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A new parameterization for the drift-free simulation in the Libor Market Model

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

We present an efficient procedure to simulate the dynamics of Libor Market Model that avoids the use of drift dependent paths in Monte Carlo simulation. We follow a drift-free simulation methodology by first simulating certain martingales and then obtaining the involved forward Libor rates in terms of them. More precisely, we propose a parameterization of those martingales so that the desired properties of the continuous models can be maintained after the discretization procedure when using either any intermediate forward measure or the spot one. Thus, the need of using the terminal measure to maintain these properties can be overcome. Finally, some numerical results concerning caplets pricing illustrate that the proposed method outperforms other ones existing in the literature.

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Notes

  1. The simulation time step \(\delta t\) is taken ensuring that the tenor dates are simulation dates.

  2. All market data have been obtained from a private stripping of Analistas Financieros Internacionales with data of Bloomberg on April 11, 2013.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, Francisco Tomás y Valiente, 7, 28049 , Madrid, Spain

    José L. Fernández

  2. Laboratoty of Analysis and Mathematical Modelling for Applied Sciences (LAMCA), Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina-Jadim Botánico 110, Rio de Janeiro, 22460-320, Brazil

    María R. Nogueiras

  3. Department of Mathematics, Faculty of Informatics, Universidade da Coruña, Campus Elviña s/n, 15071-A , Coruña, Spain

    Marta Pou & Carlos Vázquez

Authors
  1. José L. Fernández
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  2. María R. Nogueiras
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  3. Marta Pou
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  4. Carlos Vázquez
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Corresponding author

Correspondence to Carlos Vázquez.

Additional information

This paper has been partially funded by MICINN (Project MTM2010–21135–C02-01) and by Xunta de Galicia (Ayuda CN2011/004 cofunded with FEDER funds).

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Fernández, J.L., Nogueiras, M.R., Pou, M. et al. A new parameterization for the drift-free simulation in the Libor Market Model. RACSAM 109, 73–92 (2015). https://doi.org/10.1007/s13398-014-0167-5

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  • DOI: https://doi.org/10.1007/s13398-014-0167-5

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