DEL MORAL, Pierre; RÉMILLARD, Bruno; RUBENTHALER, Sylvain

doi:10.1007/978-3-642-25746-9_4

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DEL MORAL, Pierre
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

RÉMILLARD, Bruno
Groupe d'études et de recherche en analyse des décisions (GERAD)

RUBENTHALER, Sylvain
Laboratoire Jean Alexandre Dieudonné [LJAD]

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Communication dans un congrès

Ce document a été publié dans

Numerical Methods in Finance, Numerical Methods in Finance, Numerical Methods in Finance, Bordeaux June 2011, 2011-06-01, Bordeaux. 2012, vol. 12, p. 115-143

Springer

Résumé en anglais

It can be shown that when the payoff function is convex and decreasing (re- spectively 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.< Réduire

Mots clés en anglais

Mathematical finance

convexity

American option

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MONTE CARLO APPROXIMATIONS OF AMERICAN OPTIONS THAT PRESERVE MONOTONICITY AND CONVEXITY

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Résumé en anglais

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