SIAM Journal on Scientific and Statistical Computing
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
A New Error Estimate of the Fast Gauss Transform
SIAM Journal on Scientific Computing
A Jump-Diffusion Model for Option Pricing
Management Science
Application of the Fast Gauss Transform to Option Pricing
Management Science
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
An efficient and easily parallelizable algorithm for pricing weather derivatives
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Fast Approximation of the Discrete Gauss Transform in Higher Dimensions
Journal of Scientific Computing
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This paper develops algorithms for the pricing of discretely sampled barrier, lookback, and hindsight options and discretely exercisable American options. Under the Black-Scholes framework, the pricing of these options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. We compute these convolutions efficiently using the double-exponential integration formula and the fast Gauss transform. The resulting algorithms have computational complexity of O(nN), where the number of monitoring/exercise dates is n and the number of sample points at each date is N, and our results show the error decreases exponentially with N. We also extend the approach and provide results for Merton's lognormal jump-diffusion model.