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From a quant point of view, how would you explain Multi Fractals Models in few words ? I have the level to take these courses, but won't be able to do it next year, so I want to know what I am missing.

What would they bring to someone who has already learned stochastic Calculus with Ito's integral?

Would they be more useful for front office or middle office?

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General note: This is related to an earlier question that was split because of a suggestion from another user. –  chrisaycock Jun 17 '13 at 15:13

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Multi-fractal models can be applied to the modeling and forecasting of volatility. I read the following book with much interest and actually setup couple models in order to compare performance vs Garch family models and the application of multi-fractals much better captures discontinuous regime-changes than traditional volatility models.

Multifractal-Volatility Forecasting

So, I would say that multi-fractal models definitely find applicability at quant and front office desks, however, I believe it can also equally applied in risk management, such as the estimation of Value-at-Risk. Think of assets whose volatility double from one day to the next. Traditional methods would hugely trail such regime-changes while multi-fractal models look to be much more adaptive to regime switching.

Caveat: I still try to work through the last chapters with more advanced math and not everything is yet entirely clear to me. I do this more on the side so, I am not sure whether I will be able to add more value very soon. But I may be able to post some code I used to setup a few models.

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Thanks for your answer. I would like to know one more thing: how fractals are linked to finance ? Is this just a the way curve are modeled ? –  lmorin Jun 24 '13 at 13:04
    
Here are the websites for the authors of the book studies2.hec.fr/jahia/Jahia/calvet and runmycode.org/CompanionSite/site.do?siteId=18 Download the Excel spreadsheet or the Matlab code to see how the model is structured. –  bill_080 Jun 30 '13 at 15:35
    
Here's a paper that is referenced in one of the above links papers.ssrn.com/sol3/papers.cfm?abstract_id=821714 –  bill_080 Jun 30 '13 at 15:42
    
+1 - I have a similar side interest in these. I look at and compare different multi-fractal time-frames (if time-frame makes sense in this contact). They seem to capture something of the experience of market-time, an idea difficult to define, but anyone who has watched prices ticking long enough has a sense of it. I haven't quantified this yet, but I often see extreme volatility in fine (intraday) time-frames seem jump, like an electron jumps valences, to longer time-frames one or two weeks later. Just an observation now, but it has my curiosity. –  Jagra Jul 15 '13 at 21:22
    
@Imorin, Fractals appear in finance because of the Levy processes. The usual Brownian motion is a fractal and Levy processes with an alpha-stable increments are already multifractals. –  vkrouglov Jul 24 '13 at 7:49

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