After agonising over the almost haphazard notations on the lecture notes provided by my course on Black-Derman-Toy interest rate model, and getting absolutely nothing out of it after almost 2 hours of my life, I decided to appeal to Emmanuel Derman himself.
And soon the whole gist of the story became clear to me. It was not particularly because the original paper was well written--and it was sparkling in its clarity, as befits a typical Fischer Black paper--but because the idea was essentially very simple. Add-and-subtract simple. Heartbreakingly simple.
And I looked back to my lecture notes. I was not alone in getting all muddled up reading them, judging from the collective confusion in the class after the lecture. And I had to wonder, and perhaps never getting a satisfactory answer--how could anyone make something simple appear so incomprensible.
Richard Feynman once said, "If you can't explain anything simply, you don't know what you're talking about." Does the guy really understand what he is teaching? This is a complete and systemic breakdown of communication. And we, as the students, are made to pay, with our time, with our money, with our pride. Sometimes, I find no difference between institutional education and institutional abomination.
Now I realised I had missed the point completely when my rudimentary understanding of the Black-Derman-Toy was cruelly exposed in an exam. In order to back out a r(2,-2) short rate, I had to perform tons of frustrating calculations, which I had later realised was completely unnecessary had I actually understood the powerful concept of state pricing. With state pricing, I could back out short rates, yield curve, and even forward yield curves. And that was what our lecture notes had been driving at all along. I learn, I learn...But the notations are still terrible!