Efficient, almost exact simulation of the Heston stochastic volatility model

We deal with several efficient discretization methods for the simulation of the Heston stochastic volatility model. The resulting schemes can be used to calculate all kind of options and corresponding sensitivities, in particular the exotic options that cannot be valued with closed-form solutions. We focus on to the (computational) efficiency of the simulation schemes: though the Broadie and Kaya (2006) paper provided an exact simulation method for the Heston dynamics, we argue why its practical use might be limited. Instead we consider efficient approximations of the exact scheme, which try to exploit certain distributional features of the underlying variance process. The resulting methods are fast, highly accurate and easy to implement. We conclude by numerically comparing our new schemes to the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jackel scheme, the Full Truncation scheme of Lord et al. and the Quadratic Exponential scheme of Andersen.