Monte Carlo valuation of multidimensional American options through Grid computing
Résumé
We investigate several ways to implement a financial algorithm on a Grid architecture. The chosen algorithm is used to value an American stock option on the maximum of several assets. Such an evaluation has been a standard case in financial mathematics for the last years. These stock options become more and more common but cannot be easily valuated: the complexity of the usual algorithms grows exponentially with some parameters (number of assets involved, number of exercise date). Algorithms based on simulation (Broadie and Glasserman, [2,3]) often need prohibitive computational efforts. Fu and al. [4] show that for a option on five assets, some methods do not terminate in less than ten hours of computational time (tests made on a Sun Ultra5 in 2000), whereas a trader in a financial institution doesn’t have more than a few minutes to deal with the valuation of such an option. As a consequence, recent papers tend to explore parametrization methods for the space state or the exercise frontier. Longstaff and Schwartz ’s algorithm [8], proposed in 2001, belongs to this trend. However, results seems to be very sensitive to the parameters and the choice of basis functions. Investigation on the loss of precision must be made.