Introduction

In the realm of operational risk management, understanding the potential impact of losses is crucial for effective risk assessment. The process of deriving a loss distribution is a fundamental step in this endeavor. A loss distribution illustrates the possible outcomes of losses, enabling financial institutions to gauge the range of potential financial impacts. In this chapter, we will explore how a loss distribution is derived from an appropriate loss frequency distribution and loss severity distribution using the powerful tool of Monte Carlo simulation.

Deriving Loss Distribution: Monte Carlo Simulation

Deriving a loss distribution involves capturing the interplay between the frequency and severity of losses. The process employs Monte Carlo simulation, a technique that uses random sampling to model various scenarios and their associated probabilities.

1) Loss Frequency Distribution: The loss frequency distribution represents the number of losses that occur within a given period. By analyzing historical data or expert opinions, we can develop a probability distribution for the occurrence of losses. Let’s consider a hypothetical example: a bank experiences on average 3 operational losses per month, with a standard deviation of 1.5.

2) Loss Severity Distribution: The loss severity distribution characterizes the magnitude of individual losses. Similar to the frequency distribution, historical data or expert assessments can be used to construct a probability distribution for loss amounts. Suppose in our example, the average loss amount is $10,000 with a standard deviation of $5,000.

3) Monte Carlo Simulation: The essence of Monte Carlo simulation lies in generating random samples from the frequency and severity distributions. Each random sample represents a potential loss event. By combining the sampled frequency and severity, we obtain a range of possible loss amounts. Repeating this process thousands of times results in a comprehensive set of simulated loss scenarios.

Example: Let’s say we run 10,000 Monte Carlo simulations for our bank. In one iteration, the simulation selects a frequency of 4 losses and a severity of USD 9,000. In another, it picks a frequency of 2 losses and a severity of USD 12,000. By calculating the product of frequency and severity for each simulation, we obtain a distribution of potential loss amounts.