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Valuing Early-Exercise Interest-Rate Options With Multi-Factor Affine Models

Author

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  • SEBASTIAN JAIMUNGAL

    (Department of Statistical Sciences, University of Toronto, 100 St. George Street, Toronto ON M5S 3G3, Canada)

  • VLADIMIR SURKOV

    (The Fields Institute for Research in Mathematical Sciences, University of Toronto, 222 College Street, Toronto ON M5T 3J1, Canada;
    Department of Statistics and Actuarial Sciences, University of Western Ontario, 1151 Richmond Street, London ON N6A 5B7, Canada)

Abstract

Multi-factor interest-rate models are widely used. Contingent claims with early exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm based on a sequence of measure changes coupled with Fourier transform solutions of the pricing partial integro-differential equation to solve the pricing problem. The new algorithm, which we call the irFST method, also neatly computes option sensitivities. Furthermore, we are also able to obtain closed-form formulae for accrual swaps and accrual range notes. We demonstrate the versatility and precision of the method through numerical experiments on European, Bermudan and callable bond options, accrual swaps and accrual range notes.

Suggested Citation

  • Sebastian Jaimungal & Vladimir Surkov, 2013. "Valuing Early-Exercise Interest-Rate Options With Multi-Factor Affine Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1-29.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:06:n:s0219024913500349
    DOI: 10.1142/S0219024913500349
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    References listed on IDEAS

    as
    1. Markus Bouziane, 2008. "Pricing Interest-Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-77066-4, October.
    2. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
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    Cited by:

    1. Ali Al-Aradi & Alvaro Cartea & Sebastian Jaimungal, 2018. "Technical Uncertainty in Real Options with Learning," Papers 1803.05831, arXiv.org, revised Jul 2018.
    2. Yaowen Lu & Duy-Minh Dang, 2023. "A semi-Lagrangian $\epsilon$-monotone Fourier method for continuous withdrawal GMWBs under jump-diffusion with stochastic interest rate," Papers 2310.00606, arXiv.org.

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