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

Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach