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<p>After J.P Morgan introduced the RickMetrics, Value at Risk (VaR) has been widely used in mid-1990. Later in the early 2000&#xa0;s, expectile began to be applied in risk management for its ability to capture tail dynamics more effectively than quantiles. This paper estimates VaR and Expectile using a hybrid approach that integrates feedforward neural networks (FNN) with statistical models, including Conditional autoregressive VaR (CAViaR) model and Realized Conditional Autoregressive Expectile (CARE) model, to enhance forecasting of quantile and expectile volatility in financial markets. Both the CAViaR and CARE models use a proxy parametric approach with the asymmetric Laplace and asymmetric Gaussian distributions. To adopt this concept to the hybrid model, their corresponding negative log-likelihoods are used as loss functions to train a neural network for quantile and expectile prediction. We provide two ways of incorporating lagged forecast information into the statistical component of the resulting hybrid model, including a cross-lagged function or self-lagged function. We compare the hybrid model against pure FNN and pure statistical models through case studies of Bitcoin and Gold data, and select the best-performing model for each quantile and expectile level. Forecasts of quantiles and expectiles using the best model at each level demonstrate strong accuracy to the target data.</p>

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Neural–statistical hybrid models for value at risk and expectile forecast with applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Nia P. Chen,
  • Jennifer S. K. Chan,
  • Linh H. Nghiem

摘要

After J.P Morgan introduced the RickMetrics, Value at Risk (VaR) has been widely used in mid-1990. Later in the early 2000 s, expectile began to be applied in risk management for its ability to capture tail dynamics more effectively than quantiles. This paper estimates VaR and Expectile using a hybrid approach that integrates feedforward neural networks (FNN) with statistical models, including Conditional autoregressive VaR (CAViaR) model and Realized Conditional Autoregressive Expectile (CARE) model, to enhance forecasting of quantile and expectile volatility in financial markets. Both the CAViaR and CARE models use a proxy parametric approach with the asymmetric Laplace and asymmetric Gaussian distributions. To adopt this concept to the hybrid model, their corresponding negative log-likelihoods are used as loss functions to train a neural network for quantile and expectile prediction. We provide two ways of incorporating lagged forecast information into the statistical component of the resulting hybrid model, including a cross-lagged function or self-lagged function. We compare the hybrid model against pure FNN and pure statistical models through case studies of Bitcoin and Gold data, and select the best-performing model for each quantile and expectile level. Forecasts of quantiles and expectiles using the best model at each level demonstrate strong accuracy to the target data.