50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications
Management Science
Numerical solution of two asset jump diffusion models for option valuation
Applied Numerical Mathematics
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
The Fast Generalized Gauss Transform
SIAM Journal on Scientific Computing
An efficient and easily parallelizable algorithm for pricing weather derivatives
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
On the Heston Model with Stochastic Interest Rates
SIAM Journal on Financial Mathematics
Fast Approximation of the Discrete Gauss Transform in Higher Dimensions
Journal of Scientific Computing
Manufacturing & Service Operations Management
Heterogeneous COS pricing of rainbow options
WHPCF '13 Proceedings of the 6th Workshop on High Performance Computational Finance
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In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requiresO( NN') work when there areN' summations to compute and the number of terms appearing in each summation isN, we can reduce the amount of work toO( N +N') by using a technique called the fast Gauss transform. In this paper, we apply this technique to the multinomial method and the stochastic mesh method, and show by numerical experiments how it can speed up these methods dramatically, both for the Black-Scholes model and Merton's lognormal jump-diffusion model. We also propose extensions of the fast Gauss transform method to models with non-Gaussian densities.