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SUMMARYCalibration methods are the heart of modeling any financial process. While for the Heston model (semi) closed-form solutions exist for simple products, their evaluation involves complex functions and infinite integrals. So far, these integrals can only be solved with time-consuming numerical methods. For that reason, calibration consumes a large portion of available compute power in the daily finance business.However, more and more theoretical and practical subtleties have been discovered over the years, and today, a large number of calibration methods are available. Currently, there is no clear indication which numerical method should be used for a specific calibration purpose under given speed and accuracy constraints. With this publication, we aim at closing this gap. We derive a novel methodology for systematically finding the best methods for a well-defined accuracy target. For a practical setup, we study the available popular closed-form solutions and integration algorithms. In total, we compare 14 numerical methods, including adaptive quadrature and Fourier methods. For a target accuracy of 10 3 , we show that adaptive GaussKronrod methods are best on CPUs for the unrestricted parameter set. Furthermore, we introduce hybrid pricer methods that combine quadrature and fast Fourier transform pricers, what gives us another 2:4 speedup.

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