Analytic Loss Distributional Approach Model For Operational Risk From The Alpha-stable Doubly Stochastic Compound Processes And Implications For Capital Allocation
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilized to undertake capital estimation. It has however become well accepted to utilize a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss process corresponding to the Basel II Business line/event type. In this paper, the authors derive a novel class of doubly stochastic -stable family LDA models. These models provide the ability to capture the heavy tailed loss process typical of OpRisk whilst also providing analytic expressions for the compound process annual loss density and distributions as well as the aggregated compound process annual loss models. In particular they develop models of the annual loss process in two scenarios.