Learning Objectives: Identify the properties of an exceedance-based back test that indicate a VaR model is accurate and describe how these properties are reflected in a PIT-based back test. Explain how to derive probability integral transforms (PITs) in the context of validating a VaR model. Describe how the shape of the distribution of PITs can be used as an indicator of the quality of a VaR model.
Questions:
25.3.1. Based on the data provided, which portfolio's back test indicates a more accurate VaR model?
a. Both Portfolio X and Y
b. Only Portfolio Y
c. Only Portfolio X
d. Neither Portfolio X nor Y
25.3.2. Using the table below, determine the Statistic (Z-score) that corresponds to the PIT value on Day 4. Additionally, identify a day where the realized result was in the lower tail of the forecasted distribution, meaning the model expected a significantly higher value.
a. 1.50, Day 4
b. -5.00, Day 4
c. 1.50, Day 8
d. 3.40, Day 3
25.3.3. The risk team at Horizon Capital is reviewing their Value-at-Risk (VaR) model after a period of unexpected market volatility. To ensure the model is accurately predicting risks across all percentiles of potential losses, the team uses the Probability Integral Transform (PIT) distribution to evaluate the model’s calibration.
During their analysis, the team observes patterns in the PIT distribution and discusses whether the model is well-calibrated or requires adjustments to better capture tail risks and market dynamics.
Which of the following observations would indicate that the VaR model may have been poorly calibrated?
a. Well calibrated, the PIT distribution is uniform across [0,1], with no clustering in the tails or center.
b. Poorly calibrated, The PIT distribution exhibits a concentration of values near 0, indicating frequent underestimation of extreme losses.
c. Poorly calibrated, the PIT distribution shows slight deviations around the center but aligns well with a uniform distribution in the tails.
d. PIT distribution has skewness close to 0 and kurtosis near 3, indicating balanced calibration of the model.
Answers here:
Questions:
25.3.1. Based on the data provided, which portfolio's back test indicates a more accurate VaR model?
a. Both Portfolio X and Y
b. Only Portfolio Y
c. Only Portfolio X
d. Neither Portfolio X nor Y
25.3.2. Using the table below, determine the Statistic (Z-score) that corresponds to the PIT value on Day 4. Additionally, identify a day where the realized result was in the lower tail of the forecasted distribution, meaning the model expected a significantly higher value.
a. 1.50, Day 4
b. -5.00, Day 4
c. 1.50, Day 8
d. 3.40, Day 3
25.3.3. The risk team at Horizon Capital is reviewing their Value-at-Risk (VaR) model after a period of unexpected market volatility. To ensure the model is accurately predicting risks across all percentiles of potential losses, the team uses the Probability Integral Transform (PIT) distribution to evaluate the model’s calibration.
During their analysis, the team observes patterns in the PIT distribution and discusses whether the model is well-calibrated or requires adjustments to better capture tail risks and market dynamics.
Which of the following observations would indicate that the VaR model may have been poorly calibrated?
a. Well calibrated, the PIT distribution is uniform across [0,1], with no clustering in the tails or center.
b. Poorly calibrated, The PIT distribution exhibits a concentration of values near 0, indicating frequent underestimation of extreme losses.
c. Poorly calibrated, the PIT distribution shows slight deviations around the center but aligns well with a uniform distribution in the tails.
d. PIT distribution has skewness close to 0 and kurtosis near 3, indicating balanced calibration of the model.
Answers here:
