Quantifying Risk Using Loss Distributions

Risk is unavoidable, so quantification of risk in any institution is of great importance as it allows the management of an institution to make informed decisions. Lack of risk awareness can lead to the collapse of an institution; hence, our aim in this chapter is to cover some of the ways used to quantify risk. There are several types of risks; however, in this chapter, we focus mainly on quantification of operational risk using parametric loss distributions. The main objective of this chapter is to outline how operational risk is quantified using statistical distributions. We illustrate the application of parametric loss distributions' risk quantification using "Taxi claims data" which seems to best fit one of the loss distributions and fully illustrate how to quantify this specific data. More importantly, we also illustrate how to implement quantification of risk for two other scenarios: (i) if we assumed the underlying distribution is unknown and use the nonparametric empirical distribution approach, and (ii) when using the generalized extreme value (GEV) distribution approach. The latter two scenarios were not the main objective but were done in an effort to compare our results with some of the more commonly used techniques in real-world risk analysis scenarios.