IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1848.html
   My bibliography  Save this paper

Risk Measures Based on Benchmark Loss Distributions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Valeria Bignozzi & Matteo Burzoni & Cosimo Munari, 2018. "Risk Measures Based on Benchmark Loss Distributions," Swiss Finance Institute Research Paper Series 18-48, Swiss Finance Institute, revised Nov 2018.
  • Handle: RePEc:chf:rpseri:rp1848
    as

    Download full text from publisher

    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3088423
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tobias Fissler & Jana Hlavinov'a & Birgit Rudloff, 2019. "Elicitability and Identifiability of Systemic Risk Measures," Papers 1907.01306, arXiv.org, revised Oct 2019.
    2. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.

    More about this item

    Keywords

    risk measures; loss distributions; tail risk; capital adequacy; portfolio management; catastrophic risk; robustness; backtestability;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:chf:rpseri:rp1848. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.