Area-Efficient VLSI Computation by Charles E. Leiserson

By Charles E. Leiserson

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The actual computation of the transition intensities is done by means of linear programming, which is a time-consuming process but one that can be easily parallelized. Once the transition matrix has been constructed, prices can be computed quickly. The method is tested on geometric average options in up to ten dimensions. Accurate results are obtained, in particular when use is made of a simple bias control technique. 1 INTRODUCTION The pricing of American options has been extensively discussed in recent years (cf.

5) In applications, the number of grid points n is typically on the order 10 or 105 . In the actual implementation, we drastically reduced the number of variables by taking into consideration only variables ai j , such that the corresponding grid points x j are close to the given point xi . In this way, we simplify the feasibility problem and moreover obtain a sparse infinitesimal generator matrix. To obtain specific solutions, it is useful to convert the feasibility problem to an optimization problem by adding an objective function.

5 Boundary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Geometric Average Options . . . . . . . . . . . . . . . . . . 2 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Experimental Details . . . . . . . . . . . . . . . . . . .

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