medium · Quantitative Finance

If a market desk calibrates a Heston model and finds that the Feller condition 2κθ ≥ ξ² is violated, what is the most significant practical consequence for their numerical implementation?

1. The correlation ρ between the asset and variance must be set to zero.
2. The volatility smile becomes perfectly flat across all strikes.
3. Naive Euler discretization schemes may produce negative variances.
4. The model becomes mathematically undefined and pricing integrals diverge.

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