oops, sent the message twice, sorry.

...as someone mentioned earlier...this theory has beenaround for quite a while and still...at least in my case...I realize that there are gaps in my understanding of it...Here is another question...is the sigma in the BS formula, volatility of RETURNSor volatility of PRICE of the UNDERLYING?In the first case, sigma=0 means that the expected stock pricein the next period is S(t)*(1+r), at the end of the next period.In the second case, the expected stock pricein the next period is S(t), at the next period.I am being lazy and not taking a look at Hull,but Iexpect that the insights that I will get from the repliesof this forum will outweight the embarassment of not noticingthis very essential detail.

I think volatility of the stock = annualized standard deviation of stock returns

Reza is correct. But your conclusion that the expected future stock price is S(t)*(1+r) is not correct. First of all, to be pedantic, BS is a continuous time model so you should write:E[S(t2)|S(t1)] = exp[r*(t2-t1)]*S(t1)but even this is not correct. The expected return on the stock is not the risk-free rate. In the BS world you can pretend that it is, because BS gives preference-free pricing (meaning price does not depend on risk preference, so you can price for the simplest case, risk neutrality, and get the same answer as any other assumption). So a risk-neutral person would either believe the expected return on the stock is the risk-free rate of interest, or think he had found a arbitrage opportunity. But those of us with some risk aversion will think the expected return on the stock is greater than the risk-free rate.