Fixed Income Securities, 4th Edition

CHAPTER 1Prices, 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 group of bonds can be used to price bonds that are not part of that original group. Furthermore, a particularly persuasive 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.

Market prices on a single, fixed date are used to illustrate that the law of one price and arbitrage pricing describe the US Treasury market relatively well, but not perfectly. Bonds are not commodities: their prices reflect supply and demand characteristics that are not fully captured by their scheduled cash flows. The US Treasury's Separate Trading of Registered Interest and Principal of Securities (STRIPS) are introduced next, both as a topic of independent interest and as an additional illustration of the complex realities of pricing in bond markets.

The chapter concludes with accrued interest and day‐count conventions, which are used throughout fixed income markets and throughout this book.

For clarity of exposition, prices and ...