Self-exciting Extreme Value Models for Stock Market Crashes

Abstract

We demonstrate the usefulness of Extreme value Theory (EVT) to evaluate magnitudes of stock market crashes and provide some extensions. A common practice in EVT is to compute either unconditional quantiles of the loss distribution or conditional methods linking GARCH models to EVT. Our approach combines self-exciting models for exceedances over a given threshold with a marked dependent process for estimating the tail of loss distributions. The corresponding models allow to adopt ex-ante estimation of two risk measures in different quantiles to assess the expected frequency of different crashes of important stock market indices. The paper concludes with a backtesting estimation of the magnitude of major stock market crashes in financial history from one day before an important crash until one year later. The results show that this approach provides better estimates of risk measures than the classical methods and is moreover able to use available data in a more efficient way.