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

In the Cox-Ingersoll-Ross model dr = a(μ − r)dt + σ√r dW, what is the Feller condition guaranteeing that r never reaches zero, and does it hold for a = 0.4, μ = 5%, σ = 0.1?

The Feller condition for CIR is 2aμ at least σ squared. With the data, 2×0.4×0.05 = 0.04 exceeds σ squared of 0.01, so the condition holds and the short rate stays strictly positive.

  1. A2aμ ≥ σ²; it holds since 0.04 ≥ 0.01Correct
  2. Baμ ≥ σ²; it fails since 0.02 < 0.01 is false
  3. C2aμ ≥ σ²; it fails since 0.04 < 0.01
  4. Da ≥ σ; it holds since 0.4 ≥ 0.1
  5. 2aμ ≤ σ²; it holds since 0.04 ≤ 0.01

Explanation

The Feller condition is 2aμ ≥ σ². Here 2×0.4×0.05 = 0.04 and σ² = 0.01, so 0.04 ≥ 0.01 and the condition holds. The other options use the wrong inequality, wrong form or wrong conclusion.

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