Value at risk (VaR) analysis for fat tails and long memory in returns

Abstract

In this study, different value at risk models (VaR), which are used to measure downside investment risk, have been analyzed under different methods and stylized facts of financial time series. Downside investment risk of a single asset and of a hypothetical portfolio have first been measured by conventional VaR models (Parametrical VaR, Historical VaR, Historical Simulation VaR and Monte Carlo Simulation VaR) and then by alternative simulation models that consider fat tails (Alpha-Stable Simulation VaR) in return distributions and long memory in returns (Long Memory Simulation VaR). Empirical findings and the Duration Based Backtesting procedure indicate that the largest VaR value is obtained under Long Memory Simulation VaR that is based on the long memory in returns. This result is consistent with the findings of Mandelbrot’s various studies.