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A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions

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  • John Hull
  • Alan White

Abstract

One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate models can be accommodated. It shows how a piecewise linear volatility function can be calibrated to market data and, using market data from days during the period 2004-2013, finds a best fit to cap prices.

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  • John Hull & Alan White, 2015. "A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 443-454, March.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:3:p:443-454
    DOI: 10.1080/14697688.2014.961530
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    Cited by:

    1. Andrey Itkin, 2020. "Geometric Local Variance Gamma Model," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 6, pages 137-173, World Scientific Publishing Co. Pte. Ltd..

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