Imagine you’re trying to price a call option on a 10‑year bond that expires in three years. The bond’s price at expiry doesn’t depend on just one number—it depends on the whole shape of the yield curve at that future moment. To handle such problems, we need a model that describes how the entire term structure of interest rates can change randomly over time. In this chapter, we’ll build that kind of model from the ground up, starting with the short rate as the basic driver, and we’ll build a calibrated tree that matches today’s bond market. By the end, you’ll be able to value a wide range of interest rate derivatives with confidence.