Tail behavior of sums and differences of log-normal random variables
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to be determined by a subset of components of the Gaussian vector, and we identify the relevant components by relating the asymptotics to a tractable quadratic optimization problem. As a corollary, we characterize the limiting behavior of the conditional law of the Gaussian vector, given a linear combination of the exponentials of its components. Our results can be used either to estimate the probability of tail events directly, or to construct efficient variance reduction procedures for precise estimation of these probabilities by Monte Carlo methods. They lead to important insights concerning the behavior of individual stocks and portfolios during market downturns in the multidimensional Black-Scholes model.
Year of publication: |
2013-09
|
---|---|
Authors: | Gulisashvili, Archil ; Tankov, Peter |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
Implied volatility of basket options at extreme strikes
Gulisashvili, Archil, (2014)
-
Distance to the line in the Heston model
Gulisashvili, Archil, (2014)
-
The Heston Riemannian distance function
Gulisashvili, Archil, (2013)
- More ...