Application of Extreme Value Theory to Measure Value at Risk and Risk-Based Capital
Date Issued
2009
Date
2009
Author(s)
Hu, Shun-Ting
Abstract
Extreme returns are of the most concern to investors and regulators. Risk management is the key to reduce the impact of extreme returns. Value at Risk (VaR) has been used as a measure of risk. VaR estimates the largest potential loss to investors in a specified investment horizon at the specified confidence interval. Various VaR models have been developed under different assumptions. The extreme value theory (EVT) fits only the extreme values to a distribution instead of taking the whole distribution into consideration. We seek to apply the EVT to calculate the VaR and compare it to other models in this paper. We use five VaR models (SMA, EWMA, historical simulation, EVT estimated by MLE and PWM) and calculate VaR for two time horizons, one excludes the financial tsunami and the other one includes it. The measure of accuracy and the measure of conservatism are conducted for evaluation. The evaluation results indicate that with the utilization of the EVT, the VaR is more accurate and conservative than other traditional methodologies.e also apply the EVT to calculate the equity risk of C-1 risk factor in the risk-based capital (RBC) formula. The equity risk is measured by both the original RBC formula and the EVT. The results tell us that the equity risk estimated by the EVT is higher, which means that it is more conservative than the original formula. Since we take only extreme returns within each block into calculation, chances are that the ignorance of other values might unreliable results. More discussion of the EVT application to insurance can be conducted in the future. We provide a new point of view for the insurance regulators while setting regulations for insurance companies.
Subjects
Extreme value theory (EVT)
Value at Risk (VaR)
Risk-based capital (RBC)
Type
thesis
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