Large Deviations of Factor Models with Regularly-Varying Tails: Asymptotics and Efficient Estimation
24 Pages Posted: 14 Mar 2017 Last revised: 23 Sep 2017
Date Written: March 1, 2017
I analyze the large deviation probability of factor models generated from components with regularly-varying tails, a large subclass of heavy tailed distributions. An efficient sampling method for tail probability estimation of this class is introduced and shown to exponentially outperform the classical Monte-Carlo estimator, in terms of the coverage probability and/or the confidence interval’s length. The obtained theoretical results are applied to financial portfolios, verifying that deviation probability of the return to portfolios of many securities is asymptotically robust against the distributions of asset specific idiosyncratic risks.
Keywords: Monte-Carlo Method, Tail Estimation, Pareto Distribution
JEL Classification: C13, C15, C38, C58
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