4 ms·
Slightly off-topic: looking at his graph, I remembered the idea that internet traffic is fractal-like in time domain. http://c2.com/cgi/wiki?InternetTrafficIsFr
by dexen 15y ago
Slightly off-topic: looking at his graph, I remembered the idea that internet traffic is fractal-like in time domain. http://c2.com/cgi/wiki?InternetTrafficIsFractal http://c2.com/cgi/wiki?InternetTrafficIsFractal
...because the graph looked just like a fractal fragment to me. That coincidence, or are stock prices indeed fractal-ish in time domain?
- jerf 15y agoGoogle around for "fractal stock market" and you'll have some fun. (I don't exactly know where to start suggesting the read, or I'd give a more concrete suggestion.)
- JonnieCache 15y ago>are stock prices indeed fractal-ish in time domain? Guess what Benoît Mandelbrot studied before he started doing pure maths? ;) EDIT: for bonus points, guess why he fell out with his old friends in the 90s.
- arethuza 15y agoDid he suggest that the quants at hedge funds were merely lucky rather than supremely clever? http://liberalironist.wordpress.com/2010/10/08/book-review-the-quants-part-ii-the-meaning-of-models-statistics-and-social-science/ http://liberalironist.wordpress.com/2010/10/08/book-review-t... [Edit: I have read The Quants it's an interesting book]
- scythe 15y agoWell, they're clever for getting hired by a hedge fund for seven figures...
- JonnieCache 15y agoIt's to do with the asian and russian crises of the late 90s, which he felt showed that the black-scholes models were wrong and inferior to his own multifractal view of the market. After those crashes, he wrote articles and books attacking those ideas. http://www.scientificamerican.com/article.cfm?id=multifractals-explain-wall-street http://www.scientificamerican.com/article.cfm?id=multifracta... http://books.google.com/books/about/Misbehavior_of_markets.html?id=9w15j-Ka0vgC http://books.google.com/books/about/Misbehavior_of_markets.h...
- dxbydt 15y agoWhen you model equities as log-normal ie. log(stock price) is normally distributed, and then use the geometric brownian motion to model the underlying, which spits out derivative prices using Black-Scholes. The problem is that normal distribution is thin-tailed ie. 5 sigma events are extremely rare. So use a fat tailed distribution - which is what Mandelbrot did. He used a power-law ( Pareto ) distribution because its infinite variance permitted wider swings in price than the Gaussian. However the simplicity of using a Normal distribution is what makes Black Scholes so robust. If a thousand statisticians look at market data over a time window & model it to fit a lognormal usaing MLE, they'll come up with approximately the same parameters, so calibration is relatively easy. In fact this is one of the standard exercises in any MFE pgm - to calibrate a derivatives model corresponding to underlying data over a time window. With Mandelbrot's Paretian distribution, calibration is virtually impossible. No two people get the same parameters given the same data points on a Paretian model. There is quite a bit of literature on this very topic, in both Taleb's last book & elsewhere. Mandelbrot points out how given different time windows, the Paretian distribution can be calibrated to fit virtually anything, but the parameters will change wildly. Essentially, given the choice between an inaccurate robust simple Gaussian model with high predictive power and a supposedly accurate but un-usable Paretian model, financial engineers choose the former & add fudge-factor explanations ( eg. the vol-smile ) to augment the data. 1. http://blogs.reuters.com/justinfox/2010/10/18/why-didn%E2%80%99t-people-in-finance-pay-attention-to-benoit-mandelbrot/ http://blogs.reuters.com/justinfox/2010/10/18/why-didn%E2%80... 2. http://en.wikipedia.org/wiki/Fat_tail http://en.wikipedia.org/wiki/Fat_tail 3. http://brokensymmetry.typepad.com/broken_symmetry/2009/08/what-mandelbrot-and-fama-both-got-wrong.html http://brokensymmetry.typepad.com/broken_symmetry/2009/08/wh...
- MetaMan 15y agoThank you. I understand things a bit better now.
- gersh 15y agoEvery trader knows black-scholes doesn't work. According to black-scholes the volatility curve should be flat, but it is actually a smile. Believing black-scholes works is like believing the earth is flat.
- atakan_gurkan 15y agoYes, they are. An excellent reference is Mandelbrot's last book: http://books.google.com/books?id=DPwBTj99a7UC&printsec=frontcover&dq=mandelbrot+books&hl=en&ei=uWD7TaSNC8ubOqXpwLkE&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDoQ6AEwAQ#v=onepage http://books.google.com/books?id=DPwBTj99a7UC&printsec=f...
- iwwr 15y agoHave fractals been used in stock strategy models so far?