The Term Structure of Interest Rates: Spot, Par, and Forward Curves

Prior lessons priced fixed-income instruments by discounting all future cash flows using a single interest rate, such as the yield-to-maturity or a market reference rate (MRR) plus a discount margin. The next three lessons relax this assumption by introducing the term structure of interest rates, or the fact that interest rates vary with time-to-maturity. The ideal data to use for term structure analysis are default-risk-free zero-coupon bonds, known as spot rates or the spot curve. Since these are generally not directly observable, various estimation techniques are used. The spot curve is used to derive two other important yield curves: the par curve and the forward curve. A par curve involves bond yields for hypothetical benchmark securities priced at par, while the forward curve involves rates for interest periods starting in the future. All three of these curves are fundamental to fixed-income analysis and other applications because they represent default-risk-free rates of return for time periods that start today and in the future. We show the pricing of bonds using these different rates and establish their relationships.