Prices, Discount Factors, and Arbitrage
This chapter begins by introducing the cash flows of fixed-rate, government coupon bonds. It shows that prices of these bonds can be used to extract discount factors, which are the market prices of one unit of currency to be received on various dates in the future.
Relying on a principle known as the law of one price, discount factors extracted from a particular set of bonds can be used to price other bonds, outside the original set. A more complex but more convincing relative pricing methodology, known as arbitrage pricing, turns out to be mathematically identical to pricing with discount factors. Hence, discounting can rightly be used and regarded as shorthand for arbitrage pricing.
The application of this chapter uses the U.S. Treasury coupon bond and Separate Trading of Registered Interest and Principal of Securities (STRIPS) markets to illustrate that bonds are not commodities, meaning that their prices reflect individual characteristics other than their scheduled cash flows. This idiosyncratic component of bond valuation implies that the predictions of the simplest relative pricing methodologies only approximate the complex reality of bond markets.
The chapter concludes with a discussion of day-counts and accrued interest, pricing conventions used throughout fixed income markets and, consequently, throughout this book.
THE CASH FLOWS FROM FIXED-RATE GOVERNMENT COUPON BONDS
The cash flows from fixed-rate, government coupon ...