  Reliable calculations of financial risk require that the fat-tailed nature of
prices changes is included in risk measures. To this end, a non-Gaussian
approach to financial risk management is presented, modeling the power-law
tails of the returns distribution in terms of a Student-t distribution.
Non-Gaussian closed-form solutions for Value-at-Risk and Expected Shortfall are
obtained and standard formulae known in the literature under the normality
assumption are recovered as a special case. The implications of the approach
for risk management are demonstrated through an empirical analysis of financial
time series from the Italian stock market and in comparison with the results of
the most widely used procedures of quantitative finance. Particular attention
is paid to quantify the size of the errors affecting the market risk measures
obtained according to different methodologies, by employing a bootstrap
technique.
