In general, the properties of the conditional distribution of multiple period returns do not follow easily from the one-period data generating process. This renders computation of Value-at-Risk and Expected Shortfall for multiple period returns a non-trivial task. In this paper we consider some...

In this note it is argued that the estimation error in Value-at-Risk predictors gives rise to underestimation of portfolio risk. We propose a simple correction and end in an empirical illustration that it is economically relevant

In the estimation of risk measures such as Value at Risk and Expected shortfall relatively short estimation windows are typically used rendering the estimation error a possibly non-negligible component. In this paper we build upon previous results for the Value at Risk and discuss how the...

In the estimation of risk measures such as Value at Risk and Expected shortfall relatively short estimation windows are typically used rendering the estimation error a possibly non-negligible component. In this paper we build upon previous results for the Value at Risk and discuss how the...

Sornette et al. (1996), Sornette and Johansen (1997), Johansen et al. (2000) and Sornette (2003a) proposed that, prior to crashes, the mean function of a stock index price time series is characterized by a power law decorated with log-periodic oscillations, leading to a critical point that...

World power and gas markets have a natural relationship with global tradable carbon permits markets, including the U.S. Clean Air Act Amendments and the EU Emissions Trading Scheme, the latter officially launched in January 2005. Electric utilities operate their power plants based in part on the...