Yield Curve

Overview

When money is borrowed or lent for a given period of time, the money earns a pre-agreed to interest rate. However, the rate of interest earned is usually dependent on the period over which the money is lent. This means that interest rates are best represented as being a curve, that is, a function of the time to maturity.

Types of Curves

Even though it is typical to just refer "the curve", there are actually multiple curves, the difference being how the curve is being quoted or measured. For instance, the yield curve typically refers to a plot of current yield to maturies versus period.

There are problems with yield to maturity however, the primary issuse being that even in efficient markets and accounting for all mitigating factors like tax treatment and credit risk, two bonds structured differently (for example amortized versus bullet) will trade at different yield to maturities.

This problem can be solved by using the zero coupon bond rate versus period instead of ytm. The zero coupon bond rate is the quoted rate for a single payment at the given maturity. This rate is usually quoted in annualized terms, or possibly in continuous time terms.

From the zero coupon rate curve, once can invert the rate an obtain the discount curve, or the curve of discount rates.

Topics

• Theories of the Term Structure : various theories have been put forward to explain the shape of the curves discussed above.
• Estimating the yield curve refers to a process whereby a smooth curve, (in this case, a function of time) is calculated from a discrete set of bond prices. The smooth yield curve is then used in fixed income models to price other instruments.
• Derivations of the various rate relationships on the curve, including forward rate relationships.
• Forward Curve - Most forward looking analysis will require that the interest rate curve be simulated, either as a given fixed scenario, or through monte carlo type simulations.