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JohnFI saw your post and wondered if you (or anyone else) can help?In the first step of solving the BS PDE, how is that the -rV term is removed by the transformation: V(S,t) = e^-r(T-t) U(S,t)? I cant find any material (online or on books) that explains this step-by-step.

malley,can you ask that question in the Student Forum? The FAQs thread is more for compiling answers really!ThanksP

I think Bjork's book 1998, chapeter 6th give a very good explanation about BS model.

Thanks, I'll check that out.

malley, if u leave me your email, I got a word document with the steps I can send you.

Thanks. My email address is: malcolm_alley@yahoo.comI look forward to reading it.

I am not quite convinced the wide use of BS, as BS is clearly based on some irrealistic assumptions, e.g., EMH, no transcation costs, etc. (it is like MM, serving a sort of benchmark).What's your comment?

Black-Scholes is widely used, not so much for the accuracy of the formula, but for its usefulness in removing many of the non-linear dependencies of an option's value so that traders can focus on the volatility dimension of the option.I'm not sure efficient markets are necessary for Black-Scholes, and Leland published a modification to handle trading costs. In my opinion, the strongest assumption is that the underlying diffuses without jumps, which basically means that you do not know the direction of the next move, but you know the size of it (dW is stochastic, but dW^2 = dt, both scaled by volatility). In deriving the Black-Scholes PDE, this shows up as volatility being locally deterministic, meaning that knowing before the move how large it will be is like knowing your convexity yield from the gamma position.