Implementing loss distribution approach for operational risk

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• https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.812
• Shevchenko, P. V. (2010).

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1. OpRisk under Basel2

• Referred to as Basel 2, banks are required to hold adequate capital against OpRisk losses
• Estimation of the annual loss distribution by modeling frequency and severity of losses is a well-known actuarial technique.
• This paper considered the Bayesian inference approach that allows to account for expert judgment and parameter uncertainty which are important issues in the OpRisk management.

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4. Modeling severity tail

• One of the popular distributions to model severity is Lognormal (a heavy-tailed distribution, sub-exponential dist where the tail decays slower than any exponential tail)
• Lognormal was suggested for OpRisk at the beginning of Basel 2 development.
• accurate modeling of extremely high losses (the tail of severity distribution) is critical and other heavy-tailed distributions are often considered to be more appropriate

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5. Calculating compound distribution

• Most popular numerical methods are Monte Carlo, Panjer recursion, and fast Fourier transform (FFT) methods.

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6. Model fitting

• 저빈도 고심도 케이스에 대해서 빈/심도 추정은 매우 어려움 (very limited data for some risks)
• 추정할 때는 (i) 모수의 최적값 추정, (ii) 모수 불확실성 정량화, (iii) 모델 성능 평가 등이 있는데, 이런 것들은 frequentist 방법과 Bayesian 방법이 있음.

6.1 Frequentist approach

• 가장 전통적인 방법론