Asynchronous grid computation for American options derivatives |
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| Affiliation: | 1. RACE, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8568, Japan;2. School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;3. JGC Corporation, 2-3-1 Minato Mirai, Nishi-ku, Yokohama 220-6001, Japan;1. WEST Aquila S.r.l., L’Aquila, Italy;2. CES Laboratory, National School of Engineers of Sfax, Sfax, Tunisia;3. COINS Research Group, Prince Sultan University, Saudi Arabia;4. CISTER/INESC-TEC, ISEP, Politécnico do Porto, Portugal;5. Albacete Research Institute of Informatics, University of Castilla-La Mancha, Spain;6. ISEP, Politécnico do Porto, Portugal |
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| Abstract: | In relation with the mathematics of financial applications, the present study deals with the solution of the time dependent obstacle problem defined in a three-dimensional domain; this problem arises in the pricing of American options derivatives. In order to solve very quickly large scale algebraic systems derived from the discretization of the obstacle problem, the parallelization of the numerical algorithm is necessary. So, we present parallel synchronous, and more generally asynchronous, iterative algorithms to solve this problem. For the considered problem, arguments implying the convergence of parallel synchronous and asynchronous algorithms are given in a general framework. Finally, computational experiments on GRID’5000, the French national grid, are presented and analyzed. They allow us to compare both synchronous and asynchronous versions with local and distributed clusters and to show the interest of such methods in the context of grid computing. |
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