New Ways to Measure Catastrophic Financial Risks: “<i>VaR</i>  to the power of <i> t</i>” Measures and How to Calculate Them

Abstract

The work introduces a family of new risk measures, “VaR to the power of t”. The aim of the work is to study the properties of this family of measures and to derive formulas to calculate them. The study used methods for assessing financial risks by risk measures VaR and ES. As a result, the author proposed a new tool to measure catastrophic financial risks — “VaR to the power of t”. The study proved that for the measuring, it is sufficient to calculate the common risk measure VaR with the confidence probability changed in a certain way. The author concludes that this family of measures should find application in solving the problem of penetrating risk events with low probabilities, but with catastrophic financial losses. The study results may be of use to the regulator to assess the capital adequacy of financial institutions. If t > 1, these measures prove to be more conservative risk measures of catastrophic losses than the known risk measures VaR, ES and GlueVaR.

Keywords

• risk measure var
• risk measure es
• risk measure var squared: <i><strong>var</strong>⁽²⁾</i>
• risk measures <i>var</i> to the <i>t</i> power: <i><strong>var</strong>^(t)</i>
• risk measures gluevar
• confidence probability
• probability density distribution
• distortion risk measures
• risk appetite
• subadditivity
• tails of distribution