An efficient semi-analytical simulation for the Heston model

With splitting technique, a new semi-analytical scheme with predictable strong convergence order 1.0 is proposed for the transformed Heston model, where the variance process is displaced by the corresponding volatility process. The volatility process is decomposed into a linear SDE and an ODE, both of which have the analytical solution, but the SDE is simulated by the Euler method while the ODE is approximated analytically with a slight modification. Numerical tests show its high efficiency and accuracy in the simulation for the mean-reverting square root process.

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