Measuring risk based on stable distributions: an examination of Latin American stock indexes

Abstract

Accurate forecasting of risk is the key to sucessful risk management techniques. Given the fat-tailed characterisitic of financial returns, the assumptions of modeling these returns with the thin-tailed Gaussian distribution is inappropriate. In this paper a more accurate VaR estimate is tested using the “stable” or “α- stable” distribution, which allows for varying degrees of tail heaviness and varying degrees of skewness. Stable VaR measures are estimated and forecasted using the main Latin American stock market indexes. The results show that the stable modeling provides conservative 99% VaR estimates, while the normal VaR modeling significantly underestimates 99% VaR. The 95% VaR stable and normal estimates, using a window length of 50 observations, are satisfactory. However, increasing the window length to 125 and 250 observations worsens the stable and the normal VaR measurements.