Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach

TL;DR

This paper introduces an eigenfunction expansion method for efficiently valuing callable and putable bonds across various interest rate models, including those with jumps, outperforming existing techniques in speed and applicability.

Contribution

The paper develops a novel eigenfunction expansion approach that applies to a broad class of interest rate models, including jump-diffusions, providing faster and more versatile bond valuation.

Findings

Method is significantly faster than existing approaches for diffusion models.

Applicable to jump-diffusion and pure jump interest rate models.

Eigenfunction expansion simplifies the valuation of callable and putable bonds.

Abstract

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an eigenfunction expansion in eigenfunctions of the pricing operator with the expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump-diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a L\'{e}vy subordinator.