The s-period ahead Value-at-Risk (VaR) for a portfolio of dimension n is considered and its Bayesian analysis is discussed. The VaR assessment can be based either on the n-variate predictive distribution of future returns on individual assets, or on the univariate Bayesian model for the portfolio value (or the return on portfolio). In both cases Bayesian VaR takes into account parameter uncertainty and non-linear relationship between ordinary and logarithmic returns. In the case of a large portfolio, the applicability of the n-variate approach to Bayesian VaR depends on the form of the statistical model for asset prices. We use the n-variate type I MSF-SBEKK(1,1) volatility model proposed specially to cope with large n. We compare empirical results obtained using this multivariate approach and the much simpler univariate approach based on modelling volatility of the value of a given portfolio.
This paper addresses the issue of obtaining maximum likelihood estimates of parameters for structural VAR models with a mixture of distributions. Hence the problem does not have a closed form solution, numerical optimization procedures need to be used. A Monte Carlo experiment is designed to compare the performance of four maximization algorithms and two estimation strategies. It is shown that the EM algorithm outperforms the general maximization algorithms such as BFGS, NEWTON and BHHH. Moreover, simplification of the problem introduced in the two steps quasi ML method does not worsen small sample properties of the estimators and therefore may be recommended in the empirical analysis.
The abrupt depreciation of the zloty during the subprime crisis and fastrising prices are serious problems, because Poland, having to fulfil five Maastricht criteria, makes the dependence of her domestic inflation on price increases in the EU countries the central point of the discussion about the optimal monetary and fiscal policy rules for the next few years. The primary objective of the paper is to test out some hypotheses about the main sources of the volatility of the Polish zloty / euro exchange rate and inflation in Poland. Because several competing theoretical models describing inflationary processes are widely used, special attention is paid to their empirical verification. The working-hypotheses allowing for the country-specific features of the consumer and producer price inflation are formulated and verified in the paper.
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