Efficient Semi-Analytical Simulation for Heston Model

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With splitting technique, a new semi-analytical scheme with convergence order 1.0, is proposed with respect to the transformed Heston Model, where the variance process is displaced by the volatility process. The volatility process is decomposed into a SDE and a ODE, both of which have the analytic solution, but Euler methods is employed to simulated the SDE and the ODE is approximated analytically with subtle modification. Numerical tests show its high efficiency and accuracy in simulation for mean-reverting square root process.