## Forecasting Tail Risk via Neural Networks with Asymptotic Expansions

_IMF Working Papers, May 10, 2024_

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## Bibliographic details
- Authors: Yuji Sakurai, Zhuohui Chen
- Published: May 10, 2024
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9798400276637.001

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### Methodology and model
- Proposal: CoFiE-NN — a machine-learning-based approach for forecasting Value-at-Risk (VaR) that combines a neural network (NN) with Cornish-Fisher expansions (CoFiE).
- NN specification: Long Short-Term Memory (LSTM) is employed as the main NN specification.
- Rationale:
  - NN (LSTM) captures non-linear dynamics of high-order statistical moments due to its flexibility.
  - CoFiE preserves interpretability of outputs by using a well-known statistical formula (Cornish-Fisher expansions).

### Evaluation strategy
- Comparative frameworks:
  - Monte Carlo simulation.
  - Real data applications across different asset classes, with a focus on foreign exchange markets.
- Benchmark models for comparison:
  - EGARCH-t model.
  - Extreme Value Theory model.
  - Three conventional models in total (CoFiE-NN compared against these conventional approaches).

### Key empirical findings
- Performance:
  - CoFiE-NN outperforms the conventional EGARCH-t model and the Extreme Value Theory model in several statistical criteria for both the simulated data and the real data.
- Tail risk factor structure (under CoFiE-NN):
  - Only 20 percent of tail risk dynamics across 22 currencies is explained by one common factor.
  - In contrast, 60 percent of volatility dynamics across the same 22 currencies is explained by one common factor.
- New empirical measure:
  - Introduction of a new empirical proxy for tail risk named "tail risk ratio" under CoFiE-NN.

### Contributions and implications
- Methodological contribution: Integration of asymptotic expansions (Cornish-Fisher) with neural-network-based forecasting to balance flexibility and interpretability.
- Practical implication for risk monitoring:
  - CoFiE-NN provides improved VaR forecasts relative to standard EGARCH-t and Extreme Value Theory approaches in the reported evaluations.
  - The low common-factor share (20 percent) for tail risk across currencies implies substantial idiosyncratic tail dynamics that may necessitate currency-specific tail-risk monitoring and management, unlike volatility where a large common factor (60 percent) explains much of the variation.

### Keywords and technical terms
- Machine learning
- Neural Network
- Value-at-Risk
- LSTM
- Cornish-Fisher expansions (CoFiE)
- EGARCH-t
- Extreme Value Theory
- Tail risk ratio

*Forecasting Tail Risk via Neural Networks with Asymptotic Expansions — By Yuji Sakurai, Zhuohui Chen; May 10, 2024; 38 pages.*

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_Source: https://www.imf.org/en/publications/wp/issues/2024/05/10/forecasting-tail-risk-via-neural-networks-with-asymptotic-expansions-548841_