Flashcards in Value At Risk Deck (15):

1

## VAR WITH GARCH: How estimate VaR of your PF?

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- 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

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- 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

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- 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

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

-VaR = -q_return * M

6

## VAR WITH GARCH: drawback of GARCH

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- 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

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- 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

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

- q, psi, xi avec ^

9

## UNCOND VAR WITH EVT: Estimate VaR at 1%

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- 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

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- 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-

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- 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?

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

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

15