Efficient Simulation of Tail Probabilities of Sums of Correlated Lognormals (with S. Asmussen, S. Juneja, and L. Rojas-Nandayapa)

Summary:

Part of the motivation of this paper lies in value-at-risk calculations involving the tail of a loss distribution corresponding to a portfolio that has several stocks in a short position. We assume a Black-Scholes type economy and this gives rise to estimating the tail of correlated lognormal random variables. Most simulation methods assume either Gaussian or t-distributed factors and are justified by means of a so-called Delta-Gamma approximation (see the text of Paul Glasserman for to learn more about this approach). The algorithms in this paper concentrate on the original quantity of interest and we are even able to show vanishing relative error for some of the estimators. Also, cross-entropy implementations are studied.

Bibtex:

@Article{AsmBlaJunRo2009,

author = {S. Asmussen and J. Blanchet and S. Juneja and L. Rojas-Nandayapa},

title = {Efficient simulation of tail probabilities of sums of correlated lognormals},

journal = {Annals of Operations Research},

year = {Forthcoming},

volume = {},

pages = {}

}