Derivation of the Joint Distribution and Capitalisation of Operational Risk

Rafael Cavestany and Daniel Rodríguez

Having described in Chapter 7, the methods for creating severity and frequency distribution hybrid models with different data elements, we now look at the derivation of the joint distribution and capitalisation of operational risk, using hybrid or single-data-element models.

The process described in Chapter 7 delivers a single severity or frequency distributions per ORC, incorporating all the operational loss information contained in ILD, ED and SA. This input is then used for the determination of the joint distribution and capitalisation of operational risk. BCSG-AMA says, “The techniques to determine the aggregated loss distributions should ensure adequate levels of precision and stability of the risk measures,” also suggesting, “As such, simulation, numerical or approximation methods are necessary to derive aggregated curves (e.g. Monte Carlo simulations, Fourier Transform-related methods, Panjer algorithm and Single Loss Approximations).”

The final output of this process represents the operational risk profile main metrics utilised in the use test for integrating the capital results into day-to-day risk management.

In this chapter, we present methods for the derivation