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Flashcards in Value At Risk Deck (15):
1

VAR WITH GARCH: How estimate VaR of your PF?

- VaR: (-mu_t + q*sig_t)*M

- q=2.33

2

VAR WITH GARCH: parameter estimates

- phi negative: negative autocorr (mean reversion)

3

VAR WITH GARCH: Ljung-Box tests

- null of no autocorr (no serial corr)

- If reject: innovations and squared innovations are significantly serially correlated -> GARCH doesn't capture observed heteroskedasticity well

4

VAR WITH GARCH: 1-step forecast return and variance

- r(1) = mu + phi*r_T

- sig(1) = SQRT(w+alpha*eps^2_T+beta*sig^2_T)

5

VAR WITH GARCH: estimate VaR at 1% with forecasts

- q_return = r(1) - q*sig(1)

-VaR = -q_return * M

6

VAR WITH GARCH: drawback of GARCH

- GARCH is symmetric and has thin tails

- So it has to be modified to appropriately capture the features of the data

7

UNCOND VAR WITH EVT: estimates of xi and psi

- xi: tail index, controls for the thickness of the tail.

- If positive: implies a fat-tailed distr

- if significant: model doesn't capture the features of the data well

- psi: controls for the dispersion of the tail

8

UNCOND VAR WITH EVT: expression for quantile corresponding to a prob of 1% for the return

- q_theta = u + psi/xi * ((T/N*(1-theta))^-xi - 1)

- q, psi, xi avec ^

9

UNCOND VAR WITH EVT: Estimate VaR at 1%

- VaR = M*(u + psi/xi * ((1/x)*0.01)^-xi - 1)

- where: x: largest x realizations of negret

10

UNCOND VAR WITH EVT: drawbacks

- it assumes iidness and it depends on our choice of u

11

COND VAR WITH EVT: expression for quantile corresponding to a prob of 1% for the innovation process + quantile for return process

- q = u + psi/xi * ((T/N*(1-theta))^-xi - 1)

- q_r = sig(1)_t * q - r(1)_t

12

COND VAR WITH EVT: estimate VaR at 1%

- VaR_p = q_r * M

13

H0: xi+ = xi-

- based on the t-stat

- t = (xi+ - xi-)/SQRT(sig^2_xi+ + sig^2_xi-)

- reject if !t! > 1.96

14

UNCOND VAR WITH EVT: why is this approach inappropriate?

- it is based on the assumption that returns are iid.

- therefore it produces an uncond VaR that doesn't vary over time

15

Why cond approach better than uncond?

- cond approach incorporate a model for the vol dynamics

- and an appropriate model for the cond distr of innovations