Not homework :-)pointers to lecture notes greatly appreciated .1. Very simple, but would appreciate if someone could educate me on the theory. Given the current stock price (start value), target stock price , number of days, and historical volatility, how do I get the probability that the stock would achieve that value. I know the assumptions (normdist etc), would appreciate if someone could point me to lecture notes etc2. Also what volatility data should I use 3 month vol, 1 month vol etc. Does this depend on the number of days paramater ? 3. Are there other ways to do this, I have heard about monte carlo's etc.

Are you looking for the probability that the stock price will exceed the target price at the expiration, or the probability that the stock price will be above the target price at some point before expiration? The first is a simple Normal distribution formula:S0 = current stock priceT = target stock prices = volatilityd = driftt = time to expiryN[] is the standard cumulative Normal functionthen:N[(ln(S0/T) + d*t)/s*t^0.5 - s*t^0.5]is the probability of St being above the target price. You would use the volatility parameter for t. Be careful to distinguish whether the distribution parameters are actual or risk-neutral (in the latter case, d should equal the risk-free rate, but you get a pseudo probability for an answer, not an actual probability.In the second case there is a slightly less simple formula if the volatility is constant. If not, you'll probably have to solve by simulation.

the distributions for min and max of a Brownian motion with drift can be found in Karatzas and Shreve, or Musiela and Rutowski. MJ

Thank you,I am looking for the probability that the stock price will exceed the target price at the expiration. Hence I willuse your formula. Regards

I had heard of State Price Density, and assumed that it is related to probabilties for share price movements,but don't know exactly .Can someone please throw some light when it is used?Thanks,asd

State price densities are pseudo-probabilities. They obey the mathmatical rules of probabilities but they reflect the utility of a state in addition to its probability.Say a bond has 1 chance in 100 of defaulting in the next year. That's a probability. Say a credit default swap that pays $1,000 if the bond defaults in the next year costs $20. The state price density is 2%. It's higher than the probability because money is more valuable in a bad state (default) than a good one (no default).You can value a security by taking its expected value under the state price densities, and discounting at the risk free rate of interest. This is called risk-neutral pricing.

DronaCan we divide your task into 2?• Get the expected price of the stock at the time t (using the drift/So as an expected rate of return): Ln(St)=(Ln (So)+(d/So-(s^2)*t));• Take the matter from time T, calculating the relevant Z-value :Z=(Ln(T)-Ln(St))/(s*t^2)Well described in John C. Hull, chapter 12