Government Bonds

Valuing government-issued debt gives us the risk-free rate, a key parameter in valuation models. We focus on government bonds for this chapter. We start by discussing yields on zero-coupon debt. This leads to concepts of spot and forward interest rates and discount factors for various maturities (risk-free rates and discount factors). We discuss different yield conventions and how to convert between them. We turn next to coupon bonds—bonds with periodic fixed interest payments. We explain how to value them in terms of a portfolio of zero coupon bonds. In practice, for longer maturities, only coupon bonds exist. We discuss how to use the relationship between coupon bonds and zero-coupon bonds to estimate zero-coupon prices and yields for these maturities—a procedure known as bootstrapping. We further discuss how to use the Svensson model to fit a non-linear curve that matches actual government bond prices. The Svensson model is used by the European Central Bank and the German Bundesbank to report their interest rates. Then we discuss two lattice models of risk-free rates—the Black-Derman-Toy model and the Ho-Lee model. These models can be used to value interest-rate derivatives. Finally we discuss how we can use estimated risk-free rates for different currencies to estimate the forward exchange rate between them, using a model known as covered interest rate parity (CIRP).