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Analytical pricing of the smile in a forward LIBOR market model

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  • D. Brigo
  • F. Mercurio

Abstract

We introduce a general class of analytically tractable diffusions for modelling forward LIBOR rates under their canonical measure. The class, which is based on assuming a smooth functional dependence at expiry between a forward rate and an associated Brownian motion, is highly tractable. It implies explicit dynamics, known marginal and transition densities and explicit caplet prices at any time. As an example, we analyse the dynamics given by a linear combination of geometric Brownian motions with perfectly correlated (decorrelated) returns. We finally construct a specific model in the class that reproduces exactly the market caplet volatilities given in input. Examples of the implied-volatility curves produced by the considered models are also shown.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 3 (2003)
Issue (Month): 1 ()
Pages: 15-27

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Handle: RePEc:taf:quantf:v:3:y:2003:i:1:p:15-27

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Cited by:
  1. Koichiro Takaoka & Hidenori Futami, 2010. "The Instantaneous Volatility and the Implied Volatility Surface for a Generalized Black–Scholes Model," Asia-Pacific Financial Markets, Springer, vol. 17(4), pages 391-436, December.
  2. Jos\'e Da Fonseca & Alessandro Gnoatto & Martino Grasselli, 2012. "A flexible matrix Libor model with smiles," Papers 1203.4786, arXiv.org.

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