The effect of default risk on trading book capital requirements for public equities : an irc application for the Brazilian market

Esse é um dos primeiros trabalhos a endereçar o problema de avaliar o efeito do default para fins de alocação de capital no trading book em ações listadas. E, mais especificamente, para o mercado brasileiro. Esse problema surgiu em crises mais recentes e que acabaram fazendo com que os reguladores impusessem uma alocação de capital adicional para essas operações. Por essa razão o comitê de Basiléia introduziu uma nova métrica de risco, conhecida como Incremental Risk Charge. Essa medida de risco é basicamente um VaR de um ano com um intervalo de confiança de 99.9%. O IRC visa medir o efeito do default e das migrações de rating, para instrumentos do trading book. Nessa dissertação, o IRC está focado em ações e como consequência, não leva em consideração o efeito da mudança de rating. Além disso, o modelo utilizado para avaliar o risco de crédito para os emissores de ação foi o Moody’s KMV, que é baseado no modelo de Merton. O modelo foi utilizado para calcular a PD dos casos usados como exemplo nessa dissertação. Após calcular a PD, simulei os retornos por Monte Carlo após utilizar um PCA. Essa abordagem permitiu obter os retornos correlacionados para fazer a simulação de perdas do portfolio. Nesse caso, como estamos lidando com ações, o LGD foi mantido constante e o valor utilizado foi baseado nas especificações de basiléia. Os resultados obtidos para o IRC adaptado foram comparados com um VaR de 252 dias e com um intervalo de confiança de 99.9%. Isso permitiu concluir que o IRC é uma métrica de risco relevante e da mesma escala de uma VaR de 252 dias. Adicionalmente, o IRC adaptado foi capaz de antecipar os eventos de default. Todos os resultados foram baseados em portfolios compostos por ações do índice Bovespa.

Parametric VaR with goodness-of-fit tests based on EDF statistics for extreme returns

Parametric VaR (Value-at-Risk) is widely used due to its simplicity and easy calculation. However, the normality assumption, often used in the estimation of the parametric VaR, does not provide satisfactory estimates for risk exposure. Therefore, this study suggests a method for computing the parametric VaR based on goodness-of-fit tests using the empirical distribution function (EDF) for extreme returns, and compares the feasibility of this method for the banking sector in an emerging market and in a developed one. The paper also discusses possible theoretical contributions in related fields like enterprise risk management (ERM). © 2013 Elsevier Ltd.

Suposição de normalidade e gestão de risco: uma aplicação do var paramétrico via teste de aderência

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Variability in Modified Estimators of VaR and ES

Thesis (Master's)--University of Washington, 2016-06

Risk Aversion in a Mixed-Integer Nonlinear Approach to Support Decision-Making for a Hydro Power Producer

In this paper, a mixed-integer nonlinear approach is proposed to support decision-making for a hydro power producer, considering a head-dependent hydro chain. The aim is to maximize the profit of the hydro power producer from selling energy into the electric market. As a new contribution to earlier studies, a risk aversion criterion is taken into account, as well as head-dependency. The volatility of the expected profit is limited through the conditional value-at-risk (CVaR). The proposed approach has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems.

A risk-averse optimization model for trading wind energy in a market environment under uncertainty

In this paper, a stochastic programming approach is proposed for trading wind energy in a market environment under uncertainty. Uncertainty in the energy market prices is the main cause of high volatility of profits achieved by power producers. The volatile and intermittent nature of wind energy represents another source of uncertainty. Hence, each uncertain parameter is modeled by scenarios, where each scenario represents a plausible realization of the uncertain parameters with an associated occurrence probability. Also, an appropriate risk measurement is considered. The proposed approach is applied on a realistic case study, based on a wind farm in Portugal. Finally, conclusions are duly drawn. (C) 2011 Elsevier Ltd. All rights reserved.

Optimal offering strategies for wind power producers considering uncertainty and risk

This paper provides a two-stage stochastic programming approach for the development of optimal offering strategies for wind power producers. Uncertainty is related to electricity market prices and wind power production. A hybrid intelligent approach, combining wavelet transform, particle swarm optimization and adaptive-network-based fuzzy inference system, is used in this paper to generate plausible scenarios. Also, risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study, based on a wind farm in Portugal, are provided and analyzed. Finally, conclusions are duly drawn.

