A note on estimating market–based minimum capital risk requirements: a multivariate GARCH approach

Internal risk management models of the kind popularized by J. P. Morgan are now used widely by the world’s most sophisticated financial institutions as a means of measuring risk. Using the returns on three of the most popular futures contracts on the London International Financial Futures Exchange, in this paper we investigate the possibility of using multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models for the calculation of minimum capital risk requirements (MCRRs). We propose a method for the estimation of the value at risk of a portfolio based on a multivariate GARCH model. We find that the consideration of the correlation between the contracts can lead to more accurate, and therefore more appropriate, MCRRs compared with the values obtained from a univariate approach to the problem.

Testing for a unit root in a process exhibiting a structural break in the presence of GARCH errors

This paper considers the effect of GARCH errors on the tests proposed byPerron (1997) for a unit root in the presence of a structural break. We assessthe impact of degeneracy and integratedness of the conditional varianceindividually and find that, apart from in the limit, the testing procedure isinsensitive to the degree of degeneracy but does exhibit an increasingover-sizing as the process becomes more integrated. When we consider the GARCHspecifications that we are likely to encounter in empirical research, we findthat the Perron tests are reasonably robust to the presence of GARCH and donot suffer from severe over-or under-rejection of a correct null hypothesis.

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.

Benchmarks and the accuracy of GARCH model estimation

This paper reviews nine software packages with particular reference to their GARCH model estimation accuracy when judged against a respected benchmark. We consider the numerical consistency of GARCH and EGARCH estimation and forecasting. Our results have a number of implications for published research and future software development. Finally, we argue that the establishment of benchmarks for other standard non-linear models is long overdue.

A Double-threshold GARCH Model for the French Franc/Deutschmark exchange rate

This paper combines and generalizes a number of recent time series models of daily exchange rate series by using a SETAR model which also allows the variance equation of a GARCH specification for the error terms to be drawn from more than one regime. An application of the model to the French Franc/Deutschmark exchange rate demonstrates that out-of-sample forecasts for the exchange rate volatility are also improved when the restriction that the data it is drawn from a single regime is removed. This result highlights the importance of considering both types of regime shift (i.e. thresholds in variance as well as in mean) when analysing financial time series.

The effect of (mis-specified) GARCH filters on the finite sample distribution of the BDS test

This paper considers the effect of using a GARCH filter on the properties of the BDS test statistic as well as a number of other issues relating to the application of the test. It is found that, for certain values of the user-adjustable parameters, the finite sample distribution of the test is far-removed from asymptotic normality. In particular, when data generated from some completely different model class are filtered through a GARCH model, the frequency of rejection of iid falls, often substantially. The implication of this result is that it might be inappropriate to use non-rejection of iid of the standardised residuals of a GARCH model as evidence that the GARCH model ‘fits’ the data.

An empirical model comparison for valuing crack spread options

In this paper, we investigate the pricing of crack spread options. Particular emphasis is placed on the question of whether univariate modeling of the crack spread or explicit modeling of the two underlyings is preferable. Therefore, we contrast a bivariate GARCH volatility model for cointegrated underlyings with the alternative of modeling the crack spread directly. Conducting an empirical analysis of crude oil/heating oil and crude oil/gasoline crack spread options traded on the New York Mercantile Exchange, the more simplistic univariate approach is found to be superior with respect to option pricing performance.

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg-Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN`s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.

Estimação da razão ótima de Hedge para o IBOVESPA futuro: uma aplicação do modelo Garch bivariado

Este estudo tem o objetivo de comparar várias técnicas que podem ser empregadas para proteger posições à vista usando mercados futuros. Partindo de uma posição na qual o investidor está à mercê do mercado, adota-se as técnicas mais simples de proteção até chegar a estimação da razão ótima de hedge ou de risco mínimo utilizando o modelo condicional, modelo no qual a variância é dependente do tempo. Para justificar a utilização da razão ótima de hedge dinâmica é introduzida a possibilidade de haver custo de transação. Os dados utilizados neste estudo são o preço à vista e preço de ajuste futuro do IBOVESPA do período 13/07/90 à 14/12/95.

Avaliação do value at risk do índice Bovespa usando os modelos garch, tarch e riskmetrics tm para se estimar a volatilidade

Apresenta o método value at risk (VaR) para se mensurar o risco de mercado, sob diferentes abordagens. Analisa a série histórica do índice Bovespa no período de 1995 a 1996 por meio de testes econométricos de normalidade, autocorrelação dos retornos e raiz unitária. Comparo valor obtido a partir dos diferentes modelos de estimação de volatilidade propostos e verifica qual dos modelos foi o mais adequado para o caso estudado

Modelando o prêmio pelo risco cambial no Brasil através de modelos GARCH-M : o mercado forward reflete a visão dos economistas?

O presente estudo demonstra que o mercado brasileiro cambial de forward reflete adequadamente a visão dos economistas – obtida junto a pesquisas de mercado realizadas periodicamente pelo Banco Central do Brasil – quando se modela o prêmio pelo risco cambial através de modelos auto-regressivos condicionais generalizados de heteroscedasticidade na Média (GARCH-M).

An analysis of quit and dismissal determinants between 1988 and 1999 using the bivariate probit model

Excessive labor turnover may be considered, to a great extent, an undesirable feature of a given economy. This follows from considerations such as underinvestment in human capital by firms. Understanding the determinants and the evolution of turnover in a particular labor market is therefore of paramount importance, including policy considerations. The present paper proposes an econometric analysis of turnover in the Brazilian labor market, based on a partial observability bivariate probit model. This model considers the interdependence of decisions taken by workers and firms, helping to elucidate the causes that lead each of them to end an employment relationship. The Employment and Unemployment Survey (PED) conducted by the State System of Data Analysis (SEADE) and by the Inter-Union Department of Statistics and Socioeconomic Studies (DIEESE) provides data at the individual worker level, allowing for the estimation of the joint probabilities of decisions to quit or stay on the job on the worker’s side, and to maintain or fire the employee on the firm’s side, during a given time period. The estimated parameters relate these estimated probabilities to the characteristics of workers, job contracts, and to the potential macroeconomic determinants in different time periods. The results confirm the theoretical prediction that the probability of termination of an employment relationship tends to be smaller as the worker acquires specific skills. The results also show that the establishment of a formal employment relationship reduces the probability of a quit decision by the worker, and also the firm’s firing decision in non-industrial sectors. With regard to the evolution of quit probability over time, the results show that an increase in the unemployment rate inhibits quitting, although this tends to wane as the unemployment rate rises.