Paper: arXiv 2409.18643

Authors: Anna Kiriliouk, Chen Zhou

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This work is a well-structured book chapter illustrating extreme value theory applications to financial time series. While it relies on established methods (GARCH filtering, Weissman estimator) rather than novel theory, it provides strong empirical rigor, clear exposition, and a complete contrast between conditional and unconditional risk forecasting.

Research Flowchart

  flowchart TD
    A[Goal: Tail Risk Analysis of Financial Time Series] --> B[Input Data: S&P 500 Index]
    B --> C[Assess Serial Extremal Dependence]
    C --> D[Unconditional Risk Analysis<br/>Extreme Value Statistics]
    C --> E[Conditional Quantile Forecasting<br/>Time-Varying Volatility]
    D & E --> F[Perform Backtesting Methods]
    F --> G[Outcomes: Validated Tail Risk &<br/>Multivariate Dependence Insights]

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0 of 33 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.