Scheduling of a hydro producer considering head-dependency, price scenarios and risk-aversion

In this paper, a mixed-integer quadratic programming approach is proposed for the short-term hydro scheduling problem, considering head-dependency, discontinuous operating regions and discharge ramping constraints. As new contributions to earlier studies, market uncertainty is introduced in the model via price scenarios, and risk aversion is also incorporated by limiting the volatility of the expected profit through the conditional value-at-risk. Our approach has been applied successfully to solve a case Study based on one of the main Portuguese cascaded hydro systems, requiring a negligible computational time.

Toxoplasma-IgM and IgG-avidity in single samples from areas with a high infection rate can determine the risk of mother-to-child transmission

Anti-Toxoplasma IgG-avidity was determined in 168 serum samples from IgG- and IgM-positive pregnant women at various times during pregnancy, in order to evaluate the predictive value for risk of mother-to-child transmission in a single sample, taking the limitations of conventional serology into account. The neonatal IgM was considered the serologic marker of transmission. Fluorometric tests for IgG, IgM (immunocapture) and IgG-avidity were performed. Fifty-one of the 128 pregnant women tested gave birth in the hospital and neonatal IgM was obtained. The results showed 32 (62.75%) pregnant women having high avidity, IgM indexes between 0.6 and 2.4, and no infected newborn. Nineteen (37.25%) had low or inconclusive avidity, IgM indexes between 0.6 and 11.9, and five infected newborns and one stillbirth. In two infected newborns and the stillbirth maternal IgM indexes were low and in one infected newborn the only maternal parameter that suggested fetal risk was IgG-avidity. In the present study, IgG-avidity performed in single samples from positive IgM pregnant women helped to determine the risk of transmission at any time during pregnancy, especially when the indexes of the two tests were analysed with respect to gestational age. This model may be less expensive in developing countries where there is a high prevalence of infection than the follow-up of susceptible mothers until childbirth with monthly serology, and it creates a new perspective for the diagnosis of congenital toxoplasmosis.

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.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Incremental Prognostic Value of Myocardial Blood Flow Quantification with Rb-82 Cardiac PET in Patients With Known or Suspected CAD

Rb-82cardiac PET has been used to non-invasively assess myocardial blood flow (MBF)and myocardial flow reserve (MFR). The impact of MBF and MFR for predictingmajor adverse cardiovascular events (MACE) has not been investigated in aprospective study, which was our aim. MATERIAL AND METHODS: In total, 280patients (65±10y, 36% women) with known or suspected CAD were prospectivelyenrolled. They all underwent both a rest and adenosine stress Rb-82 cardiacPET/CT. Dynamic acquisitions were processed with the FlowQuant 2.1.3 softwareand analyzed semi-quantitatively (SSS, SDS) and quantitatively (MBF, MFR) andreported using the 17-segment AHA model. Patients were stratified based on SDS,stress MBF and MFR and allocated into tertiles. For each group, annualizedevent rates were computed by dividing the number of annualized MACE (cardiacdeath, myocardial infarction, revascularisation or hospitalisation forcardiac-related event) by the sum of individual follow-up periods in years.Outcome were analysed for each group using Kaplan-Meier event-free survivalcurves and compared using the log-rank test. Multivariate analysis wasperformed in a stepwise fashion using Cox proportional hazards regressionmodels (p<0.05 for model inclusion). RESULTS: In a median follow-up of 256days (range 168-440d), 44 MACE were observed. Ischemia (SDS≥2) was observed in95 patients who had higher annualized MACE rate as compared to those without(55% vs. 9.8%, p<0.0001). The group with the lowest MFR tertile (MFR<1.76)had higher MACE rate than the two highest tertiles (51% vs. 9% and 14%,p<0.0001). Similarly, the group with the lowest stress MBF tertile(MBF<1.78mL/min/g) had the highest annualized MACE rate (41% vs. 26% and 6%,p=0.0002). On multivariate analysis, the addition of MFR or stress MBF to SDSsignificantly increased the global χ2 (from 56 to 60, p=0.04; and from56 to 63, p=0.01). The best prognostic power was obtained in a model combiningSDS (p<0.001) and stress MBF (p=0.01). Interestingly, the integration ofstress MBF enhanced risk stratification even in absence of ischemia.CONCLUSIONS: Quantification of MBF or MFR in Rb-82 cardiac PET/CT providesindependent and incremental prognostic information over semi-quantitativeassessment with SDS and is of value for risk stratification.

