Robust Measurement of (Heavy-Tailed) Risks: Theory and Implementation

37 Pages Posted: 14 Oct 2013 Last revised: 23 Mar 2015

See all articles by Judith C. Schneider

Judith C. Schneider

University of Muenster - Finance Center Muenster

Nikolaus Schweizer

Tilburg School of Economics and Management

Date Written: August 12, 2014

Abstract

Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present an SMC (Sequential Monte Carlo) algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach.

Keywords: Robustness, Model Risk, Worst-Case Risk, Risk Management, Kullback-Leibler Divergence, Divergence Estimation, Sequential Monte Carlo

JEL Classification: G22, G32, C6

Suggested Citation

Schneider, Judith C. and Schweizer, Nikolaus, Robust Measurement of (Heavy-Tailed) Risks: Theory and Implementation (August 12, 2014). Available at SSRN: https://ssrn.com/abstract=2339724 or http://dx.doi.org/10.2139/ssrn.2339724

Judith C. Schneider (Contact Author)

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany

Nikolaus Schweizer

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

Register to save articles to
your library

Register

Paper statistics

Downloads
273
Abstract Views
1,303
rank
110,074
PlumX Metrics