International Conference on Monte Carlo techniques
Closing conference of thematic cycle

Paris July 5-8th 2016 
Campus les cordeliers
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Pricing American options using martingale bases
Jérome Lelong  1@  
1 : Laboratoire Jean Kuntzmann  (LJK)  -  Website
Université Grenoble Alpes
Tour IRMA 51 rue des Mathématiques - 53 38041 GRENOBLE CEDEX 9 -  France

In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers [2002]. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation technique to efficiently solve the optimization problem. Unlike all the regression based methods, our method can transparently deal with path dependent options without extra computations and a parallel implementation writes easily with very little communication and no centralized work. We test our approach on several multi–dimensional options with up to 40 assets and show the impressive scalability of the parallel implementation. 



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