Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Analisando o risco de uma carteira de cr��dito via simula����es de Monte Carlo

Neste trabalho, analisamos utiliza����o da metodologia CreditRLsk+ do Credit Suisse sua adequa����o ao mercado brasileiro, com objetivo de calcular risco de uma carteira de cr��dito. Certas hip��teses assumidas na formula����o do modelo CreditRisk+ n��o valem para o mercado brasileiro, caracterizado, por exemplo, por uma elevada probabilidade de defcnilt. Desenvolvemos, ent��o, uma metodologia para c��lculo da distribui����o de perdas atrav��s do m��todo de Simula����o de Monte Cario, alterando algumas hip��teses originais do modelo com objetivo de adapt��-lo ao nosso mercado. utiliza����o de simula����es tamb��m oferece resultados mais precisos em situa����es onde as carteiras possuem uma pequena popula����o de contratos, al��m de eliminar poss��veis problemas de converg��ncia do m��todo anal��tico, mesmo considerando as hip��teses do modelo original. Verifica-se ainda que tempo computacional pode ser menor que da metodologia original, principalmente em carteiras com elevado n��mero de devedores de perfis distintos com aloca����es em diversos setores da economia. Tendo em vista as restri����es acima, acreditamos que metodologia proposta seja uma alternativa para forma anal��tica do modelo CreditRisk+. Apresentamos exemplos de utiliza����o resultados providos por estas simula����es. ponto central deste trabalho real��ar import��ncia da utiliza����o de metodologias alternativas de medi����o de risco de cr��dito que incorporem as particularidades do mercado brasileiro.

Uma an��lise comparativa entre a metodologia anal��tica e a metodologia de simula����o Monte Carlo para o c��lculo do value at risk

O presente trabalho tem por objetivo descrever, avaliar comparar as metodologias anal��tica da simula����o Monte Cario para c��lculo do Value at Risk (Valor em Risco) de institui����es financeiras de empresas. Para comparar as vantagens desvantagens de cada metodologia, efetuaremos compara����es alg��bricas realizamos diversos testes emp��ricos com institui����es hipot��ticas que apresentassem diferentes n��veis de alavancagem de composi����o em seus balan��os, que operassem em diferentes mercados (consideramos os mercados de a����es, de op����es de compra de t��tulos de renda fixa prefixados).

Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The ��rst reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modi��ed information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of ��tted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy ��reaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.

A simula����o de Monte Carlo como instrumento de an��lise de riscos e sele����o de projetos

Trata da aplicabilidade da Simula����o de Monte Carlo para a an��lise de riscos e, conseq��entemente, o apoio �� decis��o de investir ou n��o em um projeto. S��o abordados m��todos de an��lise de riscos e sele����o de projetos, bem como a natureza, vantagens e limita����es da Simula����o de Monte Car��o. Por fim este instrumento tem sua viabilidade analisada sob a luz do processo de an��lise de riscos de uma empresa brasileira.

The importance of common cyclical features in VAR analysis: a Monte-Carlo study

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical features for estimates and forecasts based on vector autoregressive models. First, we show that the ��best�� empirical model developed without common cycle restrictions need not nest the ��best�� model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan-Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions.

The importance of Common-Cyclical Features in VAR analysis: a Monte-Carlo study (Preliminary Version)

Despite the belief, supported byrecentapplied research, thataggregate datadisplay short-run comovement, there has been little discussion about the econometric consequences ofthese data ���features.��� W e use exhaustive M onte-Carlo simulations toinvestigate theimportance ofrestrictions implied by common-cyclicalfeatures for estimates and forecasts based on vectorautoregressive and errorcorrection models. First, weshowthatthe���best��� empiricalmodeldevelopedwithoutcommoncycles restrictions neednotnestthe���best��� modeldevelopedwiththoserestrictions, duetothe use ofinformation criteria forchoosingthe lagorderofthe twoalternative models. Second, weshowthatthecosts ofignoringcommon-cyclicalfeatures inV A R analysis may be high in terms offorecastingaccuracy and e��ciency ofestimates ofvariance decomposition coe��cients. A lthough these costs are more pronounced when the lag orderofV A R modelsareknown, theyarealsonon-trivialwhenitis selectedusingthe conventionaltoolsavailabletoappliedresearchers. T hird, we���ndthatifthedatahave common-cyclicalfeatures andtheresearcherwants touseaninformationcriterium to selectthelaglength, theH annan-Q uinn criterium is themostappropriate, sincethe A kaike and theSchwarz criteriahave atendency toover- and under-predictthe lag lengthrespectivelyinoursimulations.

Estimation of DSGE Models: A Monte Carlo Analysis

Neste trabalho investigamos as propriedades em pequena amostra e a robustez das estimativas dos par��metros de modelos DSGE. Tomamos o modelo de Smets and Wouters (2007) como base e avaliamos a performance de dois procedimentos de estima����o: M��todo dos Momentos Simulados (MMS) e M��xima Verossimilhan��a (MV). Examinamos a distribui����o emp��rica das estimativas dos par��metros e sua implica����o para as an��lises de impulso-resposta e decomposi����o de vari��ncia nos casos de especifica����o correta e m�� especifica����o. Nossos resultados apontam para um desempenho ruim de MMS e alguns padr��es de vi��s nas an��lises de impulso-resposta e decomposi����o de vari��ncia com estimativas de MV nos casos de m�� especifica����o considerados.

Elabora����o de um modelo de valora����o quantitativa das garantias para o setor de saneamento com utiliza����o de Simula����o de Monte Carlo: o caso PPP de Esgoto para a Regi��o Metropolitana do Recife e Munic��pio de Goi��nia

A situa����o do saneamento no Brasil �� alarmante. Os servi��os de ��gua e esgotamento sanit��rio s��o prestados adequadamente somente para 59,4% e 39,7%, respectivamente, da popula����o brasileira. Para mudar este quadro, estima-se que sejam necess��rios R$ 304 bilh��es em investimentos. Parte desse volume ter�� que vir da iniciativa privada e a estrutura����o de parcerias p��blico privadas �� uma das formas de atingir este objetivo. Nestes projetos �� comum o setor p��blico oferecer garantias ao parceiro privado para assegurar a viabilidade do empreendimento. O presente trabalho apresenta um modelo para valora����o destas garantias, utilizando como estudos de caso as PPP de esgoto da regi��o metropolitana de Recife e do Munic��pio de Goiana. O resultado obtido mostrou a import��ncia desta valora����o, uma vez que dependendo do n��vel de garantia oferecida o valor presente dos desembolsos previstos para o setor p��blico variou de zero a at�� R$ 204 milh��es.