Analysis of financial risks in a GARCH framework

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Title: Analysis of financial risks in a GARCH framework
Author: Ahlstedt, Monica
Organization: Suomen Pankki
Series: Suomen Pankki. E
Series number: 11
Year of publication: 1998
Publication date: 1.3.1998
Pages: 181 s.
Keywords: ennusteet; ekonometria; mallit; valuuttakurssit; korot; Suomi; riskit; valuutat; opinnäytteet; GARCH; ARCH
Abstract: This study uses GARCH modelling to estimate and forecast conditional variances and covariances of returns calculated from a set of financial market series: twelve markka exchange rates, twelve corresponding shortterm euro interest rates and the Finnish short-term interest rate, the Finnish long-term interest rate, the Finnish all-share index and real estate prices. The variances are specified through univariate estimation and the analysis is then extended to a portfolio of assets by presenting and applying two alternative methods for covariance modelling.The first method is based on the assumption of identical autocorrelation structure for variances and covariances.The other method is based on the assumption of constant correlation.Both methods are flexible and enable the extension of the analysis to a large number of return series. The study then derives a forecast function from the models estimated from pooled data for variances and covariances of exchange rates and interest rates and from individual data for the other rates, in the form of a weighted moving average of past squared residuals.GARCH forecasts for the variances of individual return series as well as portfolios are compared in an ex post context, on the one hand, to two alternative forecasts based on piecewise homoscedastic variance models and, on the other, to actual data on squared returns. The empirical results in the study show that the estimated variance-covariance models display a high degree of similarity both across the variables and across subsamples (ie across exchange rate regimes); GARCH(1,1) seems to represent the underlying conditional variance process fairly well.In terms of persistence in the variance processes, which is nearly IGARCH(l,1), the estimated models are also remarkably similar both for the individual variables and for pooled data.Hence parsimony suggests using an integrated process to represent volatility in the sample.The study also argues that the estimated GARCH models represent a methodological and empirical improvement over those estimates typically used eg in value-at-risk calculations. Keywords: time-dependent volatility, GARCH estimation, value-at-risk models

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