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Abstract: This paper develops a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which... (Update)
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...examples come from particle physics and Bayesian statistics. Spiky integrands also arise in computational finance (Glasserman, 1 Heidelberger Shahabuddin 1999, Owen Zhou 1999) computer graphics (Veach Guibas 1995) and reliability (Hesterberg 1995) For d = 1 and...
...distribution. The method combines importance sampling and stratified sampling in the spirit of Glasserman, Heidelberger, and Shahabuddin [22, 23, 24]. But the methods in [22, 23, 24] assumed a multivariate normal distribution and, as is often the case in importance sampling,...
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BibTeX entry: (Update)
Glasserman, P., P. Heidelberger, and P. Shahabuddin, "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options," Math. Finance, 9, no. 2, 1999 (to appear). http://citeseer.ist.psu.edu/glasserman99asymptotically.html More
@misc{ glasserman99asymptotically,
author = "P. Glasserman and P. Heidelberger and P. Shahabuddin",
title = "Asymptotically Optimal Importance Sampling and Stratification for Pricing
Path-Dependent Options",
text = "Glasserman, P., P. Heidelberger, and P. Shahabuddin, Asymptotically Optimal
Importance Sampling and Stratification for Pricing Path-Dependent Options,
Math. Finance, 9, no. 2, 1999 (to appear).",
year = "1999",
url = "citeseer.ist.psu.edu/glasserman99asymptotically.html" }
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