Modelling and comparison of confidence intervals for value-at-risk and conditional value-at-risk using influence functions

Influence Functions, a rigorous statistical tool for assessing how sensitive risk measurements are to minute changes in data, are used in this work to analyze Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two significant financial risk indicators. The main objective is to generate confidence intervals for VaR and CVaR using analytical formulations based on influence functions. Three approaches were considered for the VaR estimate: the Classical method, Historical Simulation, and the Cornish-Fisher expansion, which accounts for skewness and kurtosis. For CVaR, both the Cornish-Fisher and Classical techniques were examined. The efficacy of different techniques was assessed using simulated normally distributed returns and real financial market data. The results show that the Classical and Cornish-Fisher approaches provide stable and reliable estimates for CVaR, however the Cornish-Fisher method is more helpful for VaR when return distributions deviate from normality. Despite being less consistent and more unpredictable, historical simulation is nevertheless helpful in capturing empirical tail behavior in actual data. The Cornish-Fisher and Historical techniques offer more accurate assessments of tail risk overall, even though the Classical method is adequate for routine calculations. CVaR developed from the Cornish-Fisher extension offers a more reliable and cautious metric in harsh market conditions. The proposed method improves the robustness of risk models, promotes regulatory compliance, and aids the financial sector in making better capital allocation decisions. By combining influence functions, it provides flexible and trustworthy methods for analyzing non-normal return distributions. The study evaluates coverage probabilities and average interval lengths for the generated confidence intervals to further confirm the approach’s viability.