Abstract
Expectile-based EVaR serves as a simpler and more sensitive alternative to quantile-based QVaR for financial risk measurement. This study constructs a MIDAS-Expectile regression model to leverage mixed-frequency data, employing Nonlinear Asymmetric Least Squares (NALS) for parameter estimation. Empirical analysis reveals significant risk spillovers from traditional markets (e.g., S&P 500, USD/CNY exchange rates) to cryptocurrencies, demonstrating their interconnectedness.
Key Features
- Innovative Model: Integrates MIDAS with Expectile regression for high-low frequency data synthesis.
- Risk Sensitivity: EVaR captures tail risks more effectively than conventional VaR.
- Empirical Focus: Analyzes Bitcoin, Litecoin, and other cryptocurrencies against traditional market indicators.
Methodology
1. MIDAS-Expectile Regression
The model combines low-frequency cryptocurrency returns (cryp_month) with high-frequency external factors (e.g., daily S&P 500 returns):
cryp_{month}^t = \beta_0 + \beta_1 \sum_{d=1}^D B(d; \theta_1, \theta_2) \cdot factor_{day}^{t-d/n} + u_tWeight Function: Exponential Almon polynomial ensures flexibility:
B(d; \theta) = \frac{\exp(\theta_1 d + \theta_2 d^2)}{\sum_{d=1}^D \exp(\theta_1 d + \theta_2 d^2)}2. Parameter Estimation via NALS
- Loss Function: Asymmetric weighting (τ=0.1 for left-tail emphasis).
- Convergence: Iterative Gaussian-Newton method for nonlinear optimization.
Empirical Results
| Cryptocurrency | Top Predictive Factor | β₁ (Slope) | AIC | Coverage Test (p-value) |
|----------------|-----------------------|------------|-----|--------------------------|
| Bitcoin | USD/CNY Rate | 82.55* | 381 | 0.23 (0.88) |
| Litecoin | Gold Index | -34.41* | 428 | 0.26 (0.60) |
| CRIX Index | S&P 500 | 25.94* | 294 | 0.24 (0.83) |
Key Findings:
- USD/CNY Rate: Strongest predictor for Bitcoin EVaR (β₁=82.55, p<0.01).
- Negative Spillovers: Litecoin shows inverse correlation with gold (-34.41).
FAQs
Q1: Why use Expectile over Quantile regression?
EVaR provides smoother tail-risk estimates and is computationally efficient, especially for extreme values.
Q2: How does MIDAS improve risk measurement?
By incorporating daily market data, MIDAS captures short-term volatilities missed by monthly aggregations.
Q3: Are cryptocurrencies isolated from traditional markets?
No. Significant β₁ values confirm risk contagion (e.g., S&P 500 impacts CRIX).
Conclusion
The MIDAS-Expectile model offers superior risk assessment for cryptocurrencies, highlighting their dependence on traditional markets. Policymakers and investors should monitor cross-market signals, particularly forex rates and equity indices.
👉 Explore real-time crypto risk analytics
👉 Compare EVaR vs. VaR methodologies
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