A parallel quasi-Monte Carlo approach to pricing multidimensional American options

Wan, Jie; Lai, Kevin A.; Kolkiewicz, Adam W.; Tan, Ken Seng

doi:10.1504/ijhpcn.2006.013487

Cited by 11 publications

(11 citation statements)

References 17 publications

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“…Furthermore, known statistical properties of MC carry over to scrambled quasi random sequence and thus allowing partial result validation and intermediate value checking. Wan et al [16] present a parallel strategy for pricing multidimensional American options. In the first stage, the QMC sequence is generated by independently computing equally sized blocks on the PEs using static load distribution.…”

Section: Qmc Techniques In Grid Environmentsmentioning

confidence: 99%

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Hofbauer

Uhl

Zinterhof

2006

Parallel Process. Lett.

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The splitting of Quasi-Monte Carlo (QMC) point sequences into interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower the traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the proposals made in literature so far. In numerical integration experiments we investigate the quality of single leaped QMC point sequence substreams, comparing the respective properties of Sobol', Halton, Faure, Niederreiter-Xing, and Zinterhof sequences in detail. Numerical integration results obtained on a distributed system show that leaping sensitivity varies tremendously among the different sequences and we provide examples of deteriorated results caused by leaping effects, especially in heterogeneous settings which would be expected in GRID environments.

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Section: Qmc Techniques In Grid Environmentsmentioning

confidence: 99%

Quasi Monte Carlo Integration in Grid Environments: Further Leaping Effects

Hofbauer

Uhl

Zinterhof

2006

Parallel Process. Lett.

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“…The equation of dynamic programming generalises previous work in classical mechanics. Historically applied in engineering and other areas of applied mathematics, the Hamilton-Jacobi-Bellman equation has become an important tool in decision making problems involving economics and financial markets (see Dong et al, 2015;Wan et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Parallel solution of the discretised and linearised G-heat equation

Spitéri

Ouaoua

Chau³

et al. 2018

IJHPCN

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The present study deals with the numerical solution of the G-heat equation. Since the G-heat equation is defined in an unbounded domain, we firstly state that the solution of the G-heat equation defined in a bounded domain converges to the solution of the G-heat equation when the measure of the domain tends to infinity. Moreover, after time discretisation by an implicit time marching scheme, we define a method of linearisation of each stationary problem, which leads to the solution of a large scale algebraic system. A unified approach analysis of the convergence of the sequential and parallel relaxation methods is given. Finally, we present the results of numerical experiments. . He teaches numerical analysis, optimisation and numerical solution of boundary value problems. His fields of interest are in numerical analysis, large scale nonlinear systems of evolution equations, optimal control, parallel computing and more particularly, domain decomposition methods for the solution of nonlinear boundary values problems; he is interested to apply the obtained theoretical results to applications concerning finance, image processing, mechanics, etc. He is also a scientific expert, advisor and referee for several international scientific committees and journals.

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“…But the task is not easy, especially when the number of underlying assets is large [3,21], ruling out the PDE approach [2]. Furthermore the most popular sequential algorithm is the Least Square Monte-Carlo (LSMC) method of Longstaff and Schwartz [18].…”

Section: Introductionmentioning

confidence: 99%