Extreme Value Theory (EVT) - Intro

Extreme value theory (EVT) aims to remedy a deficiency with value at risk (i.e., it gives no information about losses that breach the VaR) and glaring weakness of delta normal value at risk (VaR): the dreaded-fat tails. The key is idea is that the tail has it's own "child" distribution.

Category:

Education

Tags:

• Finance
• Quant
• Risk

[DirGun]

R.I.P VaR & Blackscholes.... I like that theory

[bionicturtledotcom]

@DirGun deep, thanks

[tapanbagchi]

Superb clarity in your words and slides! You must write a book on EVT now, unless you have done that already. Please keep up this great work!

[bionicturtledotcom]

@tapanbagchi thank you, I really appreciate such kind feedback. Candidly, I could not write such a book: EVT is deep, i am learning myself more about it ... at the time i recorded this, i was satisfied to have a shallow understanding. thanks!

[OldGoat1951]

Oops! You drew the DENSITY of the normal distribution, n(x), the probability that the normal variate, N, is in the infinitesimal interval (x, x+dx), i.e.

Pr{ x < N < x + dx} = n(x) dx

but you kept talking about the cumulative distribution function, which is

Pr{ x < N}, the integral of n(x).

Also, the term "extreme value theory" often refers to results about maxima or minima of a large number of independent random variables. No mention of that is given here.

[bionicturtledotcom]

@OldGoat1951 thanks, good point, i see why that could be confusing at the end. I wish I'd have made explicit that (of course) the CDF refers to the area under the pdf curve. As you know, it's much easier to explain the EVT idea with the more familiar pdf (as opposed to: trying to show child CDF on parent CDF).

Re: max/min of independent: I agree, good point!

[rediromasuperstar]

Very clear indeed.

[mortsde]

@mecobio As someone who is just diving into Extreme Value Theory, I was wondering if you had any suggestions for a beginners text. I'm focused on climate studies

[jdmv88]

Is the portfolio of returns created in the same way as in historial VaR (ie the historical returns) or via Monte Carlo?

Thank you!

[mecobio]

Yes, big errors!!, since the CDF is the area below the curve of PDF (or the sum in the PMF, i.e. the discrete version). Also the other error is that it is missleading to say that people add and extra distribution over the normal distribution. Recall that the sume of the PDF (or PMF) equals one, so adding one to another doesn't guarantee that one equality autmatically. Long-tailed distributions have "less shoulders" than the normal.