Volatility persistence is a stylized statistical property of financial time-series data such as exchange rates and stock returns. The purpose of this letter is to investigate the relationship between volatility persistence and predictability of squared returns.

In the paper we present robust estimation methods based on bounded innovation propagation filters and quantile regression, applied to measure Value at Risk. To illustrate advantage connected with the robust methods, we compare VaR forecasts of several group of instruments in the period of high uncertainty on the financial markets with the ones modelled using traditional quasi-likelihood estimation. For comparative purpose we use three groups of tests i.e. based on Bernoulli trial models, on decision making aspect, and on the expected shortfall.

In the article the author analyses the impact of the Financial Crisis, especially the Greek fiscal one, on the sCDS prices in Europe. The aim of the article is to assess the ability of the sCDS premia to price the risk of countries before and during the Greek crisis. The author analyses sCDS premia of maturity 10 years together with the so called bond-spreads, i.e. the spreadsbetween the countries’ bond indexes and the risk free rate of the region (in our case it was the yield of German bonds of corresponding maturity – 10 years).The idea was to check whether there occurred any discrepancies in the risk valuation via the two measures, as a consequence of the Greek crisis. The data is taken daily and covers the period of 2008‒2012. Based upon the results obtained in the research we conclude that the Greek crisis indeed influenced the relationships between the two measures of risk, however the degree of the influence was different in different countries. The relationships between the two measures of risk were totally broken only in the case of Greece, while in the other countries the relationships either were not distorted or had been broken already at the beginning of the financial crisis (2008/2009). The Greek problems were indeed reflected in volatilities of all analysed instruments; however triggering the credit event affected only Greek bonds dynamics.

We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature.

In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.

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.