scholarly journals Real-Valued Systemic Risk Measures

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1016
Author(s):  
Alessandro Doldi ◽  
Marco Frittelli
Keyword(s):  
Systemic Risk ◽  
Risk Measures ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Initial Time ◽  
Exchange Equilibrium ◽  
Coherent Measures Of Risk ◽  
Additional Information ◽  
Dynamic Framework ◽  
Natural Counterpart

We describe the axiomatic approach to real-valued Systemic Risk Measures, which is a natural counterpart to the nowadays classical univariate theory initiated by Artzner et al. in the seminal paper “Coherent measures of risk”, Math. Finance, (1999). In particular, we direct our attention towards Systemic Risk Measures of shortfall type with random allocations, which consider as eligible, for securing the system, those positions whose aggregated expected utility is above a given threshold. We present duality results, which allow us to motivate why this particular risk measurement regime is fair for both the single agents and the whole system at the same time. We relate Systemic Risk Measures of shortfall type to an equilibrium concept, namely a Systemic Optimal Risk Transfer Equilibrium, which conjugates Bühlmann’s Risk Exchange Equilibrium with a capital allocation problem at an initial time. We conclude by presenting extensions to the conditional, dynamic framework. The latter is the suitable setup when additional information is available at an initial time.

CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

2019 ◽  
Vol 34 (2) ◽  
pp. 297-315
Author(s):  
Linxiao Wei ◽  
Yijun Hu
Keyword(s):  
Standard Deviation ◽  
Portfolio Management ◽  
Risk Measures ◽  
Risk Measure ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Axiom System ◽  
Multivariate Risk ◽  
Multivariate Risk Measures ◽  
Multivariate Risk Measure

AbstractCapital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

scholarly journals Early warning of systemic risk in global banking: eigen-pair R number for financial contagion and market price-based methods

2021 ◽  
Author(s):  
Sheri Markose ◽  
Simone Giansante ◽  
Nicolas A. Eterovic ◽  
Mateusz Gatkowski
Keyword(s):  
Early Warning ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Market Price ◽  
System Stability ◽  
Conditional Value At Risk ◽  
Centrality Measures ◽  
Global Banking ◽  
Pair Method

AbstractWe analyse systemic risk in the core global banking system using a new network-based spectral eigen-pair method, which treats network failure as a dynamical system stability problem. This is compared with market price-based Systemic Risk Indexes, viz. Marginal Expected Shortfall, Delta Conditional Value-at-Risk, and Conditional Capital Shortfall Measure of Systemic Risk in a cross-border setting. Unlike paradoxical market price based risk measures, which underestimate risk during periods of asset price booms, the eigen-pair method based on bilateral balance sheet data gives early-warning of instability in terms of the tipping point that is analogous to the R number in epidemic models. For this regulatory capital thresholds are used. Furthermore, network centrality measures identify systemically important and vulnerable banking systems. Market price-based SRIs are contemporaneous with the crisis and they are found to covary with risk measures like VaR and betas.

scholarly journals Sharing Risk – An Economic Perspective

2009 ◽  
Vol 39 (2) ◽  
pp. 591-613 ◽  
Author(s):  
Andreas Kull
Keyword(s):  
Value At Risk ◽  
Risk Sharing ◽  
Risk Measures ◽  
Insurance Industry ◽  
Risk Measure ◽  
Capital Allocation ◽  
Risk Capital ◽  
Risk Class ◽  
Capital Costs ◽  
Risk Transfer

AbstractWe revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

Short Communication: Robust Market-Adjusted Systemic Risk Measures

2021 ◽  
Vol 12 (3) ◽  
pp. SC70-SC82
Author(s):  
Matteo Burzoni ◽  
Marco Frittelli ◽  
Federico Zorzi
Keyword(s):  
Systemic Risk ◽  
Short Communication ◽  
Risk Measures

Systemic Risk, Stress Testing, and Financial Contagion

2014 ◽  
pp. 282-310
Author(s):  
Calixto Lopez-Castañon ◽  
Serafin Martinez-Jaramillo ◽  
Fabrizio Lopez-Gallo
Keyword(s):  
Systemic Risk ◽  
Research Agenda ◽  
Stress Testing ◽  
Risk Measures ◽  
Banking System ◽  
Financial Contagion ◽  
Interbank Market ◽  
Coherent Risk ◽  
Central Bankers ◽  
Standard Risk

Despite the acknowledgment of the relevance of Systemic Risk, there is a lack of consensus on its definition and, more importantly, on the way it should be measured. Fortunately, there is a growing research agenda and more financial regulators, central bankers, and academics have recently been focusing on this field. In this chapter, the authors obtain a distribution of losses for the banking system as a whole. They are convinced that such distribution of losses is the key element that could be used to develop relevant measures for systemic risk. Their model contemplates several aspects, which they consider important regarding the concept of systemic risk: an initial macroeconomic shock, which weakens some institutions (some of them to the point of failure), a contagion process by means of the interbank market, and the resulting losses to the financial system as a whole. Finally, once the distribution is estimated, the authors derive standard risk measures for the system as a whole, focusing on the tail of the distribution (where the catastrophic or systemic events are located). By using the proposed framework, it is also possible to perform stress testing in a coherent way, including second round effects like contagion through the interbank market. Additionally, it is possible to follow the evolution of certain coherent risk measures, like the CVaR, in order to evaluate if the system is becoming more or less risky, in fact, more or less fragile. Additionally, the authors decompose the distribution of losses of the whole banking system into the systemic and the contagion elements and determine if the system is more prone to experience contagious difficulties during a certain period of time.

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