Capital Requirements with Defaultable Securities

24 Pages Posted: 1 Dec 2011 Last revised: 11 Mar 2014

See all articles by Walter Farkas

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich

Pablo Koch-Medina

University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Cosimo Munari

University of Zurich - Department of Banking and Finance; Swiss Finance Institute

Date Written: May 18, 2013

Abstract

We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the payoff of these assets is not necessarily bounded away from zero the resulting risk measures cannot be transformed into cash-additive risk measures by a change of numeraire. However, extending the range of eligible assets is important because, as exemplified by the recent financial crisis, assuming the existence of default-free bonds may be unrealistic. We focus on finiteness and continuity properties of these general risk measures. As an application, we discuss capital requirements based on Value-at-Risk and Tail-Value-at-Risk acceptability, the two most important acceptability criteria in practice. Finally, we prove that there is no optimal choice of the eligible asset. Our results and our examples show that a theory of capital requirements allowing for general eligible assets is richer than the standard theory of cash-additive risk measures.

Keywords: acceptance sets, eligible asset, risk measures, capital adequacy, capital efficiency, Value-at-Risk, Tail Value-at-Risk

JEL Classification: C60, G11, G22

Suggested Citation

Farkas, Walter and Koch-Medina, Pablo and Munari, Cosimo, Capital Requirements with Defaultable Securities (May 18, 2013). Insurance: Mathematics and Economics, 55 (2014); Swiss Finance Institute Research Paper No. 13-66. Available at SSRN: https://ssrn.com/abstract=1966645 or http://dx.doi.org/10.2139/ssrn.1966645

Walter Farkas (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Pablo Koch-Medina

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Cosimo Munari

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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