Part Three

Term Structure Models

Part One of this book showed how to price securities with fixed cash flows relative to the prices of other such securities. Part Two showed how to measure and hedge the interest rate risk of securities with fixed cash flows, and also described the hedging of more complex securities, provided that a pricing model for those securities had been made available. Term structure models, the subject of Part Three, are used for more general and complex pricing and hedging problems, including the following:

- Pricing a security with fixed cash flows relative to the prices of other securities with fixed cash flows when the security in question cannot, using the methods of Part One, be priced by arbitrage. An interesting example is pricing a 50-year swap when market swap rates are available out to only 30 years.
- Pricing a generic interest rate contingent claim relative to the prices of securities with fixed cash flows, where an interest rate contingent claim is a security whose cash flows depend on the level of interest rates. An option to purchase a bond at a fixed price at some future expiration date would be an example of this application: the value of the option depends on the price of the underlying bond and, therefore, on interest rates, as of the expiration date.
- Pricing an exotic derivative relative to the prices of vanilla derivatives.1 An example here would be a derivatives desk pricing a Bermudan-style swaption (i.e., an option on a swap that may ...