FRM: Lognormal value at risk (VaR)

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You can get the spreadsheet on our website. The key ideas of this lognormal VaR ("what can I expect to lose with 95% confidence under lognormal property of stock prices?") are:
* If log returns are normal, future prices are lognormal
* Future lognormal is skewed, so future mean is greater than future median
* Confidence interval uses two-tailed deviate; e.g., 1.96 @ 95%
* VaR always uses a one-tailed deviate; e.g., 1.645 @ 95%
* Don't forget this is just a model: we don't really believe stock prices follow this process exactly! We know the normal isn't realistic ....
For more financial risk videos, visit our website! www.bionicturtle.com

Опубликовано:

28 июл 2010

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Комментарии : 8

@axe863 11 лет назад

A simple generalization would be to replace geometric brownian motion with geometric fractional brownian motion w/ H in (0,1) ==> GBM is just a GFBM w/ H=1/2. From what I can recall, the only difference in the log- (fractional) normal distribution is sigma==> sigma*(T-t)^H-0.5.

@bionicturtle 13 лет назад

@akathetruthteller yes E[(e^X)] = e^[mu + sigma^2/2] but S(t) = S(0)e^[(mu - sigma^2/2)T+sigma*sqrt(T)*z] reduces to E[St] = S(0)*e^(mu*T) for the mean which is greater than the median. Not so much as shift as, to paraphrase Culp, how you define the drift

@bionicturtle 13 лет назад

@adang23 yes, thank you, of course I agree that is more correct! (i don't think it impacts anything subsequently ... I confuse myself sometimes because "expected return" mu can be defined either as mu-variance/2 or just mu but clearly your are right about the LN() distribution).

@DrHerbertBarber 3 года назад

Nice example. May be nice if you showed everyone how to actually calculate drift (return), as well, rather than just assume, to use when appropriate.

@adang23 13 лет назад

I think it is more accurate to say ln(S_T/S_0) follows a N(mu-0.5sigma^2,sigma^2) distribution, rather than N(mu, sigma^2) distribution...

@vanvivoi 9 лет назад

Hey, thank you so much for the great video. Can you give me a hint in which bibliography sources I can get these formulas? Thanks a bunch :D

@rexz9338 5 лет назад

I like the video but I might have to point out something here. The result and definition of Mean are not accurate here. ln(S_T/S_0)~N(u, sigma^2), then when you calculate expectation(mean) of S_T, it should be integral of (g(x)f(x)dx), which equals to S_0*e^(u-(sigma^2)/2) i.e. the result of the median in the video. Then you use the expectation to calculate the confidence interval and VaR with the approximation to normal distribution. The definition of VaR and confidence interval both deal with the expectation(mean) instead of the median.

@akathetruthteller 13 лет назад

man, you should double check. i think for lognormal RV. E(X) =exp( mu + sigma^2/2) and median = exp(mu). you are implying a shift of calculation somehow.