**4. Conclusion**

We have discovered that there are many methods used in quantifying operational risk. Therefore, it is proven handy for a risk analyst or anyone that is working in the risk analysis department of any institution to possess vast knowledge of multiple statistical concepts, and methods to apply in any given situation as each risk requires a different quantification approach. The Taxi claims data we have analyzed provides a good foundation for analyzing operational risk, but it does not represent all possible situations one might find in real life. Because Taxi claims are limited to the highest replacement value of a Taxi; in our case, we have realized that our data does not contain very extreme values; therefore, high losses are limited. The possibility of ruin would likely be due to the risk class of "high frequency and low magnitude." Using the Taxi claim data, we have provided a good example of how operational risk may be quantified and observed that the log-normal distribution is a better fit in this case. Nevertheless, it failed to model the extreme values of the Taxi claims data. Hence, the GEV distribution can be used to model those extreme values. However, in our research work, we did not dwell much on the GEV distribution. We used four approaches to calculate VaR in our analysis.

According to existing empirical evidence, the overall pattern of operational loss severity data is characterized by significant kurtosis, severe right-skewness, and a very heavy right tail caused by multiple outlying incidents. Fitting some of the common parametric loss distributions such as Weibull, log-normal, Pareto, gamma distributions, and so on is one way to calibrate operational losses. One disadvantage of utilizing these distributions is that they may not suit both the centre and the tails perfectly. Mixture distributions may be explored in this scenario. EVT can be used to fit a GPD to extreme losses surpassing a high predetermined threshold. The characteristics of the GPD distributions which are derived using the EVT approach are very sensitive to extreme data and the choice of threshold, which is a drawback of this approach.

The disadvantages of using loss distributions are that they do not model well many datasets in the presence of outliers and extreme values. Consequently, [2]'s Chapters 7 and 8 discuss other possible replacements for the loss distributions, e.g. alpha-stable distributions, GEV distribution, and GPD. The latter two distributions are part of EVT family of distributions.

Overall, it appears from the literature study done for this chapter that operational risk managers are focused on developing a model that would accurately represent the likelihood of the tail occurrences and producing a model that would realistically account for the probability of losses reaching a large amount is essential. Because, the latter is important for estimating the VaR.

Since we mainly focused on parametric distributions, and it might be interesting to use the nonparametric approach to quantify risk and some other mixture of distributions method. Therefore, this means that some of the possible additions to research work can be looking at more complex statistical distributions with better tail capturing ability. We also looked at multiple ways of finding VaR and from our findings, and we noticed that the empirical approach was the better way of quantifying the Taxi claims data's risk—note though the conclusion reached is data-dependent, which means it that a different conclusion will be made for a different dataset.
