stotastic

If you go to Google and search for “Black Scholes” you are bound to come across a long list of articles that derive the Black-Scholes PDE and Call Price formula. Before I learned about the more technical issues of stochastic calculus and martingale measures, I would read these derivations and assume the authors were the experts. There always seemed to be some hand waving going on, but I figured it was just a complex subject and I just didn’t fully understand all the details. Now, some years later and after having formally learned the material, I find myself in disbelief at how sloppy and often wrong some of these derivations are. As an example, take a look at Wikipedia’s article on the Black Scholes model. Now forget everything you just read. This article is my attempt to straighten things out. I will try to be more rigorous than most, but I may skip over some of the regularity conditions which concern the pure math types.

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