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Article

An Efficient Lattice Algorithm for the LIBOR Market Model

Tim Xiao
The Journal of Derivatives Fall 2011, 19 (1) 25-40; DOI: https://doi.org/10.3905/jod.2011.19.1.025
Tim Xiao
is a senior director of Risk Analytics at Capital Markets Risk Management with CIBC in Toronto, ON, Canada.
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  • For correspondence: tim.xiao@CIBC.com
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Abstract

Interest rate derivatives are a vitally important, and highly diverse, class of financial instruments. The LIBOR market model (LMM) framework greatly simplifies pricing the simpler types by modeling the forward rate at every maturity as being lognormal. But path-dependent payoffs, such as for a callable instrument or a range accrual note, introduce major problems. The workhorse for valuing such contracts in the equity space is the binomial or trinomial lattice. In this article, Xiao develops a pricing lattice within the LMM, with a grid-type architecture (rather than a tree), and shows that performance of the lattice-based model is orders of magnitude faster than Monte Carlo simulation.

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The Journal of Derivatives: 19 (1)
The Journal of Derivatives
Vol. 19, Issue 1
Fall 2011
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An Efficient Lattice Algorithm for the LIBOR Market Model
Tim Xiao
The Journal of Derivatives Aug 2011, 19 (1) 25-40; DOI: 10.3905/jod.2011.19.1.025

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An Efficient Lattice Algorithm for the LIBOR Market Model
Tim Xiao
The Journal of Derivatives Aug 2011, 19 (1) 25-40; DOI: 10.3905/jod.2011.19.1.025
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  • Article
    • Abstract
    • THE LIBOR MARKET MODEL
    • THE LATTICE PROCEDURE IN THE LMM
    • CALIBRATION
    • NUMERICAL IMPLEMENTATION
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • ENDNOTE
    • REFERENCES
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