Capital Requirements with Defaultable Securities

Walter Farkas, Pablo Koch-Medina and Cosimo Munari
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Walter Farkas: University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zurich
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

No 13-66, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 (search for similar items in EconPapers)
JEL-codes: C60 G11 G22 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2013-12
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1366

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