Hi, I havea basic question. sorry if its too simple.... i can use any if these following as a process for stocks. which would be more suitable under what kind of circumstances. S=S*Exp( (mu-0.5*sigma*sigma) * dt + sigma * sqrt(dt) * z) S=S*Exp( (mu) * dt + sigma * sqrt(dt) * z) thanks

the second one is wrong

sorry,second one should have been S(t+dt)=S(t) + S(t)* ( (mu) * dt + sigma * sqrt(dt) * z) whats wrong with this? thanks

WannaBeDude,This equation, >> S=S*Exp( (mu-0.5*sigma*sigma) * dt + sigma * sqrt(dt) * z)if mu is equals your asset's rate of return and z is a Wiener process, would make the discounted asset price process S/B (B=bank account) a martingale.

thanks anton.

Take the log on both sides of:and you get:This is not an equality, the S on the left hand side is S(t+dt) while the S on the right hand side is S(t). So if we subtract S(t) from both sides, we get the log return of S. The right hand side is then simply:Then take your (revised) second equation:divide through by S and subtract 1 to convert the left hand side into a simple return. The right hand side becomes:So the models are similar except the first specifies that the log return has constant volatility, the second says the arithmetic return has constant volatility. The only other apparent difference is the adjustment to the drift term in the first equation. However, this is factor needed to make the expected arithmetic return equal to mu in both cases.Which is more reasonable? If a stock goes from $50 to $100, do you expect its dollar volatility to double (that is, do you think the chance of a $2 price move in a day is now the same as the chance of a $1 move at $50)? When USD/EUR is 1.2, do you expect 50% more volatility in the rate than when it was 0.8? Would that make sense if you stated the rate as EUR/USD instead?Empirically, volatilities are not constant in either log or arithmetic returns. Over short periods of time for most assets it doesn't matter much anyway. Log returns are more tractable analytically, and have the usually desireable property that the price cannot become negative. Arithmetic returns are simpler to work with numerically, and make sense for things than can be negative (like spreads).

Hi Aaron, Thanks a lot. Exactly the explanantion i was looking for. I understand it now. Thanks Again,WannaBeDude.