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Value-at-Risk is a family of measures used to help the owner of a position to assess its "worst case value".

3 votes

Parametric VaR with Student-t distribution

You got some things wrong: You don't have to devide sd by $\sqrt{n}$, the division is already part of the definition of $sd$. The $t$ distribution has a parameter $\nu$, the degrees of freedom. The v …
Richi Wa's user avatar
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1 vote

Value-at-Risk of the sum of three independent lognormal random variables with different conf...

After your remarks: So you have 3 lines of business and calculate VaR's for them: $$ VaR_{99.9\%}(L_1) ,VaR_{99.5\%}(L_2) \text{ and } VaR_{99\%}(L_3), $$ so if we speak in terms of events you model a …
Richi Wa's user avatar
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11 votes
3 answers
10k views

How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g. page 130 here for the formula). It involves the skewness and the excess-kurtosis of returns. The formula is clear and well studie …
Richi Wa's user avatar
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3 votes

VaR for portfolio of funds

No matter how you calculate the VaR (historical simulation, covariance approach, MC) I assume that you work on historical data or data derived from the history of assets, risk factors and theresuch. …
Richi Wa's user avatar
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1 vote

How to backtest the VaR model?

you should backtest in the future. Thus you calculate your VaR based on the last 250 business days and then look at the return tomorrow. You have to do this in a rolling/sliding fashion. Your approach …
Richi Wa's user avatar
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4 votes
Accepted

How to extrapolate VaR?

It depends on the method by which you calculate VaR. Some models (t-distributuion, normal) lead to a form of VaR such that it is just scaled volatility: $$ VaR = c \sigma $$ with some proper $c$ (e.g. …
Richi Wa's user avatar
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0 votes
Accepted

VaR interpretation for positive returns

What do you model? If negative returns are losses, then what is your interest in the "risk" of the positive ones. Most naturally you could look at quantiles of your distribution. The 1%-quantile is t …
Richi Wa's user avatar
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2 votes

What does this formula (to derive annualized volatility from VaR) mean?

I guess you want to calculate vola pa for SRRI. The logic is the following: If you have a VaR Limit for $1/m$ th of a year (e.g. if $m = 12$ then for one month which is equivalent to $20$ banking d …
Richi Wa's user avatar
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3 votes

Backtesting VaR model violation independence

The following thesis deals with VaR back testing procedures in the Basel framework link. In chapter 7 tests for violation clustering are presented. An R implementation of the runs test is e.g. given i …
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3 votes

Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

the risk neutral drift is needed for pricing of derivatives. For a $100\%$ equity portfolio you can take the real world drift - sometimes a good guess is a drift of zero. For fixed-income you could d …
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0 votes

Parametric/Analytical VaR

Let's start with one observation: Take a random variable of the form $X=\mu + \sigma Z$ for some real $\mu$ and $\sigma>0$ then $$ P[X \le x] = P[X-\mu \le x - \mu] = P[\frac{X-\mu}{\sigma} \le \frac …
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2 votes

Are these steps correct to calculate Value-at-Risk with a Monte Carlo simulation?

Concerning the weighted portfolio returns. If you have weights $w_i$ and individual returns $r_i$ of your assets then it is only precisely true that the portfolio return $r$ is given by the scalar pro …
Richi Wa's user avatar
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1 vote

Monte Carlo VaR assuming logistic distribution

If you want to get rid of the Gaussian returns, then you could have a look at Lévy processes. You could assume a t-distribution for returns for fatter tails or you could have a look at so called varia …
Richi Wa's user avatar
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1 vote
Accepted

Is Value-at-Risk translation invariant?

Translation invariance of a risk measure $\rho$ is defined as $$ \rho(X+k) = \rho(X)-k, $$ where $X$ is a random variable such that $\rho(X)$ exists and $k$ is a constant. The meaning is that if I ad …
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0 votes

Parametric VaR of a portfolio including a swap

Similar to dm63's answer: if you are the fixed payer in the swap: add a long fixed rate bond with coupon equal to the fixed rate and notional equal to the notional of the swap. add a short Floater w …
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