Abstract
Under Basel III the minimum capital requirement due to operational risk is computed as the 99th quantile of the annual total loss distribution. This annual loss distribution is a result of the convolution between the loss frequency and the loss severity distributions. The estimation of parameters of these two distributions i.e. frequency and severity distributions is not only essential but crucial to obtaining reliable estimates of operational risk measures. In practical applications, Poisson and lognormal distributions are used to fit these two distributions respective. The maximum likelihood method, the method of moments as well as the probability-weighted moments used to obtain the parameters of these distributions can sometimes produce nonsensical estimates due to estimation risk and sample bias. This paper proposes a different calibration of the frequency and the severity distributions based on Bayesian method with Gibbs sampler. Further to that, the paper models the severity distribution by making use of the lognormal and the generalised Pareto distribution simultaneously. Simulated results suggest that computed operational value at risk estimates based of this new method are unbiased with minimum variance.
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References
Castillo E, Hadi AS (1997) Fitting the generalized Pareto distribution to data. J Am Stat Assoc 92(440):1609–1620
De Zea Bermudez P, Turkman MA (2003) Bayesian approach to parameter estimation of the general ized Pareto distribution. Test 12(1):259–277
Hosting JRM, Wallis JR (1987) Parameter and quantile estimation for the generalized pareto distribution. Technometrics 29:339–349
Hull J (2012) Risk management and financial institutions, + Web Site, vol 733. Wiley, New York
Smith RL (1984) Threshold methods for sample extremes. In: Trago de Oliveita J (ed) Statistical extremes and applications. Springer, Netherlands, pp 621–638
Teply P (2012) The application of extreme value theory in operational risk management. Ekono micky Casopis 60(7):698–716
Lin TT, Lee C-C, Kuan Y-C (2013) The optimal operational risk capital requirement by applying the advanced measurement approach. Centr Eur J Oper Res 21(1):85–101
Sklar A (1959) Fonctions de Répartition à n Dimensions et leurs Marges, vol 8. Publication de L’Institut de Statistique de L’Universsité de Paris, pp 229–231
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Muteba Mwamba, J.W. (2017). Computation of Operational Value at Risk Using the Severity Distribution Model Based on Bayesian Method with Gibbs Sampler. In: Dinçer, H., Hacioğlu, Ü. (eds) Risk Management, Strategic Thinking and Leadership in the Financial Services Industry . Contributions to Management Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47172-3_8
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DOI: https://doi.org/10.1007/978-3-319-47172-3_8
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