[R-SIG-Finance] Artificial price series

[Ron Michael]

Hi Worik, I have been following this thread in "http://r.789695.n4.nabble.com/Artificial-price-series-td3443230.html", for quite a time now, however could not convince myself in one aspect. You said that simple RW model is not quite satisfactory (Horace Tso:: evidence is clear that financial prices are anything but brownian motion) hence, many people suggested GBM for that. But I could not understand why they are essentially different. I have:

for vanilla RW:   log(S[t+1]) = log(S[t]) + epsilon~N(.,.)
for vanilla GBM:  log(S[t+1]) = log(S[t]) + (mu - 0.5sigma^2) + epsilon~N(.,.)

Of course hare I am comparing both **vanilla** type and if I want to incorporate other features like jump, heavy tail etc., then I can incorporate those features in either case. Therefore driven by some common sense, why those 2 models would be fundamentally different? Only difference I see that, I generally do not include Intercept in RW, because including an Intercept signifies some deterministic trend in the underlying price, which also makes sense.

Additionally Mark says, "returns follow brownian motion", did he mean to say that **price** follows brownian motion?

Any clarification would be highly appreciated.

Thanks,