Derivatives

CHAPTER 10Bonds: Duration and Convexity

Aims

• To demonstrate how spot-rates for different maturities give rise to the (spot) yield curve.
• To show how duration and convexity can be used to provide an approximation to the change in bond prices, after a change in the yield to maturity (YTM).

10.1 YIELD CURVE

Investors borrow (and lend) money over different periods of time. For example, to borrow money today and pay back the principal and interest in 1 year's time, the cost of borrowing might be p.a. To borrow today and pay back the principal and interest in 2 years' time (i.e. there are no interim payments), then the quoted interest rate might be p.a. Because each of these interest rates are quoted for borrowing from today, over a fixed horizon (with no interim payments), they are known as spot-rates (or spot yields).

The (spot) yield curve shows the relationship between (spot) interest rates for different maturity investments. We assume we are dealing with risk-free investments – there is no risk of default. For example, the yield curve at 10 a.m. today might look like that in Figure 10.1. The yield curve in Figure 10.1 is upward sloping, which simply means that if you borrow money at 10 a.m. today then the longer the maturity of your loan, the higher the (spot) interest you will ...