Evaluating callable and putable bonds: An eigenfunction expansion approach

Dongjae Lim*, Lingfei Li, Vadim Linetsky

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

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 Lévy subordinator.

Original languageEnglish (US)
Pages (from-to)1888-1908
Number of pages21
JournalJournal of Economic Dynamics and Control
Volume36
Issue number12
DOIs
StatePublished - Dec 1 2012

Keywords

  • Callable bonds
  • Eigenfunction expansions
  • Interest rate models
  • Optimal stopping
  • Option pricing
  • Options embedded in bonds
  • Stochastic games
  • Stochastic time changes

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics

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