Giacomo Scandolo

Robustness and sensitivity analysis of risk measurement procedures

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ‘risk measure’ that summarizes the risk of the portfolio. We define the notion of ‘risk measurement procedure’, which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.

Risk Measures and Capital Requirements for Processes

In 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 presented.

Assessing Financial Model Risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.

Liquidity risk and coherent risk measures

We 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 V ℒ(p) that depends on a new notion of ‘liquidity policy’ ℒ. The function V ℒ(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 V ℒ(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.

Decision SupportAssessing financial model risk

Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a given class: the absolute measure of model risk, the relative measure of model risk and the local measure of model risk. Each of the measures has a specific purpose and so allows for flexibility. We illustrate the various notions by studying some relevant examples, so as to emphasize the practicability and tractability of our approach.

Measuring Model Risk in the European Energy Exchange

It has been shown that model risk has an important effect on any risk measurement procedures, hence its proper quantification is becoming crucial especially in energy markets, where market participants face several kinds of risks (such as volumetric, liquidity, and operational risk). Therefore, relaxing the assumption of normality and using a wide range of alternative distributions, we quantify the model risk in the German wholesale electricity market (the European Energy Exchange, EEX) by studying day–ahead electricity prices from 2001 to 2013 using the well-established setting of GARCH–type models. Taking advantage of this long price history, we investigate the “time evolution” of the measured model risk across years by adopting a rolling window procedure. Our results confirm that the increasing complexity of energy markets has affected the stochastic nature of electricity prices which have become progressively less normal through years, hence resulting in an increased model risk.

Fukushima effect on commodity prices

This paper analyzes the effect of the earthquake occurred in March 2011 in Japan on nuclear power generation. More specifically as natural consequence, the hypothesis of moving towards generating sources different from nuclear are explored. Given the CO2 constraints and the discussion on biomass generation affecting the agricultural commodities prices, in a long-term perspective it is expected to observe a migration from thermal conventional electricity generation to renewable generation. Therefore, this study is provides some evidence on the effect of nuclear crisis caused by Fukushima on commodities prices of both energy and agricultural markets. We perform an event study analysis of abnormal returns considering short, medium and long run horizons.