de Heston ’ s Stochastic Volatility Model Implementation , Calibration and Some Extensions

To take into account leverage effect, Wiener stochastic processes W1,W2 should be correlated dW1 · dW2 = ρdt. The stochastic model (1.2) for the variance is related to the square-root process of Feller (1951) and Cox, Ingersoll and Ross (1985). For the square-root process (1.2) the variance is always positive and if 2κθ > σ 2 then it cannot reach zero. Note that the deterministic part of process (1.2) is asymptotically stable if κ > 0. Clearly, that equilibrium point is Vt = θ .