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Answer: The bank collects the daily realization of the portfolio Profit/Loss and calculate the risk model's probability of observing a realization below the actual Profit/Loss.
## Explanation **Probability Integral Transform (PIT)** derivation: For each day, the bank: 1. Collects the actual portfolio Profit/Loss realization 2. Calculates the **cumulative probability** of observing a P/L value **below** the actual realization using the risk model This is mathematically expressed as: \[ PIT_t = F_t(L_t) \] where: - \(F_t\) is the cumulative distribution function of the risk model - \(L_t\) is the actual loss realization **Why Option A is correct**: - PIT represents the cumulative probability up to the actual realization - It's the probability of observing a value **below** the actual P/L - If the model is correct, PIT values should be uniformly distributed U(0,1) **Why Option B is incorrect**: - PIT is not the probability of observing the exact P/L value - It's the cumulative probability up to and including the actual value - For continuous distributions, the probability of any single value is zero This PIT-based approach allows regulators to test both unconditional coverage and independence properties of the VaR model.
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A US bank is required to submit PIT-based backtesting information for each sub-portfolio, for each business day, on an ongoing basis. Which of the following statements correctly describe the derivation of PITs performed by the bank?
A
The bank collects the daily realization of the portfolio Profit/Loss and calculate the risk model's probability of observing a realization below the actual Profit/Loss.
B
The bank collects the daily realization of the portfolio Profit/Loss and calculate the risk model's probability of observing a realization equal to the actual Profit/Loss.
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