I had the good fortune of meeting Barone-Adesi today, the man behind the closed form solution for american option. I managed to speak to him about 15 min and was amazed by his enthusiasm and the way he could connect ideas from fluid dynamics, physics, mathematics, fractal geometry. He cautioned me not to think about doing anything on the American option side as he had spent a pretty long time on the field and felt that there are more interesting things to look at in the non-american option side of things.