Efficient simulation of tail probabilities of sums of correlated lognormals

Asmussen, Søren, Blanchet, José, Juneja, Sandeep and Rojas-Nandayapa, Leonardo (2011) Efficient simulation of tail probabilities of sums of correlated lognormals. Annals of Operations Research, 189 1: 5-23. doi:10.1007/s10479-009-0658-5

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Author Asmussen, Søren
Blanchet, José
Juneja, Sandeep
Rojas-Nandayapa, Leonardo
Title Efficient simulation of tail probabilities of sums of correlated lognormals
Journal name Annals of Operations Research   Check publisher's open access policy
ISSN 0254-5330
Publication date 2011-09
Year available 2009
Sub-type Article (original research)
DOI 10.1007/s10479-009-0658-5
Volume 189
Issue 1
Start page 5
End page 23
Total pages 19
Place of publication Secaucus, NJ, U.S.A.
Publisher Springer New York
Collection year 2012
Language eng
Formatted abstract
We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be efficient as the tail probability of interest decreases to zero. The first estimator, based on importance sampling, involves a scaling of the whole covariance matrix and can be shown to be asymptotically optimal. A further study, based on the Cross-Entropy algorithm, is also performed in order to adaptively optimize the scaling parameter of the covariance. The second estimator decomposes the probability of interest in two contributions and takes advantage of the fact that large deviations for a sum of correlated lognormals are (asymptotically) caused by the largest increment. Importance sampling is then applied to each of these contributions to obtain a combined estimator with asymptotically vanishing relative error.
Keyword Black-Scholes model
Correlated lognormals
Cross-entropy method
Importance sampling
Rare-event simulation
Vanishing relative error
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online: 28 October, 2009.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2012 Collection
ERA 2012 Admin Only
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Citation counts: TR Web of Science Citation Count  Cited 11 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 02 Dec 2010, 13:51:54 EST by Dr Leonardo Rojas-nandayapa on behalf of School of Mathematics & Physics