Estimating Model Risk of VaR under Different Approaches: Study on European Banks

Authors

DOI:

https://doi.org/10.52934/wpz.151

Keywords:

VaR, Monte Carlo, model risk, precision, historical simulation, GARCH

Abstract

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.

References

Basel Committee on Banking Supervision. (2004). Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework. Bank for International Settlements.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1

Danielsson, J., James, K. R., Valenzuela, M., Zer, I. (2016). Model risk of risk models. Journal of Financial Stability, 23, 79–91. https://doi.org/10.1016/j.jfs.2016.02.002

Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773

Ferenstein, E., Gąsowski, M. (2004). Modelling stock returns with AR-GARCH processes. Statistics and Operations Research Transactions, 28(1), 55–68.

Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer Science+Business Media.

Holton, G. A. (2014). Value-at-Risk: Theory and Practice, Second Edition. Value-atrisk. https://www.value-at-risk.net (accessed: 17th November 2021).

Pasieczna, A. H. (2019). Monte Carlo Simulation Approach to Calculate Value at Risk: Application to WIG20 and MWIG40. Financial Sciences, 24(2), 61–75. https://doi.org/10.15611/fins.2019.2.05

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Published

2021-12-31

How to Cite

Pasieczna, A. H., & Szydłowska, M. J. (2021). Estimating Model Risk of VaR under Different Approaches: Study on European Banks. Contemporary Management Problems, 9(2(19), 65–76. https://doi.org/10.52934/wpz.151

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