According to that article prices are log normal. I experimented by plotting Bollinger bands on the log(price) and got exactly the same number of band crossings as when I plotted the usual bollinger bands. My sample was small, a 30 price average on one issue. Did I overlook something? It looks like, preliminarily at least, that for trading purposes, standard Bollinger bands would hardly be less useful than the "real deal".
I think Peter Ponzo said in his article that he was assuming the distribution to be lognormal instead of normal to simplify the math. It is NOT the real deal... it is just a model construct based on correct math. He is just showing how things should have been done mathematically starting with similar concepts and assumptions as Bollinger Band (Peter was a math professor)... But you probably got further than I did by playing with his stuff... Thanks for sharing. I think you can probably email him with questions since he is an educator at heart... just don't abuse the nice guy. Keep me posted!