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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Calculating and Using Implied Spot (Zero-Coupon) Rates

The implied spot curve is arguably the second most important calculation in yield curve analysis after the implied forward curve. This curve will be the sequence of spot (or zero-coupon) rates that are consistent with the prices and yields on coupon bonds. The implied spot curve is a great example of “bootstrapping” in that the result of one calculation is used in the subsequent one. This is not going to involve a specific formula; instead it is a process best learned by working through an example.

Suppose that we observe price and yield data on four actively traded benchmark securities for the same risk class, for instance, government bonds (see Table 5.1).

We need some simplifying assumptions ...

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