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Conditional and dynamic convex risk measures
No full textWe extend the definition of a convex risk measure to a conditional framework
where additional information is available.We characterize these risk measures
through the associated acceptance sets and prove a representation result in terms
of conditional expectations.A suitable regularity property of conditional risk measures
is defined and discussed. Finally, we introduce the concept of a dynamic
convex risk measure as a family of successive conditional convex risk measures
and characterize those satisfying some natural time consistency properties.As a reference
example, illustrating all the proposed developments, we introduce a suitably
defined dynamic version of the class of entropic risk measure
Assessing model risk in financial and energy markets using dynamic conditional VaRs
Full text linkIt has been recognized that model risk has an important effect on any risk measurement procedures, particularly when dealing with complex markets and in the presence of a wide range of implemented models. We consider a normalized measure of model risk for the forecast of daily Value-at-Risk, combined with a model selection and an averaging procedure. This allows us to restrict the set of plausible models on a daily basis, making the initial choice of competing models less crucial and then yielding a more reliable assessment of model risk. Using AR-GARCH-type models with different distributions for the innovations, we assess the dynamics of model risk for different financial assets (a stock, an equity index, an exchange rate) and commodities (electricity, crude oil and natural gas) over 15 years
OPTIMAL PORTFOLIO ALLOCATION WITH CVAR: A ROBUSTAPPROACH
Full text linkThe paper discuss the sensitivity to the presence of outliers of the portfolio optimization procedure based on the expected shortfall as a measure of risk. A robust approach based on the forward search is then suggested which seems to give quite good results
Liquidity risk theory and coherent measures of risk
No full textWe discuss liquidity risk from a pure risk-theoretical point of view in the axiomatic context of coherent measures of risk. We propose a formalism for liquidity risk that is compatible with the axioms of coherency. We emphasize the difference between 'coherent risk measures' (CRM) ρ(X ) defined on portfolio values X as opposed to 'coherent portfolio risk measures' (CPRM) ρ(p) defined on the vector space of portfolios p, and we observe that in the presence of liquidity risk the value function on the space of portfolios is no longer necessarily linear. We propose a new nonlinear 'Value' function VL(p) that depends on a new notion of 'liquidity policy' L. The function VL(p) naturally arises from a general description of the impact that the microstructure of illiquid markets has when marking a portfolio to market. We discuss the consequences of the introduction of the function VL(p) in the coherency axioms and we study the properties induced on CPRMs. We show in particular that CPRMs are convex, finding a result that was proposed as a new axiom in the literature of so called 'convex measures of risk'. The framework we propose is not a model but rather a new formalism, in the sense that it is completely free from hypotheses on the dynamics of the market. We provide interpretation and characterization of the formalism as well as some stylized examples.Liquidity risk, Portfolio value, Coherent risk measures,
RISK MEASURES AND CAPITAL REQUIREMENTS FOR PROCESSES
No full textIn this paper we propose a generalization of the concepts of convex and coherent risk
measures to a multiperiod setting, in which payoffs are spread over different dates. To
this end, a careful examination of the axiom of translation invariance and the related
concept of capital requirement in the one-period model is performed. These two issues
are then suitably extended to the multiperiod case, in a way that makes their operative
financial meaning clear. A characterization in terms of expected values is derived for
this class of risk measures and some examples are presente
A worldwide analysis of the energy regulatory tasks and activities through the lenses of entropy and unsupervised statistical learning
Full text linkThis paper provides an overview of tasks and activities of world energy regulatory authorities, through their regional associations. Regulatory practices are investigated when looking at federal, state and national authorities’ replies to two surveys on electricity and gas markets. Empirical results show that the implementation of the energy regulation can be context-specific. Indeed, regulators’ powers and tools show diversity, even among groups of regulators belonging to the same regional associations and then expected to act homogeneously. To inspect the similarity across regulators, a statistical index and an unsupervised statistical learning technique are proposed. The usage of these two methods is recommended to inspect the status of the regulatory harmonization, and to inspect if uniformed and coordinated energy policy actions are achieved in view of global resolutions towards a low carbon transition, and delineated environmental and sustainable goals
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