Abstract
The extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. This paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution. L-moment ratio diagram is being used to find the appropriate distributions among the distributions. L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pakistan Limited. Thereafter, the probability weighted moment (PWM) method has been used in order to estimate the parameters of probability distributions. Furthermore, Anderson–Darling (AD) goodness-of-fit test is employed to test the goodness of fit among GEV and GL distributions, and it is clear from the results that the GL distribution is more reliable and applicable for extreme minima of Byco Petroleum Company in the Pakistan stock exchange market. EVT and traditional methods are used for value-at-risk (VaR) analysis. The analysis indicates that EVT methods are more suitable for risk measurement in comparison with traditional methods.
Highlights
Academic Editor: Ishfaq Ahmad e extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. is paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution
L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pakistan Limited. ereafter, the probability weighted moment (PWM) method has been used in order to estimate the parameters of probability distributions
We examined the behavior of stock exchange extremes by fitting the whole data and subperiods of Byco Petroleum Pakistan Limited. e results of both GEV and GL distributions were presented in the tables with the AD p value
Summary
Returns are independent and identically distributed (iid). After dividing the extremes into subperiods of daily, weekly, and monthly, further job is to look for the suitable distributions for the data. High value of standard deviation shows that the distribution of extremes is largely spread. In the frame reference of finance, it means that high values of the shape parameter depict large negative returns or heightened probability of crash (Aparicio and Estrada [20]). Probability weighted moment method is used to estimate the parameter of distributions. (iv) λ4 1/4 E((X4: 4) − 3 (X3: 4) + 3(X2: 4) − (X1: 4)) α0 − 12α1 + 30α2 − 20α3 e step after estimating parameters is to know which distribution is the best fit. After properly modeling the distributions of extremes, lower quantiles have been put to use in order to calculate VaR estimates. For VaR validation, we employed Christoffersen [23] test
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
