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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

A Mumbai-based insurer uses a one-factor short-rate model to value long-term guarantees. Which is a recognised limitation of relying on a one-factor model for this purpose?

A one-factor model implies perfectly correlated movements in yields across all maturities, so it cannot capture twists or changes in curve shape. This matters for long-term guarantees. It can still be simulated and calibrated, so the other statements are false.

  1. AIt implies that changes in rates at all maturities are perfectly correlated, so it cannot capture twists of the yield curveCorrect
  2. BIt cannot be simulated by Monte Carlo methods
  3. CIt always produces an inverted yield curve
  4. DIt requires the market price of risk to be zero
  5. It cannot be calibrated to any market data

Explanation

With one source of randomness, yields at different maturities move together in perfect correlation, so the model cannot reproduce independent slope or curvature changes. The other statements are false: such models can be simulated and calibrated and do not force an inverted curve or a zero market price of risk.

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