When should I use a no-arbitrage model vs an equilibrium model?

Q: When should I use a no-arbitrage model vs an equilibrium model?

The choice hinges on purpose: pricing vs. forecasting.\n\nNo-arbitrage models (Ho-Lee, Hull-White, HJM, BGM) take the observed curve as given and ensure model-implied bond prices reproduce market prices exactly. Use them when:\n- Pricing derivatives (swaptions, Bermudans, callable bonds)\n- Marking trading books\n- Ensuring risk-neutral consistency with hedges\n\nEquilibrium models (Vasicek, CIR) derive the term structure from fundamental assumptions about the short rate process and investor risk preferences. Use them when:\n- Long-horizon scenario generation (ALM, pension, insurance)\n- Academic research on curve shape drivers\n- Generating REAL-WORLD (not risk-neutral) rate paths for capital projections\n\nA concrete example: at Tidewater Mutual Insurance, the ALM team uses a CIR-based real-world scenario generator to project liabilities 30 years out, while the hedging desk uses a calibrated Hull-White for pricing the swaption collars it uses to hedge those liabilities. Same firm, two models, different purposes.\n\nKey mnemonic: No-arbitrage models FIT the curve; equilibrium models EXPLAIN the curve.\n\nFor CFA Level II exam questions, the answer is usually no-arbitrage for pricing traded derivatives and equilibrium for theoretical/conceptual questions about what drives the term structure.

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AcadiFi · Accepted Answer

The choice hinges on purpose: pricing vs. forecasting.

No-arbitrage models (Ho-Lee, Hull-White, HJM, BGM) take the observed curve as given and ensure model-implied bond prices reproduce market prices exactly. Use them when:
- Pricing derivatives (swaptions, Bermudans, callable bonds)
- Marking trading books
- Ensuring risk-neutral consistency with hedges

Equilibrium models (Vasicek, CIR) derive the term structure from fundamental assumptions about the short rate process and investor risk preferences. Use them when:
- Long-horizon scenario generation (ALM, pension, insurance)
- Academic research on curve shape drivers
- Generating REAL-WORLD (not risk-neutral) rate paths for capital projections

A concrete example: at Tidewater Mutual Insurance, the ALM team uses a CIR-based real-world scenario generator to project liabilities 30 years out, while the hedging desk uses a calibrated Hull-White for pricing the swaption collars it uses to hedge those liabilities. Same firm, two models, different purposes.

Key mnemonic: No-arbitrage models FIT the curve; equilibrium models EXPLAIN the curve.

For CFA Level II exam questions, the answer is usually no-arbitrage for pricing traded derivatives and equilibrium for theoretical/conceptual questions about what drives the term structure.

When should I use a no-arbitrage model vs an equilibrium model?

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