Efficient Trees for CIR and CEV Short Rate Models

39 Pages Posted: 29 Mar 2007

See all articles by Sanjay K. Nawalkha

Sanjay K. Nawalkha

University of Massachusetts Amherst - Isenberg School of Management

Natalia Beliaeva

Suffolk University - Department of Finance

Date Written: February 2007

Abstract

This paper presents efficient binomial and trinomial trees for the Cox, Ingersoll, and Ross (CIR) and the constant-elasticity-of-variance (CEV) short rate models. We correct an error in the original square root transform of Nelson and Ramaswamy [1990], and modify their transform by truncating the tree exactly at the zero-boundary. This not only allows us to create computationally more efficient trees for the CIR square-root process, but also for the entire class of CEV models of the short rate. Our simulations show fast convergence and significantly improved performance of the truncated-tree approach over the Nelson-Ramaswamy approach.

Keywords: Trees, Binomial, Trinomial, American options, CIR, Cox Ingersoll and Ross, Constant Elasticity of Variance, Short rate, caps, interest rate

JEL Classification: G0, G10, G11, G12, G21

Suggested Citation

Nawalkha, Sanjay K. and Beliaeva, Natalia, Efficient Trees for CIR and CEV Short Rate Models (February 2007). Available at SSRN: https://ssrn.com/abstract=976819 or http://dx.doi.org/10.2139/ssrn.976819

Sanjay K. Nawalkha (Contact Author)

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

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

Natalia Beliaeva

Suffolk University - Department of Finance ( email )

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

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