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Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach

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  • Dongjae Lim
  • Lingfei Li
  • Vadim Linetsky

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.

Suggested Citation

  • Dongjae Lim & Lingfei Li & Vadim Linetsky, 2012. "Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach," Papers 1206.5046, arXiv.org.
  • Handle: RePEc:arx:papers:1206.5046
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    4. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    5. Tong, Zhigang & Liu, Allen, 2022. "Pricing variance swaps under subordinated Jacobi stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    6. Zhigang Tong & Allen Liu, 2018. "Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    7. Zhigang Tong & Allen Liu, 2017. "Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-24, June.
    8. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    9. Li, Lingfei & Linetsky, Vadim, 2014. "Optimal stopping in infinite horizon: An eigenfunction expansion approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 122-128.
    10. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    11. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2019. "Gauge transformations in the dual space, and pricing and estimation in the long run in affine jump-diffusion models," Papers 1912.06948, arXiv.org, revised Dec 2019.
    12. Hyungbin Park, 2015. "Sensitivity Analysis of Long-Term Cash Flows," Papers 1511.03744, arXiv.org, revised Sep 2018.
    13. Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Papers 1403.5402, arXiv.org.

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