Nonparametric estimation of Value-at-Risk

A method to estimate an extreme quantile that requires no distributional assumptions is presented. The approach is based on transformed kernel estimation of the cumulative distribution function (cdf). The proposed method consists of a double transformation kernel estimation. We derive optimal bandwidth selection methods that have a direct expression for the smoothing parameter. The bandwidth can accommodate to the given quantile level. The procedure is useful for large data sets and improves quantile estimation compared to other methods in heavy tailed distributions. Implementation is straightforward and R programs are available.

Beyond Value-at-Risk : GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed-form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between Glue-VaR, Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) is explained. Tail-subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in non-financial problems such as health, safety, environmental or catastrophic risk management

Avaluació del risc ambiental de productes farmacèutics en l'àmbit català

S’ha dut a terme una Avaluació del Risc Ambiental dels productes farmacèutics més consumits en l’àmbit català treballant sobre un model de planta de tractament d’aigües residuals determinat. La Concentració ambiental estimada (PEC) pel medi aquàtic s’ha calculat a partir de dades fisicoquímiques dels fàrmacs tenint en compte una sèrie d’hipòtesis i suposicions prèvies. La Concentració estimada de no-efecte (PNEC) s’ha estimat mitjançant dades d’ecotoxicitat extretes de l’ECOSAR. Es considera que hi ha afecció al medi quan la relació PEC/PNEC excedeix d’1; en aquest estudi s’ha obtingut que l’Ibuprofèn, el Diclofenac i l’Atorvastatina superen aquest valor suposant, per tant, un risc per al medi ambient. D’aquesta manera es mostra que l’eliminació dels fàrmacs durant el procés de la depuració de les aigües residuals no resulta totalment eficient.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

Stochastic optimal bid to electricity markets with environmental risk constraints

There are many factors that influence the day-ahead market bidding strategies of a generation company (GenCo) in the current energy market framework. Environmental policy issues have become more and more important for fossil-fuelled power plants and they have to be considered in their management, giving rise to emission limitations. This work allows to investigate the influence of both the allowances and emission reduction plan, and the incorporation of the derivatives medium-term commitments in the optimal generation bidding strategy to the day-ahead electricity market. Two different technologies have been considered: the coal thermal units, high-emission technology, and the combined cycle gas turbine units, low-emission technology. The Iberian Electricity Market and the Spanish National Emissions and Allocation Plans are the framework to deal with the environmental issues in the day-ahead market bidding strategies. To address emission limitations, some of the standard risk management methodologies developed for financial markets, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), have been extended. This study offers to electricity generation utilities a mathematical model to determinate the individual optimal generation bid to the wholesale electricity market, for each one of their generation units that maximizes the long-run profits of the utility abiding by the Iberian Electricity Market rules, the environmental restrictions set by the EU Emission Trading Scheme, as well as the restrictions set by the Spanish National Emissions Reduction Plan. The economic implications for a GenCo of including the environmental restrictions of these National Plans are analyzed and the most remarkable results will be presented.

Emotion and reason in everyday risk perception

Although research has documented the importance of emotion in risk perception, little is knownabout its prevalence in everyday life. Using the Experience Sampling Method, 94 part-timestudents were prompted at random via cellular telephones to report on mood state and threeemotions and to assess risk on thirty occasions during their working hours. The emotions valence, arousal, and dominance were measured using self-assessment manikins (Bradley &Lang, 1994). Hierarchical linear models (HLM) revealed that mood state and emotions explainedsignificant variance in risk perception. In addition, valence and arousal accounted for varianceover and above reason (measured by severity and possibility of risks). Six risks were reassessedin a post-experimental session and found to be lower than their real-time counterparts.The study demonstrates the feasibility and value of collecting representative samples of data withsimple technology. Evidence for the statistical consistency of the HLM estimates is provided inan Appendix.

The value of useless information

There are many situations in which individuals have a choice of whether or notto observe eventual outcomes. In these instances, individuals often prefer to remainignorant. These contexts are outside the scope of analysis of the standard vonNeumann-Morgenstern (vNM) expected utility model, which does not distinguishbetween lotteries for which the agent sees the final outcome and those for which hedoes not. I develop a simple model that admits preferences for making an observationor for remaining in doubt. I then use this model to analyze the connectionbetween preferences of this nature and risk-attitude. This framework accommodatesa wide array of behavioral patterns that violate the vNM model, and thatmay not seem related, prima facie. For instance, it admits self-handicapping, inwhich an agent chooses to impair his own performance. It also accommodatesa status quo bias without having recourse to framing effects, or to an explicitdefinition of reference points. In a political economy context, voters have strictincentives to shield themselves from information. In settings with other-regardingpreferences, this model predicts observed behavior that seems inconsistent witheither altruism or self-interested behavior.

