We have spent several chapters building interest rate models. Vasicek, CIR, Hull and White, Ho and Lee, Black-Derman-Toy. Each one chosen for its nice mathematical properties, clean closed-form solutions, and easy calibration. But here is the uncomfortable question Wilmott asks in Chapter 36: do any of these models actually match what interest rates do in the real world?
In the last chapter, we saw one-factor models for interest rates. You pick a model, choose some parameters, and out comes a theoretical yield curve. But here is the problem: that theoretical yield curve almost certainly does not match the actual yield curve you see in the market. And if your model gives wrong prices for plain vanilla bonds, how can you trust it to price anything more complex?
We are leaving the world of options for a bit and entering the world of fixed income. This is the world of bonds, interest rates, and cashflows. Chapter 13 of Wilmott’s book is a self-contained introduction that does not require anything from earlier chapters. If you have ever wondered what a yield curve is or why bond traders care about something called “duration,” this is the post for you.