Paper: arXiv 2311.17239

Authors: Andrea Teruzzi

Abstract

The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent data. This research proposes an expectile-based approach for assessing the tail risk of dependent data. Expectile is a summary statistic that generalizes the concept of mean, as the quantile generalizes the concept of the median. We present the empirical findings for a dataset of cryptocurrencies. We propose a method for dynamically evaluating the level of the expectiles by estimating the level of the expectiles of the residuals of a heteroscedastic regression, such as a GARCH model. Finally, we introduce the Marginal Expected Shortfall (MES) as a tool for measuring the marginal impact of single assets on systemic shortfalls. In our case of interest, we are focused on the impact of a single cryptocurrency on the systemic risk of the whole cryptocurrency market. In particular, we present an expectile-based MES for dependent data.

Complexity vs Empirical Score

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

Why this score: The paper provides a solid theoretical extension of Extreme Value Theory and expectiles to weakly dependent data, combined with a GARCH setup for dynamic risk estimation. It applies these concepts effectively to systemic risk in cryptocurrency markets using Marginal Expected Shortfall (MES), offering a well-rounded mix of quantitative rigor and empirical application.

Research Flowchart

  flowchart TD
    A[Research Goal: Estimate Tail & Systemic Risk in Cryptocurrencies] --> B[Data Input: Cryptocurrency Market Return Series]
    B --> C[Method: GARCH Modeling for Dynamic Volatility & Residual Extraction]
    C --> D[EVT & Expectile Estimation: Model Extreme Tail Risk of Residuals]
    D --> E[Systemic Risk Tool: Calculate Expectile-based Marginal Expected Shortfall]
    E --> F[Outcomes: Dynamic Tail Risk Metrics & Single-Asset Systemic Impact Measures]

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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.