Risk management critically depends on the assumptions made about the distribution of stock returns. This paper applies extreme value methods to investigate the limiting distribution of the extreme returns of the NIKKEI225, FTSE100 and S&P500 indices as well as the indices of some of largest...

We propose nonparametric estimators for conditional value-at-risk (VaR) and expected shortfall (ES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous...

The Pareto-Normal-Pareto (PNP) distribution assumes that, for log returns of financial series, the innovations are normally distributed between two threshold values with Pareto tails below and above the respective thresholds. These threshold values can be estimated by maximum likelihood...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its...

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of...