Risk sharing with the monarch: Excusable defaults and contingent debt in the age of Philip II, 1556-1598

Contingent sovereign debt can create important welfare gains. Nonetheless,there is almost no issuance today. Using hand-collected archival data, we examine thefirst known case of large-scale use of state-contingent sovereign debt in history. Philip IIof Spain entered into hundreds of contracts whose value and due date depended onverifiable, exogenous events such as the arrival of silver fleets. We show that this allowedfor effective risk-sharing between the king and his bankers. The data also stronglysuggest that the defaults that occurred were excusable they were simply contingenciesover which Crown and bankers had not contracted previously.

Speculation, risk premia and expectations in the yield curve

An affine asset pricing model in which traders have rational but heterogeneous expectations aboutfuture asset prices is developed. We use the framework to analyze the term structure of interestrates and to perform a novel three-way decomposition of bond yields into (i) average expectationsabout short rates (ii) common risk premia and (iii) a speculative component due to heterogeneousexpectations about the resale value of a bond. The speculative term is orthogonal to public informationin real time and therefore statistically distinct from common risk premia. Empirically wefind that the speculative component is quantitatively important accounting for up to a percentagepoint of yields, even in the low yield environment of the last decade. Furthermore, allowing for aspeculative component in bond yields results in estimates of historical risk premia that are morevolatile than suggested by standard Affine Gaussian term structure models which our frameworknests.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Transportation choices and the value of statistical life

This paper exploits an unusual transportation setting to estimate the value of a statistical life(VSL). We estimate the trade-offs individuals are willing to make between mortality risk andcost as they travel to and from the international airport in Sierra Leone (which is separated fromthe capital Freetown by a body of water). Travelers choose from among multiple transportoptions ? namely, ferry, helicopter, hovercraft, and water taxi. The setting and original datasetallow us to address some typical omitted variable concerns in order to generate some of the firstrevealed preference VSL estimates from Africa. The data also allows us to compare VSLestimates for travelers from 56 countries, including 20 African and 36 non-African countries, allfacing the same choice situation. The average VSL estimate for African travelers in the sample isUS$577,000 compared to US$924,000 for non-Africans. Individual characteristics, particularlyjob earnings, can largely account for the difference between Africans and non-Africans; Africansin the sample typically earn somewhat less. There is little evidence that individual VSL estimatesare driven by a lack of information, predicted life expectancy, or cultural norms around risktakingor fatalism. The data implies an income elasticity of the VSL of 1.77. These revealedpreference VSL estimates from a developing country fill an important gap in the existingliterature, and can be used for a variety of public policy purposes, including in current debateswithin Sierra Leone regarding the desirability of constructing new transportation infrastructure.

Value of clinical factors in selecting postmenopausal women with rheumatoid arthritis for bone densitometry.

Criteria to decide which patients with rheumatoid arthritis (RA) should be examined by dual energy x ray absorptiometry (DXA) are currently not available. The rheumatologists from Amsterdam have proposed preliminary criteria based on clinical risk factors (age, disease activity, and functional status). These criteria are preliminary and not widely accepted but might be helpful in practice. The value of the proposal in a group of Spanish postmenopausal women with RA is analysed. METHODS DXA (lumbar spine and femoral neck) was performed in 128 patients recruited from a clinical setting, and the proposed criteria were applied. T and Z scores were established for a Spanish reference population. RESULTS The mean (SD) age of the patients was 61.3 (10.7) and mean duration of the postmenopausal period 14.5 (10.1) years. Mean duration of RA was 13.7 (7.7) years. Mean C reactive protein was 22 (21) mg/l; mean erythrocyte sedimentation rate 26 (18) mm/1st h; and mean Health Assessment Questionnaire score 1.25 (0.79). Ninety (70%) patients fulfilled the proposed criteria. Their sensitivity for the diagnosis of osteoporosis (T score ¿¿2.5 SD) was 86% and their specificity, 43%. Positive predictive value was 54% and negative predictive value, 79%. CONCLUSIONS The proposed criteria seem a good screening method for the selection of those patients with RA whose bone mineral density should be assessed as the sensitivity and negative predictive value are acceptable.

Residual Stress Measurement on a MEMS Structure With High-Spatial Resolution

A new approach to the local measurement of residual stress in microstructures is described in this paper. The presented technique takes advantage of the combined milling-imaging features of a focused ion beam (FIB) equipment to scale down the widely known hole drilling method. This method consists of drilling a small hole in a solid with inherent residual stresses and measuring the strains/displacements caused by the local stress release, that takes place around the hole. In the presented case, the displacements caused by the milling are determined by applying digital image correlation (DIC) techniques to high resolution micrographs taken before and after the milling process. The residual stress value is then obtained by fitting the measured displacements to the analytical solution of the displacement fields. The feasibility of this approach has been demonstrated on a micromachined silicon nitride membrane showing that this method has high potential for applications in the field of mechanical characterization of micro/nanoelectromechanical systems.

Testing extreme value copulas to estimate the quantile

Testing weather or not data belongs could been generated by a family of extreme value copulas is difficult. We generalize a test and we prove that it can be applied whatever the alternative hypothesis. We also study the effect of using different extreme value copulas in the context of risk estimation. To measure the risk we use a quantile. Our results have motivated by a bivariate sample of losses from a real database of auto insurance claims. Methods are implemented in R.