Bond instrument discount factors

Bond prices are expressed per 100 nominal —that is, as a percentage of the bond s face value. (The convention in certain markets is to quote a price per 1,000 nominal, but this is rare.) For example, if the price of a U.S. dollar-denominated bond is quoted as 98.00, this means that for every 100 of the bond s face value, a buyer would pay 98. The principles of pricing in the bond market are the same as those in other financial markets the price of a financial instrument is equal to the sum of the present values of all the future cash flows from the instrument. The interest rate used to derive the present value of the cash flows, known as the discount rate, is key, since it reflects where the bond is trading and how its return is perceived by the market. All the factors that identify the bond—including the nature of the issuer, the maturity date, the coupon, and the currency in which it was issued—influence the bond s discount rate. Comparable bonds have similar discount rates. The following sections explain the traditional approach to bond pricing for plain vanilla instruments, making certain assumptions to keep the analysis simple. After that, a more formal analysis is presented. 

Our starting point is a set of zero curve tenors (or discount factors) obtained from a collection of market instruments such as cash deposits, futures, swaps, or coupon bonds. We therefore have a set of tenor points and their respective zero rates (or discount factors). The mathematics of cubic splines is straightforward, but we assume a basic understanding of calculus and a familiarity with solving simultaneous linear equations by substitution. An account of the methods analyzed in this section is given in Burden and Faires (1997), which has very accessible text on cubic spline interpolation. ... 

All bond instruments are characterized by the promise to pay a stream of future cash flows. The term structure of interest rates and associated discount function is crucial to the valuation of any debt security and underpins any valuation framework. Armed with the term structure, we can value any bond, assuming it is liquid and default-free, by breaking it down into a set of cash flows and valuing each cash flow with the appropriate discount factor. Further characteristics of any bond, such as an element of default risk or embedded option, are valued incrementally over its discounted cash flow valuation. 

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