Convolution-FFT for option pricing in the Heston model

We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on branch-cut adjustments or empirically tuned damping parameters, our approach yields a stable integrand even under large frequency oscillations. Crucially, we derive fully analytical error bounds that quantify both truncation error and discretization error in terms of model parameters and grid settings. To the best of our knowledge, this is the first work to provide such explicit, closed-form error estimates for an FFT-based convolution method specialized to the Heston model. Numerical experiments confirm the theoretical rates and illustrate robust, high-accuracy option pricing at modest computational cost.