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Abstract

The primary objective of this article is to provide a comprehensive yet accessible introduction to stable distributions within the context of financial modelling. Traditional financial models often rely on the normal (Gaussian) distribution to analyze asset returns; however, this approach is inadequate in capturing the significant variations and extreme events observed in real-world financial markets. Financial returns frequently exhibit heavy tails and greater kurtosis, making it essential to adopt more sophisticated models that better represent these fluctuations. One such alternative is the Laplace distribution, a class of probability distributions characterized by heavy tails. This distribution provides a more accurate depiction of substantial price swings and extreme events, which are crucial for risk assessment and portfolio management. Furthermore, the Laplace distribution allows for a broader range of dependence structures, making it a valuable tool for financial analysts. By incorporating stable distributions, financial models can enhance predictive accuracy and risk evaluation strategies.