Before revision:  This yields an efficient method to compute prices of power payoffs and Fourier transforms . European calls and puts as well as binaries and asset-or-nothing options can then be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005).
After revision:  This yields an efficient method to compute prices of power payoffs and Fourier transforms . European calls and puts as well as binaries and asset-or-nothing options can be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005).