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EN
This paper reports our estimates of the Value at Risk using Monte Carlo simulations for which we developed a computer program. Our approach involves obtaining Monte Carlo parameters by fitting real historical data of different periods to probability distributions. We applied the algorithm to the WIG20 and mWIG40 stock indices, and performed simulations for the Value at Risk at 95% and 99% confidence intervals over six estimation periods ranging from 1 trading day to 250 trading days. This approach was evaluated using the percentage failures and the Kupiec Proportion of Failures test. Our results indicate that this method is highly influenced by the choice of past historical and estimation period lengths considered. Overall, we observed that the Monte Carlo computational scheme is a reliable method for quantifying VaR when parametrized well.
EN
The objective of this research is to estimate the model risk, represented as precision, and the accuracy of the Value at Risk (VaR) measure, under three different approaches: historical simulation (HS), Monte Carlo (MC), and generalized ARCH (GARCH). In this work, to analyze the VaR model, the accuracy and precision were used. Estimation of the accuracy and precision was done under the three approaches for four European banks at 95 and 99% confidence levels. The percentage crossings and Kupiec POF were used to judge the model accuracy, whereas the ratio of the maximum and minimum VaR estimates, and the spread between the maximum and minimum VaR estimates were used to estimate the model risk. This was achieved by changing input parameters, specifically, the estimation time window (125, 250, 500 days). Implications/Recommendations: The accuracy alone is not sufficient to evaluate a model and precision is also required. The temporal evolution of the precision metrics showed that the VaR approaches were inconsistent under different market conditions. This article focuses on the accuracy and precision concepts applied to estimate model risk of the Value at Risk (VaR). VaR is the foundation for sophisticated risk metrics, including systemic risk measures like Marginal Expected Shortfall and Delta Conditional Value at Risk. Thus, understanding the risk associated with the use of VaR is crucial for finance practitioners.
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