Beyond normality: Capital market Value-at-Risk modelling using symmetric and asymmetric Laplace distributions

Evidence on parametric VaR employing both Laplace (exhibiting excessive kurtosis) and asymmetric Laplace (additionally being skewed), “tent-shaped” probability distributions is available, although it remains relatively limited. The research procedure in the paper pursued two primary objectives: to back-test both distributions and assess their ability to capture extreme events, and to determine whether the distribution that best fits the entire empirical distribution is also the one that performs best in back-testing in long-term. The indices considered include WIG30, BVP, CAC, DAX, FTM, HSI, NKX, SHC, SPX and TWSE. The tests were performed using daily data for period between 31 December 1998, and 30 June 2025. Across the ten markets studied, both distributions generally outperformed historical simulation and the normal probability distribution, with the asymmetrical Laplace distribution particularly outperforming the Laplace distribution in capital markets that are likely to be skewed for higher confidence levels (0.99 and 0.975) considered.