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Hard · Algorithms & Data Structures · Quant Trader interview question · FFT, Option Pricing, Carr-Madan, Computational Complexity
You're tasked with pricing a large number of European options using the Carr-Madan FFT approach. The direct integration method for calculating option prices from the characteristic function has a computational complexity of $O(N^2)$ , where $N$ is the number of grid points used for the integration. The FFT-based Carr-Madan method offers significant speedup. Assuming you are using $N$ grid points, what is the primary reason for the computational efficiency gain of the Carr-Madan FFT method,