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Risk Sensitivities Of Bermuda Swaptions

Author

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  • VLADIMIR V. PITERBARG

    (Bank of America, 5 Canada Square, London E14 5AQ, UK)

Abstract

A new approach to the problem of computing risk sensitivities of Bermuda swaptions in a lattice, or PDE, framework is presented. The algorithms developed perform the task much faster and more accurately that the traditional approach in which the Greeks are computed numerically by shocking the appropriate inputs and revaluing the instrument. The time needed to execute the tradition scheme grows linearly with the number of Greeks required, whereas our approach computes any number of Greeks for a Bermuda swaption in nearly constant time. The new method explores symmetries in the structure of Bermuda swaptions to derive recursive relations between different Greeks, and is essentially model-independent. These recursive relations allow us to represent risk sensitivities in a number of ways, in particular as integrals over the "survival" density. The survival density is obtained as a solution to a forward Kolmogorov equation. This representation is the basis for practical applications of our approach.

Suggested Citation

  • Vladimir V. Piterbarg, 2004. "Risk Sensitivities Of Bermuda Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 465-509.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:04:n:s0219024904002487
    DOI: 10.1142/S0219024904002487
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    References listed on IDEAS

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    1. M. A. H. Dempster & J. P. Hutton, 1997. "Fast numerical valuation of American, exotic and complex options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 1-20.
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    Cited by:

    1. Nan Chen & Yanchu Liu, 2014. "American Option Sensitivities Estimation via a Generalized Infinitesimal Perturbation Analysis Approach," Operations Research, INFORMS, vol. 62(3), pages 616-632, June.
    2. Denis Belomestny & G. Milstein & John Schoenmakers, 2010. "Sensitivities for Bermudan options by regression methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 117-138, November.
    3. Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
    4. Christian Fries & Joerg Kampen, 2010. "Global existence, regularity and a probabilistic scheme for a class of ultraparabolic Cauchy problems," Papers 1002.5031, arXiv.org, revised Oct 2012.

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