Probability in Finance: Density Functions and First-Exit Times
Most of derivative pricing theory goes out of its way to avoid thinking about probability. The whole point of hedging and no-arbitrage is to eliminate uncertainty. You do not need to know where the stock is going; you just need to build a portfolio that does not care. But Chapter 10 of Wilmott’s book asks us to step back and look at the randomness underneath. Where might the stock actually end up? How long before it hits a certain level? These questions matter for American options, for speculation, and for understanding what the math is really doing.