Discount Factor
The cash flows of a coupon bond consist of periodic coupon payments and a par value payment at maturity.
The price of a bond consists of an ordinary annuity portion (the coupons) and a lump sum single cash flow (the par amount).
Bond prices can be generated from discount functions. Prices are calculated by summing the product of each cash flow and its applicable discount rate.
Law Of One Price
Since investors do not care about the origin of a cash flow, all else equal, a cash flow from one bond is just as good as a cash flow from another bond. This phenomenon is commonly referred to as the law of one price.
P-STRIPS & C-STRIPS
Treasury STRIPS can be used to create specific fixed-income cash flow streams. P-STRIPS typically trade at fair value, while longer-term C-STRIPS tend to trade cheap, and shorter-term C-STRIPS tend to trade rich.
Constructing a Replicating Portfolio
To create a replicating portfolio using multiple fixed-income securities, we must determine the face amounts of each fixed-income security to purchase, which match the cash flows from the bond we are trying to replicate.
Arbitrage Opportunities
An arbitrage profit can be made if violations of the law of one price exist. By short selling a “rich” security and using the proceeds to purchase a similar “cheap” security, an investor can make a riskless profit with no investment.
Clean and Dirty bond pricing
Valuation of bonds between coupon payment dates requires the calculation of accrued interest and a modification to the bond pricing formula. Values derived between coupon dates will include accrued interest. This is also known as the dirty price. Subtracting the accrued interest from the dirty price gives the clean price of the bond.
Common day-count conventions
Accrued interest calculations vary across classes of bonds because of differing day count conventions. The most common day count conventions are actual/actual and 30E/360.
