Efficient Trees for CIR and CEV Short Rate Models

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.

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