Capital requirements with defaultable securities

Walter Farkas, Pablo Koch-Medina and Cosimo Munari

Insurance: Mathematics and Economics, 2014, vol. 55, issue C, 58-67

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 numéraire. 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 assets; Risk measures; Capital adequacy; Defaultable securities; Value-at-Risk; Tail Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C60 G11 G22 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:55:y:2014:i:c:p:58-67

DOI: 10.1016/j.insmatheco.2013.11.009

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