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Affine Lattice Models

Author

Listed:
  • CLAUDIO ALBANESE

    (Department of Mathematics, Imperial College of Science and Technology, University of London, SW7 2AZ, London, UK)

  • ALEXEY KUZNETSOV

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

Abstract

We introduce a new class of lattice models based on a continuous time Markov chain approximation scheme for affine processes, whereby the approximating process itself is affine. A key property of this class of lattice models is that the location of the time nodes can be chosen in a payoff dependent way and one has the flexibility of setting them only at the relevant dates. Time stepping invariance relies on the ability of computing node-to-node discounted transition probabilities in analytically closed form. The method is quite general and far reaching and it is introduced in this article in the framework of the broadly used single-factor, affine short rate models such as the Vasiček and CIR models. To illustrate the use of affine lattice models in these cases, we analyze in detail the example of Bermuda swaptions.

Suggested Citation

  • Claudio Albanese & Alexey Kuznetsov, 2005. "Affine Lattice Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 223-238.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002986
    DOI: 10.1142/S0219024905002986
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    Cited by:

    1. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2022. "Non-local Solvable Birth–Death Processes," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1284-1323, June.

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