Forward Rate Volatilities, Swap Rate Volatilities, and the Implementation of the LIBOR Market
Model
August 2000
John Hull, and Alan White
ABSTRACT
This paper is concerned with the implementation of the LIBOR market model and its extensions. It develops and tests
an analytic approximation for calculating the volatilities used by the market to price European swap options from
the volatilities used to price interest rate caps. The approximation is very accurate for the range of market parameters
normally encountered and enables swap option volatility skews to be implied from cap volatility skews. It also
allows the LIBOR market model to be calibrated to broker quotes on caps and European swap options so that other
interest rate derivatives can be valued.
Subject: Investment/Derivatives, Investment/Fixed Income,Valuation
Classification: Theoretical, Empirical
John Hull
Institution: Stern School of Business, New York University
Email: jhull@stern.nyu.edu
Telephone: (212) 998-0758
Home Page: http://www.stern.nyu.edu/~hull
Alan White
Institution: Joseph L. Rotman School of Management, University of Toronto
Email: awhite@rotman.utoronto.ca
Telephone: (416) 978 3689
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