The Laplace probability distribution to model extreme events in finance

Resumo

This study aims to examine the Laplace probability distribution as a superior model for capturing extreme events in financial markets. Probability distributions have been employed in the financial industry to model and quantify financial phenomena. The assumption persists that oscillations in financial signals follow a Normal distribution; however, in reality, financial phenomena often deviate from this model. Benoît Mandelbrot stated: “…there are typically so many ‘outliers’ that fitted to the mean square of price changes are much lower and flatter than the distribution of the data themselves.” Events such as financial crises are regarded as extreme. Evidence shows that when extreme events occur, they cause significant damage to the global economy. The appearance of such outliers prompts academics and practitioners to adopt more suitable models for predicting extreme values in financial markets, especially in asset returns.

To address the limitations of the Normal distribution in modelling atypical asset return values, the author investigates the Laplace distribution, a heavy-tailed alternative. As demonstrated in this work, the Laplace distribution aligns more closely with the empirical distributions of asset returns. Visual and analytical inspection of the data convincingly supports the assertion that the Laplace distribution offers a better fit for the empirical distribution of asset returns. To reinforce this claim, higher-order statistical moments and Normality tests are also conducted.