Timeline for Consensus on Cauchy distribution for stock prices
Current License: CC BY-SA 4.0
9 events
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| Feb 12, 2021 at 8:31 | history | edited | Bob Jansen♦ | CC BY-SA 4.0 |
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| Nov 17, 2013 at 15:40 | comment | added | Bob Jansen♦ | Your suggestion might work, we didn't test that. The downside is that skewness is now hard to model. We didn't publish our findings, it was just a university project with a strict deadline so we worked on the effects of aggregation. Later I asked about this on here and got a very nice answer here: quant.stackexchange.com/a/3678/848 I think the most promising approach is to assume a more friendly distribution such as the Student-$t$ or even the normal with heteroskedasticity (e.g. GARCH or Regime Switch). This will create kurtsosis and allows you to model volatility clustering. | |
| Nov 8, 2013 at 21:15 | comment | added | rwolst | Right, I imagine MCing a sample mean isn't very useful for these distributions although there could be workarounds (e.g. taking advantage of symmetry and using the median). However I do appreciate the warning. Did you happen to publish (post online) anything on this in your research? | |
| Nov 8, 2013 at 18:22 | comment | added | Bob Jansen♦ | Basically what I'm saying is this: don't repeat my mistakes. Playing solitaire is probably just as productive ;) | |
| Nov 8, 2013 at 18:21 | comment | added | Bob Jansen♦ | We found that MC doesn't really work because of the variance of the distribution you're simulating: you're pretty much guaranteed that your sample contains outliers and so even a simple statistic such as the mean will fluctuate wildly between samples (as it must). | |
| Nov 8, 2013 at 17:22 | comment | added | rwolst | Hi Bob, thanks for the answer. I'm not so worried about whether common methods of analysis would work or not, for example I can just Monte Carlo sim, although I take your point "If it works well, we would probably know by now." I'll have a look into it anyway, can't do any harm. | |
| Nov 7, 2013 at 13:03 | comment | added | Bob Jansen♦ | Except when $\alpha=2$ the variance of a stable distribution is infinite. This fact makes most common methods of analysis impossible. So my conclusion was all of them except the normal are unsuitable. | |
| Nov 7, 2013 at 12:03 | comment | added | SlowLearner | Thanks for this. Was your conclusion was that there was no stable distribution to modelling stock prices or that the Cauchy was unsuitable? (Or something else entirely...) | |
| Nov 6, 2013 at 19:10 | history | answered | Bob Jansen♦ | CC BY-SA 3.0 |