Every fixed-income desk begins with the same question: what is a future cash flow worth today? The answer is encoded in discount factors — one number per maturity, extractable directly from observable Treasury prices without assuming anything about why rates are at their current level. This note derives the discount function from a set of coupon bonds, proves that the law of one price makes those factors unique, and shows what happens when the law is violated: an explicit arbitrage trade collects free money by buying the cheap bond and selling its replicating portfolio.
The discount factors developed here are the raw material for everything in this unit. Spot rates and forward rates (Lesson 2) re-express the same information as rates of return. Yield-to-maturity (Lesson 3) compresses the full discount function into a single number with known limitations. Duration and DV01 (Topic 2) then measure how bond prices respond when the discount function shifts.
Learning objectives. By the end of this note you should be able to:
- state the discount factor and express a bond price as a linear combination of discount factors;
- extract discount factors by sequential bootstrapping from a set of coupon bond prices;
- state the law of one price and construct the replicating-portfolio proof of its necessity under no-arbitrage;
- describe STRIPS and explain why C-STRIPS are fungible while P-STRIPS are bond-specific.
In this lesson
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- The time value of money and discount factors
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- Treasury bond structure and price quotation
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- Bootstrapping discount factors
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- The law of one price
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- Treasury STRIPS
The full lesson, with worked examples and exercise solutions, is for members.
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