A new method for fast computation of cumulative distribution functions by fractional FFT

抄録

We consider computation of cumulative distribution functions from their corresponding characteristic functions. We may use some known formulas with singular integrals for the computation. It is, however, difficult to speed up the computation with such formulas, because the fast Fourier transform (FFT) cannot be applied directly to them. Based on existing works for pricing of financial derivatives, we propose a fast method for the computation with fractional FFT and obtain accurate results on the entire real line.