Every fixed-income derivative — an interest rate swap, a swaption, a mortgage-backed security — is ultimately priced by discounting its promised cash flows. This topic builds the discounting framework from the ground up: what a bond is, what a discount factor is, and why the structure of interest rates across maturities matters before any model is introduced.
The four lessons move in a deliberate arc. They begin with the rawest pricing object — the discount factor — and show how to extract it from observable bond prices. They then introduce two ways of expressing the same information (spot rates, forward rates) and reveal why they must be related by a no-arbitrage identity. Yield-to-maturity then enters as a practical summary measure — compact, widely quoted, but with a hidden pitfall that every practitioner must understand. The topic closes with the institutional details that separate theoretical pricing from real-world execution: accrued interest, day-count conventions, and the curve-fitting problem that arises as soon as the maturity grid has gaps.
By the end of this topic you should be able to:
- extract discount factors by bootstrapping a set of coupon bond prices;
- convert between discount factors, spot rates, and forward rates, and explain the slope of the term structure in terms of forward rates;
- state the three limitations of yield-to-maturity as a return measure and when it is safe to use yield;
- price a bond that does not settle on a coupon date, accounting for accrued interest and compounding-convention choice.
In this lesson
- Contents
- The big picture
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