How do I bootstrap a zero-coupon yield curve from coupon bond prices for FRM Part I?

Question

AcadiFi · Accepted Answer

Bootstrapping works iteratively. Start with the shortest instrument, usually a six-month T-bill trading at 98.75 per 100 face. The zero rate solves 100 = 98.75 * (1 + z0.5/2), giving z0.5 = 2.53%. For the one-year bond with a 3% coupon priced at 100.20, discount the first coupon at z0.5 and solve for z1.0: 100.20 = 1.5/(1+z0.5/2) + 101.5/(1+z1.0/2)^2. Each subsequent maturity uses all previously bootstrapped rates to discount earlier cash flows, leaving only the final zero rate as the unknown.

```mermaid
flowchart TD
  A[6M Bill Price] --> B[Solve z0.5]
  B --> C[1Y Bond Price]
  C --> D[Solve z1.0]
  D --> E[1.5Y Bond]
  E --> F[Solve z1.5]
```

Key pitfalls: mismatched day counts between instruments (actual/360 vs 30/360), stale mid-quotes, and missing maturities that force interpolation. For FRM, remember that bootstrapping produces a piecewise curve that may not be smooth, which is why practitioners layer splines on top.

How do I bootstrap a zero-coupon yield curve from coupon bond prices for FRM Part I?

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