Market Risk and Var Models 3: Backtesting

Question 1

What is the best solution for VaR backtesting?

Answer 1

Consistency between frequency of losses and VaR confidence interval

Question 2

Which economic result should we compare with VaR?

Answer 2

P&L obtained by using previous day portfolio and revauling it at the new market conditions (static P&L)

Question 3

What is a type 1 error?

Answer 3

Reject a good model

Question 4

What is a type 2 error?

Answer 4

Accept a bad model

Question 5

What is the Kupiec approach to testing models?

Answer 5

Null hp: the actual empirical frequency of exceptions, π = x/N, is equal to the theoretical desired one, p
If H₀ is true, then the probability of observing x exceptions in a sample of N observations is given by the binomial distribution:
prob(x|p,N) = (^N_x) * p^x * (1-p)^N-x

Question 6

What is the unconditional likelihood ratio test?

Answer 6

LR_uc = -2 * ln[(p^x * (1-p)^N-x)/(π^x * (1-π)^N-x)]

chi squraed distribution