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Toward a coherent Monte Carlo simulation of CVA

Author

Listed:
  • Abbas-Turki Lokman A.

    (Institut für Mathematik, TU Berlin, Building MA, Straße des 17. Juni 136, 10623 Berlin, Germany)

  • Bouselmi Aych I.

    (Laboratoire d' Analyse et de Mathématiques Appliquées, 5, Boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France)

  • Mikou Mohammed A.

    (Département des Mathématiques, EISTI Campus de Cergy, Avenue du Parc, 95011 Cergy-Pontoise Cedex, France)

Abstract

This paper is devoted to the simulation of the Credit Valuation Adjustment (CVA) using a pure Monte Carlo technique with Malliavin calculus (MCM). The procedure presented is based on a general theoretical framework that includes a large number of models as well as various contracts, and allows both the computation of CVA and its sensitivity with respect to the different assets. Moreover, we provide the expression of the backward conditional density of assets vector that can be simulated off-line in order to reduce the variance of the CVA estimator. Using the suitability of MCM to parallel architectures and thus to a Graphic Processing Unit (GPU) implementation, we show that the results obtained are accurate once a sufficient number of trajectories is simulated. Both complexity and accuracy are studied for MCM and regression methods and are compared to the square Monte Carlo benchmark.

Suggested Citation

  • Abbas-Turki Lokman A. & Bouselmi Aych I. & Mikou Mohammed A., 2014. "Toward a coherent Monte Carlo simulation of CVA," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 195-216, September.
    • Handle: RePEc:bpj:mcmeap:v:20:y:2014:i:3:p:195-216:n:3
    DOI: 10.1515/mcma-2013-0026
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    References listed on IDEAS

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