October 11th, 2011, 12:49 pm
QuoteOriginally posted by: arnablostbeingThanx all...the model is a continuous model but we want the total volume at year endings which is just the sum of X_t s at t=1,2,3...n.So no integration only summation.I have used the monte carlo simulation.Mean and variance estimates are reasonable not t he percentile estimates.In literature there is no exact solution to the distriution of sum of lognormals.I suspect your distribution can be determined exactly with a little algebra. Write out exactly the random variable you want the distribution for, in the case n=3.Now write it in terms of the independent increments x_j = log S(j)/S(j-1).What is the characteristic function for that sum?Invert it to get your distribution.Generalize to all n.If this is not clear, post your steps up until the part where you get stuck.p.s. This might be a lot harder than I suggested.
Last edited by
Alan on October 11th, 2011, 10:00 pm, edited 1 time in total.