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Plugging in a different probability distribution into GBM?

rockstarlive

Joined
7/6/13
Messages
2
Points
11
Hey everyone,
Was just wondering if a different probability distribution than lognormal was used to predict future stock prices, would there be any problems etc that would compromise the validity of the model?
 
lognormal is used to standardize the different stock returns into a normal distribution with a base 10, i suppose. the assumption is that stock returns are normally distributed. with a different probability distribution, the risk is that the model returns are assumed to follow that probability. if it doesn't, then the validity is compromised for sure. just sayin.
 
Hm ok, I was just thinking of doing some research on the accuracy of GBM predictions using the lognormal assumption vs other different distributions. Bad idea?
 
rockstarlive said:
Hm ok, I was just thinking of doing some research on the accuracy of GBM predictions using the lognormal assumption vs other different distributions. Bad idea?
Click to expand...

Don't think this will be groundbreaking work. The volatility smile present in all options markets implies distributions which are not lognormal.
 
Keith Tan said:
lognormal is used to standardize the different stock returns into a normal distribution with a base 10, i suppose.
Click to expand...
No, prices are assumed to be lognormal, which is a consequence of geometric normal returns. If you want to even consider there being a base at all, it's e, not 10.

As far as the question regarding using other distributions in simulations or whatever: yes, absolutely, use different distributions. Nothing will inherently break because of it. People typically use jump-diffusion models to make things a bit more realistic -- essentially adding a Poisson shock on top of a lognormal price process (which also requires rebalancing your volatility inputs, fyi).

There is lots and lots of evidence that stock returns are not normal. It doesn't take many daily observations to quickly realize the distribution is leptokurtic. Take a look at Benoit Mandelbrot's work.
 
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