Imagine you hold a lottery ticket that pays off depending on the final price of a stock. How much should you pay for it today? It feels like gambling, but with options there is a clever, risk‑free way to build that same payoff using the stock and a bank loan. The binomial model turns that idea into a step‑by‑step recipe. By the end of this chapter you will be able to price both European and American options — and handle dividends — using nothing more than simple arithmetic and a clear tree structure.