Risk Measures Based on Benchmark Loss Distributions

Valeria Bignozzi, Matteo Burzoni and Cosimo Munari
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Valeria Bignozzi: Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi
Matteo Burzoni: ETH Zurich
Cosimo Munari: University of Zurich - Department of Banking and Finance; Swiss Finance Institute

No 18-48, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We introduce a class of quantile-based risk measures that generalize Value at Risk (VaR) and, likewise Expected Shortfall (ES), take into account both the frequency and the severity of losses. Under VaR a single confidence level is assigned regardless of the size of potential losses. We allow for a range of confidence levels that depend on the loss magnitude. The key ingredient is a benchmark loss distribution (BLD), i.e.~a function that associates to each potential loss a maximal acceptable probability of occurrence. The corresponding risk measure, called Loss VaR (LVaR), determines the minimal capital injection that is required to align the loss distribution of a risky position to the target BLD. By design, one has full flexibility in the choice of the BLD profile and, therefore, in the range of relevant quantiles. Special attention is given to piecewise constant functions and to tail distributions of benchmark random losses, in which case the acceptability condition imposed by the BLD boils down to first-order stochastic dominance. We provide a comprehensive study of the main finance theoretical and statistical properties of LVaR with a focus on their comparison with VaR and ES. Merits and drawbacks are discussed and applications to capital adequacy, portfolio risk management and catastrophic risk are presented.

Keywords: risk measures; loss distributions; tail risk; capital adequacy; portfolio management; catastrophic risk; robustness; backtestability (search for similar items in EconPapers)
JEL-codes: D81 G32 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2018-01, Revised 2018-11
New Economics Papers: this item is included in nep-ore and nep-rmg
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1848

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