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John Henry
Mathematics

Hao Wang, Mentor

VaR and VaR Confidence Intervals for Heavy Tailed Distributions

Value at Risk (VaR) is the amount of money that may be lost on a portfolio over a given period of time with a given level of confidence. In this research, we consider VaR confidence intervals for market data coming from a heavy tailed distribution and construct a density function that fits the histogram of the market data. Scenario simulation tests extreme value cases. We derive the density function and its mean, standard deviation, skewness, and kurtosis. Resulting confidence intervals are shown to be more accurate than those reached when market data is assumed to be normal.