This article aims at underlying the importance of a correct modelling of the heavy-tail behavior of extreme values of financial data for an accurate risk estimation. Many financial models assume that prices follow normal distributions. This is not true for real market data, as stock (log-)returns show heavy-tails. In order to overcome this, price variations can be modeled using stable distribution, but then, as shown in this study, we observe that it over-estimates the Value-at-Risk. To overcome these empirical inconsistencies for normal or stable distributions, we analyze the tail behavior of price variations and show further evidence that power-law distributions are to be considered in risk models. Indeed, the efficiency of power-law risk models is proved by comprehensive backtesting experiments on the Value-at-Risk conducted on NYSE Euronext Paris stocks over the period 2001-2011.
