Hi,I am currently reading some articles about pricing products by using martingales. I cannot find anywhere explained how you calculate an expectation under a 'new' measure (I guess it's a bit too basic..). I wrote a simple example out in the attached PDF. Basicly I have a stock and a money market account. I change the measure of the stock such that it has a drift equal to the MMA. So the ratio has no drift under the Q measure. But if I am going to simulate the expectation (I keep a fixed IR), what process do I use for the stock? The process with the measure Q? Can I then just simulate 1 big 'jump' to the point where the asian tail starts and from there on simulate each day??Thanks a lot,Prak Picture file with the same question (tidy):Tidy, typed explanation of my question

I'm not really sure I understand what your question is. However, just a quick look: are you really trying to use an arithmetic brownian motion? Or did you want a geometric? Also I think you are missing a dt in your C-M-G terms. Is this homework? What's the "asian Tail" bit about?

Look for an article from Pelsser on the mathematical foundations of convexity correction, from memory this contains what you are after.

QuoteOriginally posted by: PaperCutI'm not really sure I understand what your question is. However, just a quick look: are you really trying to use an arithmetic brownian motion? Or did you want a geometric? Also I think you are missing a dt in your C-M-G terms. Is this homework? What's the "asian Tail" bit about?Yes, you're right.. I foregot a dt in (5)For simplicity let's foreget about the asian tail. I just want to price the claim V on s<t. In fact all I need then is e^{-r(T-s)}E_Q(V(T,S(T)). The first part is just deterministic (as I assume just a constant r, then I am left with E_Q(V(T,S(T)). If I want to 'calculate' this expectation by using simulation. What process do I need to simulate? Can I just draw some standard normal distr. numbers, for equation (4)??thanks!!Prak

QuoteOriginally posted by: prakQuoteOriginally posted by: PaperCutI'm not really sure I understand what your question is. However, just a quick look: are you really trying to use an arithmetic brownian motion? Or did you want a geometric? Also I think you are missing a dt in your C-M-G terms. Is this homework? What's the "asian Tail" bit about?Yes, you're right.. I foregot a dt in (5)For simplicity let's foreget about the asian tail. I just want to price the claim V on s<t. In fact all I need then is e^{-r(T-s)}E_Q(V(T,S(T)). The first part is just deterministic (as I assume just a constant r, then I am left with E_Q(V(T,S(T)). If I want to 'calculate' this expectation by using simulation. What process do I need to simulate? Can I just draw some standard normal distr. numbers, for equation (4)??thanks!!PrakWell yes - and no. First, let's just double check: are you sure you want arithmetic brownian motion? Secondly, using this equation requires you do something: either a) "solve" it for S(t) or b) "discretize" itand then simulate using the random numbers you discussed.