SIMULATING THE HESTON MODEL VIA THE QE METHOD WITH A SPECIFIED ERROR TOLERANCE
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The Quadratic Exponential (QE) model is a market standard simulation method for the Heston stochastic volatility model. We identify certain numerical problems with the standard discretization and modify the original method to correct these problems. We implement our modified QE scheme for the Heston model in the Guaranteed Automatic Integration Library (GAIL)|a suite of algorithms that includes Monte Carlo and quasi-Monte Carlo methods for multidimensional integration and computation of means. GAIL computes answers to satisfy user-defined error tolerances. We also implement variance reduction techniques for our modified QE scheme in GAIL. The numerical results show that our modified scheme is fast and accurate, and satisfies the user-defined error tolerances.