What are the main categories of interest rate models used in fixed income?

Question

AcadiFi · Accepted Answer

Interest rate models fall into two philosophical camps. Equilibrium models (Vasicek, CIR) derive the term structure from assumptions about the short rate process.

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```mermaid
graph TD
    A[Interest Rate Models] --> B[Equilibrium]
    A --> C[No-Arbitrage]
    B --> D[Vasicek]
    B --> E[CIR]
    C --> F[Hull-White]
    C --> G[HJM/BGM]
```

Models also differ by number of factors. One-factor models (short rate only) are tractable but cannot capture curve twists. Two- or three-factor models (short rate plus slope, or HJM with volatility structure) handle more realistic dynamics.

For CFA Level II, focus on conceptual differences: equilibrium models are academic and parsimonious; no-arbitrage are calibrated for trading desks. Practitioners pricing Bermudan swaptions at a bank like Meridian Capital Partners overwhelmingly use no-arbitrage models because mispricing the underlying curve is unacceptable. Model choice also depends on the instrument — caps/floors favor BGM, callable bonds favor Hull-White trees.

What are the main categories of interest rate models used in fixed income?

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