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Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity

  • Pierre Del Moral
  • Bruno RémillardEmail author
  • Sylvain Rubenthaler
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 12)

Abstract

It can be shown that when the payoff function is convex and decreasing (respectively increasing) with respect to the underlying (multidimensional) assets, then the same is true for the value of the associated American option, provided some conditions are satisfied. In such a case, all Monte Carlo methods proposed so far in the literature do not preserve the convexity or monotonicity properties. In this paper, we propose a method of approximation for American options which can preserve both convexity and monotonicity. The resulting values can then be used to define exercise times and can also be used in combination with primal-dual methods to get sharper bounds. Other application of the algorithm include finding optimal hedging strategies.

Keywords

American option Bermudan option Simulation Exercise region Snell envelope Dynamic programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pierre Del Moral
    • 1
    • 2
  • Bruno Rémillard
    • 3
    Email author
  • Sylvain Rubenthaler
    • 4
  1. 1.INRIA Bordeaux-Sud Ouest, Bordeaux Mathematical InstituteUniversité Bordeaux ITalence cedexFrance
  2. 2.Centre de Mathématiques AppliquéesÉcole Polytechnique CNRSPalaiseauFrance
  3. 3.Department of Management Sciences and GERADHEC MontréalMontréalCanada
  4. 4.Laboratoire de mathématiques J.A. DieudonnéUniversité de Nice-Sophia AntipolisNice cedex 02France

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