Learning Objectives: Explain how a loss distribution is derived from an appropriate loss frequency distribution and loss severity distribution using Monte Carlo simulations. Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency and severity distributions. Describe how to use scenario analysis in instances when data is scarce.
Questions:
24.8.1. You are an operational risk analyst at a large bank. Based on historical data, you have determined that the average number of operational risk loss events per year follows a Poisson distribution with a mean of 5. To derive the overall loss distribution, you need to combine the loss frequency distribution with an appropriate loss severity distribution using Monte Carlo simulations.
Given:
a. Sample from the Poisson distribution to determine the number of loss events (n) in a year, then sample n times from the lognormal distribution to determine the loss amounts. Sum the loss amounts and repeat the process many times to obtain the overall loss distribution.
b. Calculate the 99.9th percentile of the Poisson distribution and multiply it by the mean of the lognormal distribution to obtain the 99.9th percentile of the overall loss distribution.
c. Sample from the lognormal distribution to determine the loss severity for each event, then use the mean of the Poisson distribution to calculate the total annual loss. Repeat the process many times to obtain the overall loss distribution.
d. Add the mean of the Poisson distribution to the mean of the lognormal distribution, then calculate the 99.9th percentile of the resulting distribution to obtain the 99.9th percentile of the overall loss distribution.
24.8.2. When estimating loss frequency and severity distributions for operational risk, financial institutions often rely on external data from vendors to supplement their internal loss data. However, this data may introduce biases and inaccuracies in the estimation process.
Old Crow Bank is using a loss that recently occurred at Bank A to estimate the severity of a similar loss at its institution. Given the information below, what is the loss that Old Crow most likely modeled for its bank, given the difference in size between the two banks?
a. $11,250,000.00
b. $22,500,000.00
c. $27,319,384.90
d. $4,050,000.00
24.8.3. Scenario analysis is a valuable tool for estimating loss frequencies and severities in operational risk management, particularly when historical data is scarce or unavailable. It relies on the expertise of operational risk professionals to generate plausible scenarios and estimate the associated frequencies and severities.
Which of the following statements BEST describes how scenario analysis can be used to estimate loss frequencies for rare but high-impact events?
a. Operational risk experts assign each scenario to a category based on the expected frequency of occurrence (e.g., once every 1,000 years, once every 100 years, etc.), and the corresponding average frequency is used in the analysis.
b. Operational risk experts directly estimate the mean and standard deviation of the loss frequency distribution for each scenario, which are then used in Monte Carlo simulations.
c. Operational risk experts estimate the 1st and 99th percentiles of the loss frequency distribution for each scenario, and these values are fitted to a lognormal distribution to determine the mean and standard deviation.
d. Operational risk experts assign a fixed loss frequency to each scenario based on industry benchmarks, regardless of the specific characteristics of the financial institution.
Answers here:
Questions:
24.8.1. You are an operational risk analyst at a large bank. Based on historical data, you have determined that the average number of operational risk loss events per year follows a Poisson distribution with a mean of 5. To derive the overall loss distribution, you need to combine the loss frequency distribution with an appropriate loss severity distribution using Monte Carlo simulations.
Given:
- The loss frequency follows a Poisson distribution with a mean of 5.
- The loss severity follows a lognormal distribution with a mean of $100,000 and a standard deviation of $50,000.
a. Sample from the Poisson distribution to determine the number of loss events (n) in a year, then sample n times from the lognormal distribution to determine the loss amounts. Sum the loss amounts and repeat the process many times to obtain the overall loss distribution.
b. Calculate the 99.9th percentile of the Poisson distribution and multiply it by the mean of the lognormal distribution to obtain the 99.9th percentile of the overall loss distribution.
c. Sample from the lognormal distribution to determine the loss severity for each event, then use the mean of the Poisson distribution to calculate the total annual loss. Repeat the process many times to obtain the overall loss distribution.
d. Add the mean of the Poisson distribution to the mean of the lognormal distribution, then calculate the 99.9th percentile of the resulting distribution to obtain the 99.9th percentile of the overall loss distribution.
24.8.2. When estimating loss frequency and severity distributions for operational risk, financial institutions often rely on external data from vendors to supplement their internal loss data. However, this data may introduce biases and inaccuracies in the estimation process.
Old Crow Bank is using a loss that recently occurred at Bank A to estimate the severity of a similar loss at its institution. Given the information below, what is the loss that Old Crow most likely modeled for its bank, given the difference in size between the two banks?
a. $11,250,000.00
b. $22,500,000.00
c. $27,319,384.90
d. $4,050,000.00
24.8.3. Scenario analysis is a valuable tool for estimating loss frequencies and severities in operational risk management, particularly when historical data is scarce or unavailable. It relies on the expertise of operational risk professionals to generate plausible scenarios and estimate the associated frequencies and severities.
Which of the following statements BEST describes how scenario analysis can be used to estimate loss frequencies for rare but high-impact events?
a. Operational risk experts assign each scenario to a category based on the expected frequency of occurrence (e.g., once every 1,000 years, once every 100 years, etc.), and the corresponding average frequency is used in the analysis.
b. Operational risk experts directly estimate the mean and standard deviation of the loss frequency distribution for each scenario, which are then used in Monte Carlo simulations.
c. Operational risk experts estimate the 1st and 99th percentiles of the loss frequency distribution for each scenario, and these values are fitted to a lognormal distribution to determine the mean and standard deviation.
d. Operational risk experts assign a fixed loss frequency to each scenario based on industry benchmarks, regardless of the specific characteristics of the financial institution.
Answers here:
