Séance TA3 - Méthodes Monte-Carlo / Monte-Carlo Methods
Jour mardi, le 05 mai 2009 Salle Gérard Parizeau Président Pierre L'Écuyer
Présentations
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10h30- 10h55 |
Approximate Solutions to Dynamic Hedging with Transaction Costs by Least-Squares Monte Carlo |
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Pierre-Alexandre Tremblay, Université de Montréal, Informatique et Recherche Opérationelle, Montréal, Québec, Canada The Least-Squares Monte Carlo (LSM) algorithm of Longstaff and Schwarz approximates the value of american-style options using a combination of dynamic programming and linear regression. We extend the LSM algorithm to find approximate solutions for the problem of optimal dynamic hedging with transaction costs and present some examples. |
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10h55- 11h20 |
Quasi-Monte Carlo for Markov Chains: Application to Option Pricing |
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Adam L'Archevêque Gaudet, Université de Montréal, Informatique et recherche opérationnelle/CIRRELT/GERAD, Montréal, Québec, Canada Pierre L'Écuyer, GERAD, Université de Montréal, Informatique et recherche opérationnelle/CIRRELT/GERAD, C.P. 6128, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3J7 We present a randomized quasi-Monte Carlo method specially designed for the simulation of Markov chains, called array-RQMC. We give examples showing that this method can reduce the variance considerably in option pricing. In an Asian option example, we observe an O(1/n^2) convergence rate for the variance, whereas standard Monte Carlo gives O(1/n). |
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11h20- 11h45 |
American Option Pricing with Randomized Quasi-Monte Carlo |
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Maxime Dion, Université de Montréal, DIRO Pierre L'Écuyer, GERAD, Université de Montréal, Informatique et recherche opérationnelle/CIRRELT/GERAD, C.P. 6128, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3J7 We combine least-squares Monte Carlo with randomized Quasi-Monte Carlo methods (including array-RQMC) for the pricing of American options, where exercise policies must be optimized. We obtain significant variance reductions in comparison with standard Monte Carlo. |