Liquidity-adjusted risk measures

Weber, Stefan; Anderson, Warwick; Hamm, Anna-Maria; Knispel, Thomas; Liese, M.; Salfeld, Thomas

doi:10.1007/s11579-012-0092-3

Cited by 22 publications

(12 citation statements)

References 12 publications

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“…This was one of the reasons in Föllmer & Schied (2002) to go beyond coherence and to introduce the general notion of a convex risk measure. A similar argument applies to liquidityadjusted valuation and risk measures, see Remark 3.11 in Weber, Anderson, Hamm, Knispel, Liese & Salfeld (2013).…”

Section: Convex and Coherent Risk Measuresmentioning

confidence: 78%

The Axiomatic Approach to Risk Measures for Capital Determination

Föllmer

Weber

2015

Annu. Rev. Financ. Econ.

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The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.

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Section: Convex and Coherent Risk Measuresmentioning

confidence: 78%

The Axiomatic Approach to Risk Measures for Capital Determination

Föllmer

Weber

2015

Annu. Rev. Financ. Econ.

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“…Acerbi and Scandolo (2007) define a coherent standard risk measure on the liquidity-adjusted value of the portfolio. Weber, Anderson, Hamm, Knispel, Liese, and Salfeld (2013) extend this approach and construct cash-invariant liquidity-adjusted risk measure. Allaj (2017) presents a theoretical framework for incorporating of liquidity risk, arising from a bank's trading activities in securities, into the standard risk measures and discusses the VaR measure.…”

Section: Complying With the Regulatory Requirementsmentioning

confidence: 99%

Stress Testing of Liquidity Maturity Transformation Risk in Banks

Schmitt¹

2018

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One of the main causes of the past crisis was the inability of financial institutions to acquire funding at appropriate costs. The importance of applying a good liquidity risk measurement system becomes apparent. The present paper provides an approach to the measurement of liquidity maturity transformation risk within a stress testing framework, for middle-sized banks. The costs of liquidity arising due to a downturn in refinancing conditions are calculated by using modern risk measures. The forward-looking way is based on a liquidity gap report, where the consideration of the counterbalancing capacity enables to gain an insight into the real liquidity needs. The measurement of both, the portfolio-value in the respective time bucket and liquidity costs, is possible. Applying the expected shortfall can easily be included into the calculation. The results show that by using historical simulation, if no sufficient data are available, expected shortfall delivers an approximate value. Still, it can serve as an indicator of insurance against extreme events. The present approach combines a scenario-based view to a possible distress with a quantitative risk measurement. Therewith, it contributes to the bank's wide stress testing as required by the regulatory authorities.

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“…For precisely this reason, convex risk measures were introduced in [18,20], rendering the curve (ρ(λX)) λ≥0 nonlinear. Nonetheless, explicit use of convex risk measures to quantify liquidity risk has been quite limited, and all such studies go well beyond the traditional setting by using more complex types of risk measures, such as liquidity-adjusted risk measures [1,39,25] or set-valued risk measures [26,24].…”

Section: Introductionmentioning

confidence: 99%

Liquidity, Risk Measures, and Concentration of Measure

Lacker

2018

Mathematics of OR

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Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form (ρ(λX)) λ≥0 , where ρ is a convex risk measure and X a random variable, and we call such a curve a liquidity risk profile. The shape of a liquidity risk profile is intimately linked with the tail behavior of the underlying X for some notable classes of risk measures, namely shortfall risk measures. We exploit this link to systematically bound liquidity risk profiles from above by other real functions γ, deriving tractable necessary and sufficient conditions for concentration inequalities of the form ρ(λX) ≤ γ(λ), for all λ ≥ 0. These concentration inequalities admit useful dual representations related to transport inequalities, and this leads to efficient uniform bounds for liquidity risk profiles for large classes of X. On the other hand, some modest new mathematical results emerge from this analysis, including a new characterization of some classical transport-entropy inequalities. Lastly, the analysis is deepened by means of a surprising connection between time consistency properties of law invariant risk measures and the tensorization of concentration inequalities.

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Liquidity-adjusted risk measures

Cited by 22 publications

References 12 publications

The Axiomatic Approach to Risk Measures for Capital Determination

The Axiomatic Approach to Risk Measures for Capital Determination

Stress Testing of Liquidity Maturity Transformation Risk in Banks

Liquidity, Risk Measures, and Concentration of Measure

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