medium · Quantitative Finance

A Heston stochastic volatility model is calibrated with κ = 2.0, θ = 0.04, and ξ = 0.50.

Does this calibration satisfy the Feller condition, and what is its significance?

  1. Yes, since 0.16 is greater than or equal to 0.25, variance is guaranteed to remain strictly positive.
  2. No, because the mean-reversion speed parameter κ must exceed a value of 5.0 for the condition to hold true.
  3. Yes, the Feller condition holds simply because the long-run variance parameter θ is strictly positive by assumption here.
  4. No, 0.16 ≥ 0.25 is false, so the Feller condition is NOT satisfied. Significance: variance can reach zero.

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