hard · Quantitative Finance
A practitioner is calibrating a Heston stochastic volatility model with parameters κ = 1.5 (mean reversion speed), θ = 0.04 (long-run variance), and ξ = 0.45 (volatility of variance). The current variance v_t is 0.03.
Does this calibration satisfy the Feller condition, and what is the operational consequence for a Monte Carlo simulation using a naive Euler discretization?
- The condition 2κξ ≥ θ^2 is violated, which implies the stock price process will exhibit explosive growth (moment explosion) at short tenors.
- The Feller condition 2κθ ≥ ξ^2 is violated (0.12 < 0.2025), meaning the variance process can reach zero; a naive Euler scheme may produce negative variances.
- The Feller condition is satisfied (0.12 > 0.045), ensuring the variance stays strictly positive and the simulation is stable without boundary adjustments.
- The condition is satisfied because κ + θ > ξ, ensuring the mean reversion is strong enough to pull the variance away from the zero-origin.
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