Advancing Risk Management with GAS-1F: Value at Risk and Expected Shortfall Estimation

Value at Risk (VaR) and Expected Shortfall (ES) are critical metrics for quantifying financial risk. VaR estimates the maximum potential loss within a specific timeframe, while ES captures the average loss that exceeds the VaR threshold. Accurate estimation of these risk measures is vital for financial institutions; however, traditional methods often falter in addressing the dynamic volatility of financial data. This study explores the One-Factor Generalized Autoregressive Score (GAS-1F) semiparametric model, a novel approach that incorporates elicitability into its score function to circumvent distributional assumptions. Elicitability guarantees alignment between the estimated loss function and the true underlying risk measure. The GAS-1F model excels as a two-tiered, semiparametric framework for estimating VaR and ES. By applying this model to historical data from the S&P 500 index, we demonstrate its effectiveness in estimating these risk metrics. The model operates in two stages: first, it estimates the volatility of the data, reflecting the extent of price fluctuations. This estimated volatility is then utilized to calculate VaR and ES for each data point, generating a time series of daily values that offer a comprehensive view of potential risks investors face. The Diebold-Mariano test reveals that the GAS-1F model achieves superior accuracy compared to the widely used GARCH parametric model in estimating VaR and ES for stock prices. This enhanced accuracy can significantly benefit financial institutions, providing informed risk management decisions and valuable insights for short-term investors, particularly day traders, by facilitating more effective risk management strategies.