Medidas de Perda na Avalia ção do Desempenho de Fundos de Investimentos

Uma das medidas de performance mais utilizada e a medida de Sharpe. A sua utiliza c~ao e inadequada quando as rendibilidades n~ao seguem uma distribui c~ao normal, assim originou o aparecimento de uma variedade de medidas alternativas. Em fun c~ao disso, surge ent~ao a quest~ao de saber se essas medidas alternativas produzem rankings signi cativamente diferentes da que se obt em com a medida de Sharpe. Apesar da exist^encia de muitos estudos emp ricos sobre esta problem atica a resposta n~ao e consensual. Neste trabalho fez-se a compara c~ao entre o ranking produzido pela medida de Sharpe e as algumas medidas alternativas, as que se baseiam no Low Partial Moments (Omega, Sortino, Kappa3 e Upside Potential Ratio) e, as que se baseiam no VaR - Value-at-Risk (ERV - Excess Return on VaR, ERMV - Excess Return on Modi ed VaR, ERCV - Excess Return on Conditional VaR e ERV? - Excess Return com VaR hist orico). Utilizando 26 fundos de investimentos norte-americanos, com registo di ario das rendibilidades para o per odo de Janeiro 2000 a Setembro 2009, encontrou-se um elevado coe ciente de correla c~ao de Spearman e de Kendall entre a medida de Sharpe e as alternativas, bem como as alternativas entre si, excepto para Upside Potential Ratio que os coe cientes s~ao relativamente baixos. Os resultados permitem concluir que existe uma medida que proporciona ordena c~oes diferentes.

Medidas de Perda na Avaliacão do Desempenho de Fundos de Investimentos

Uma das medidas de performance mais utilizada e a medida de Sharpe. A sua utilizacão e inadequada quando as rendibilidades não seguem uma distribuicão normal, assim originou o aparecimento de uma variedade de medidas alternativas. Em fun c~ao disso, surge então a questão de saber se essas medidas alternativas produzem rankings signi cativamente diferentes da que se obt em com a medida de Sharpe. Apesar da existencia de muitos estudos emp ricos sobre esta problem atica a resposta não e consensual. Neste trabalho fez-se a comparacão entre o ranking produzido pela medida de Sharpe e as algumas medidas alternativas, as que se baseiam no Low Partial Moments (Omega, Sortino, Kappa3 e Upside Potential Ratio) e, as que se baseiam no VaR - Value-at-Risk (ERV - Excess Return on VaR, ERMV - Excess Return on Modi ed VaR, ERCV - Excess Return on Conditional VaR e ERV? - Excess Return com VaR hist orico). Utilizando 26 fundos de investimentos norte-americanos, com registo di ario das rendibilidades para o per odo de Janeiro 2000 a Setembro 2009, encontrou-se um elevado coe ciente de correla c~ao de Spearman e de Kendall entre a medida de Sharpe e as alternativas, bem como as alternativas entre si, excepto para Upside Potential Ratio que os coe cientes s~ao relativamente baixos. Os resultados permitem concluir que existe uma medida que proporciona ordena c~oes diferentes.

Buy-and-Hold Strategies and Comonotonic Approximations

[cat] En aquest article estudiem estratègies “comprar i mantenir” per a problemes d’optimitzar la riquesa final en un context multi-període. Com que la riquesa final és una suma de variables aleatòries dependents, on cadascuna d’aquestes correspon a una quantitat de capital que s’ha invertit en un actiu particular en una data determinada, en primer lloc considerem aproximacions que redueixen l’aleatorietat multivariant al cas univariant. A continuació, aquestes aproximacions es fan servir per determinar les estratègies “comprar i mantenir” que optimitzen, per a un nivell de probabilitat donat, el VaR i el CLTE de la funció de distribució de la riquesa final. Aquest article complementa el treball de Dhaene et al. (2005), on es van considerar estratègies de reequilibri constant.