Forecasting Tail Risk via Neural Networks with Asymptotic Expansions

IMF Working Papers, May 10, 2024

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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).

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).

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.

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.

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