MODELLING STOCK PRICES OF A BANK WITH EXTREME VALUE DISTRIBUTIONS
Abstract
The study investigates the application of Extreme Value Theory in modelling stock prices, aiming to capture the tail behaviour and extreme movements that conventional distributions often fail to represent accurately. The use of Extreme Value Theory has gained considerable attention in the field of finance due to its ability to model rare events, such as financial crises or market crashes. By incorporating Extreme Value Theory, researchers aim to improve risk management, portfolio optimization, and pricing of financial derivatives. In this study, the Log-normal, Weibull, Gamma, and Normal distributions were used to model the stock price closing data, with a specific focus on extreme value distributions. Both graphical explorations and goodness-of-fit criteria were considered together to evaluate the suitability of these distributions. When assessing the data, it was observed that the Weibull distribution provided the best fit for the given stock price closing data.
Keywords
Extreme value theory, Generalized extreme value distribution, Tail behaviour, Stock prices, Risk management
References
- [1] Bachelier L. Théorie de la spéculation. in annales scientifiques de l'école normale supérieure 1900; 17: 21-86, http://dx.doi.org/10.24033/asens.476.
- [2] Ţiţan AG. The efficient market hypothesis: review of specialized literature and empirical research. Procedia Economics and Finance 2015; 32: 442-449.
- [3] Masoliver J, Montero M, Porrà JM. A dynamical model describing stock market price distributions. Physica A: Statistical Mechanics and its Applications 2000; 233(3-4): 559-567.
- [4] Cont R. Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance 2001; 1(2): 223–236.
- [5] Mirsadeghpour Zoghi SM, Sanei M, Tohidi G, Banihashemi S, Modarresi N. The effect of underlying distribution of asset returns on efficiency in dea models. Journal of Intelligent & Fuzzy Systems 2021; 40(5): 10273-10283.
- [6] Ahmad Z, Mahmoudi E, Dey S. A new family of heavy tailed distributions with an application to the heavy tailed insurance loss data. Communications in Statistics-Simulation and Computation 2022; 51(8): 4372-4395.
- [7] Mandelbrot BB. The Variation of Certain Speculative Prices. Springer, New York, 1997.
- [8] Yousof HM, Tashkandy Y, Emam W, Ali MM, Ibrahim M. A new reciprocal Weibull extension for modelling extreme values with risk analysis under insurance data. Mathematics 2023; 11(4): 966.
- [9] Gebizlioglu OL, Şenoğlu B, Kantar YM. Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution. Journal of Computational and Applied Mathematics 2011; 235(11): 3304-3314.
- [10] Kowan T, Mahalapkorkiat C, Samakrat T, Sumritnorrapong P. Probability distributions for modelling of covid-19 cases and deaths in Thailand. Computer Science 2022; 17(4): 1499-1506.