making an assumption about the relationship between the expected loss and the

Making an assumption about the relationship between

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making an assumption about the relationship between the expected loss and the unexpected loss. So, there is no need for the supervisor to determine a multiplication factor (gamma) under this approach. Also the bank itself determines the structure of business lines and event types. For more details about this approach, one will be referred to Chapter 6. 26
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6 Using LDA-based AMA approach Once loss data are collected, it must be sorted and filtered for any irrelevancy, before one can start to measure the probability of an operational loss and the potential size of an operational loss. The LDA approach involves modeling the loss severity and the loss frequency separately and than combining these distributions via Monte Carlo simulations or other statistical techniques to form an aggregated loss distribution for each loss type/business line combination, for a given time horizon. The main issue is to fit the distribution of observed total loss points to a curve of total loss occurrences. It is this curve that will allow extrapolation from data points to determine the likely amount of total maximum losses or minimum capital required at any given percentile. The biggest challenge when dealing with fitting the distribution, is selecting the distribution that fits the tail of the observed data for 99.9% confidence interval. 6.1 The loss frequency distribution A statistical manner to determine the loss frequency distribution will be discussed here. Our goal is to find the best distribution that can describe the random occurrences of the loss events. By counting the occurrence of the loss events in the loss database one can determine the frequencies of the events. Afterwards one can use statistical methods to fit several distributions on the data of the loss events. In practice, many banks that use the LDA approach assume that the operational loss frequencies follow a Poisson distribution. The Poisson distribution is most commonly used to model the number of random occurrences of some phenomenon in a specified unit of space or time. For the LDA approach, it will be used to model the number of loss events in a period. The Poisson distribution has only one parameter, ij , which is the mean and the variance of an Poisson distribution. Assuming that the probabilty distribution for every business line and event type combination, different parameters will be applied. In figure 9 one can see the graph of the Poisson distribution. Figure 9: shows the distribution density of Poisson distribution Figure 9 shows a histogram that is obtained by splitting the range of the data into equal size bins. The number of points from the loss data set that falls into each bin is represented in a percentage. Vertical axis: Frequency shown in percentage (counts for each bin).
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