Financial Crisis, Capital Requirement, and Stress Tests: Evidence from the Extreme Value and Stable Paretian Estimates

Stress tests are exercises to determine the losses that might occur under “unlikely but plausible” circumstances. The objective of this chapter is to demonstrate that the “fat tail” of the stable Paretian distribution can capture the extraordinary risk during financial crisis, as well as normal market conditions. Rather than assuming a normal distribution and then add the “stress tests,” a stable Paretian VaR will capture both and is more parsimonious statistically. The Central Limit Theorem and probability theory are applicable to the “stress tests.” (Diebold et al., J Risk Finance 1(2):30–35, 2000) believe that extreme value statistics are preferable. This argument is valid if regulators and corporations are interested in managing “extreme risk” only. The soundness and the safety of the financial markets and the banking system and the “externality” issues, however, reveal that good risk management must consider “normal market” conditions as well as “crisis” that will be captured by the density of the whole distribution, not just the tails. In this chapter, a relatively new technique will be used to choose the appropriate number of “extremes.” The difficulty in estimating the density of the stable Paretian distribution will be overcome by using a simple and reliable Fourier series method.