Tail Risk Analysis for Financial Time Series

TL;DR

This chapter demonstrates how extreme value statistics can be used to assess tail risks in financial time series, accounting for serial dependence, with a case study on the S&P 500 index.

Contribution

It compares unconditional and conditional quantile forecasting methods for tail risk estimation in serially dependent financial data.

Findings

Serial dependence affects tail risk estimates

Unconditional and conditional methods provide different risk assessments

Backtesting validates the proposed approaches

Abstract

This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk estimation, unconditional and conditional quantile forecasting. We use the S&P 500 index as a case study to assess serial (extremal) dependence, perform an unconditional and conditional risk analysis, and apply backtesting methods. Additionally, the chapter explores the impact of serial dependence on multivariate tail dependence.