**1. Introduction**

The topic presented in this chapter serves to give novice risk readers an idea of how institutions quantify their operational risks using parametric loss distributions. For various financial institutions, risk is classified into different components. Firstly though, risk is defined as the probability of an event and the potential loss. Put differently, [1] defined risk as a condition in which there is a possibility of an adverse deviation from the desired outcome that is expected or hoped for. Secondly, [2] provides an excellent account of four main categories of financial risks (more applicable in the banking sector), i.e. credit risk, market risk, operational risk, and others. For more discussion on some of the latter mentioned risks, see [3]'s Chapter 7 and the corresponding tools and techniques discussed in [3]'s Chapter 8. In this chapter, we are focusing mainly on the quantification of operational risk.

There have been multiple instances in the previous century of many big multinational firms experiencing total collapse due to a lack of risk control. For instance, employees may embezzle funds from the firm, rogue employees may make unauthorized deals, etc. For best examples of the latter, see Chapter 1 of [2] and Chapter 20 of [3]. Note though, in the South African context, the best example for poor operational risk management are Steinhoff, Hullett, Venda Building Society (VBS) mutual bank, Eskom, South African Airways (SAA) and more recently the Capitec bank computer systems failure during a peak period of the month in 2022. It is worth mentioning that a variety of sources have indicated that, in most instances, losses incurred due to operational risk normally would originate from poor management practices, outsourcing nonstrategic activities, or external factors.

In this chapter, a study on operational loss data will be conducted. We hope to determine the loss distribution that best fits the data by performing goodness-of-fit tests to the proposed models and estimating the parameters using appropriate statistical methods so that it can be possible to forecast or quantify the loss to be anticipated.

To date, financial institutions are making it a norm to manage their exposure to different types of risks, see [4]. Quantification of risk is of great importance, a proper evaluation of risk in any financial institution is an uncertainty problem that may easily lead to the bankruptcy of that firm and would consequently become a major concern for national and international financial regulatory bodies. This research work is compiled to contribute to the improvement of the quantification of operational risk using the loss distribution approach (LDA). According to [5], operational risk is the probability of loss resulting from insufficient or unsuccessful internal processes, people, and systems or from external events. Consequently, in the next section, we review the five most common parametric loss distributions namely: Pareto, Burr, gamma, Weibull, and log-normal distributions. These loss distributions are reviewed mainly in the aspect of quantification of operational risk.

This topic is applicable to a wide variety of fields as all institutions face some certain type of risk which if left unnoticed and unmanaged, could lead to total collapse of the firm or the worldwide economy (as seen in the last two global financial crises the domino effect). Operational risk is quantified in several institutions; according to [6], this is done because we cannot predict the future for certain, but we can prepare and anticipate it. Risk quantification gives us an insight into what we can anticipate. Quantification of risk is done in several financial institutions, e.g. banks, universities, insurance companies, etc. The limitation of our research is as follows: it is applicable in scenarios when the underlying operational loss data fits (or almost fits) the loss distributions considered here (i.e. Pareto, Burr, gamma, Weibull, and log-normal distributions). In the event of the data not passing the goodness-of-fit tests for any of the latter distributions, then in the concluding section (i.e. Section 4), we shall list different alternatives approaches that the readers need to consider.

Note that the field of risk identification and quantification has become more important as globalization is expanding. To date, different financial institutions are realizing the importance of quantifying risk to avoid huge losses that may even result in bankruptcy. The aspect of risk quantification is pivotal in making the best business decisions.

Therefore, the rest of the chapter is structured as follows: in Section 2, we review several publications that have covered operational risk using different loss distributions. Moreover, we take note of various approaches that were used to quantify risk exposure. Next, in Section 3, we use a dataset to illustrate quantification of risk using loss distributions. Given that this research work is a continuation of previous literature studies, in Section 4, we provide some concluding remarks and offer several possible future research topics.
