F. Akesson and J. P. Lehoczy. Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Science, 46:1171-1187, 2000. Home/Search Document Details and Download
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Recent Advances In Randomized Quasi-Monte Carlo Methods - L'Ecuyer (Correct)
....e ort, i.e. that the eciency is improved. A second class of methods that can reduce the variance of QMC estimators for certain functions are dimension reduction methods. Among this class are the Brownian bridge technique of Ca isch and Moskovitz [12] approaches based on principal components [1, 2], and various methods discussed by Fox [33] for generating Poisson and other stochastic processes. Typically, these methods are used when f is de ned in terms of a stochastic process for which a sample path is generated using the uniform numbers u i1 ; u is provided by a point u i in ....
F. Akesson and J. P. Lehoczy. Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Science, 46:1171-1187, 2000.
On the Use of Quasi-Monte Carlo Methods in Computational Finance - Lemieux, L'Ecuyer (1 citation) (Correct)
....variance of the function in a way that concentrates the remaining variance in very small regions, and this makes it harder for QMC to improve upon MC. Techniques for reducing the e#ective dimension are useless to improve MC simulations, but they can greatly enhance the performance of QMC methods [9, 32, 1, 10, 27, 2]. We discuss two of them: the Brownian bridge (BB) and the principal components (PC) techniques. The idea of BB was first introduced in [9] and can be used to generate a Brownian motion at T di#erent times B(t 1 ) B(t T ) by using T uniform numbers u 1 , u T . Instead of ....
....this decomposition [1] An advantage of this approach over BB is that it can be used to generate prices of correlated assets whereas BB can only be applied for generating prices coming from a single path. However, PC requires more computation time than BB for the generation of the prices, but see [2] for a way of speeding up PC. 5 Broadening the Range of Applications We conclude this paper by discussing applications that go beyond the context discussed in Section 3. One such application is the estimation of derivatives (or gradients) of prices with respect to one (or more) parameter(s) ....
F. Akesson and J. P. Lehoczy. Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Science, 46:1171--1187, 2000.
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