Value-at-risk and extreme value distributions for financial returns

Abstract

The ability of the Generalised Extreme Value (GEV) and Generalised Logistic (GL) distributions to fit extreme financial returns in the stock, commodities and bond markets is assessed. The empirical results indicate that the too much celebrated GEV is not the most appropriate model for the data since the fatter tailed GL is found to provide better descriptions of the extreme returns. Extreme Value Theory (EVT) based VaR estimates are then derived and compared to those generated by traditional methods. The results show that when the focus is on the really ruinous events which are located deep into the tails of the returns distribution, the EVT methods used in this study can be particularly useful since they produce VaR estimates that outperform those derived by the traditional methods at high confidence levels. However, these estimates were found to be considerably higher than those derived by traditional VaR models; consequently leading to higher capital reserves for financial institutions.

Importance of Generalized Logistic Distribution in Extreme Value Modeling

“…Moreover, the three models can be considered as the limit distribution of extremes in different situations. These results justify the theoretical importance of the empirical findings, that GL can be a suitable model over GEV model for extremes of share market data, see for example [1, 25,26]. Many papers also show that GL distribution provides an adequate distribution in hydrological application, for eg.…”

“…[1, 23,24] etc. Also [25] empirically showed that GL is better than GEV to model extreme movements in the stock, commodities and bond markets.…”

The Distribution Analysis for Extreme Returns of Nikkei 225 Index: Based on the Extreme Value Distribution of GEV and GL

“…[8] Concluded that the GP is the better model as there is less wasting of data. However, [9] states that although the GP distribution does have its advantages over the GEV, it is subjected to more serial dependence. [9] Therefore applied a non-overlapping sub period technique to the financial data to reduce dependency.…”

“…However, [9] states that although the GP distribution does have its advantages over the GEV, it is subjected to more serial dependence. [9] Therefore applied a non-overlapping sub period technique to the financial data to reduce dependency. He then fit the Generalized Logistic (GL) distribution and the GEV to the data and compared the results to determine which model better describes the extreme events.…”

“…[10] Applied GEV and BGEVA models to the sample of Italian SMEs from 2006 to 2011 and found each of the two model is better than the logistic regression. [9] Introduced the option of probability weighted moments as a more efficient way to estimate parameters instead of the maximum likelihood approach, which was the method used in [8]. Each sub period is analyzed and the better fit distribution is assigned to each sub period, where after he concluded that the extremes are generally better characterized by the GL distribution.…”