Backtesting of risk measures in dynamic models.

Details

Supervisors

Hafner, Christian

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enThis thesis, entitled Backtesting of Risk Measures in Dynamic Models, was prepared in partial fulfillment of the requirements for the Master’s degree in Actuarial Sciences at the Université Catholique de Louvain. Its primary aim is to provide a comprehensive overview of three tail risk measures, namely Value-at-Risk, Expected Shortfall, and Expectiles, along with their theoretical properties and practical backtesting within dynamic volatility frameworks, such as GARCH and GJR-GARCH. Chapters 1 and 2 introduce the motivation to move beyond traditional variance-based risk metrics and define the three risk measures. Chapter 3 develops the stochastic volatility models used to generate and estimate the risk measures, while Chapter 4 presents the backtests performed to validate them. Chapter 5 applies these concepts to historical S&P 500 data, comparing estimation and backtesting results under normal and Student-t innovations. The final chapter summarizes key insights and suggests directions for future research. I hope that this work not only deepens our understanding of backtesting methodologies but also offers practical guidance for risk managers seeking robust, tail-focused tools in volatile markets.