options, Interest Rate Trees, Jumps, Vasicek Model, American options

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 Vasicek Model (December 27, 2006). https://doi.org/10.3905/jod.2008.710896. Available at SSRN: https://ssrn.com/abstract=966282 or http://dx.doi.org/10.2139/ssrn.966282

Natalia Beliaeva (Contact Author)

Suffolk University - Department of Finance ( email )

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

Sanjay K. Nawalkha

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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