Download or read book Efficient Option Pricing by Frame Duality with the Fast Fourier Transform written by Justin Kirkby and published by . This book was released on 2016 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a method for efficiently inverting analytic characteristic functions using frame projection, as in the case of Heston's model and exponential Levy models. Utilizing the duality theory of Riesz bases, we derive analytical formulas for coefficients of the orthogonally projected density, which are computed numerically with exponential convergence by the FFT. Convergence is demonstrated for geometric Asian options as well as the pricing of baskets of European options. The method is compared to state-of-the-art procedures to demonstrate its efficiency and robustness, without requiring any user-supplied "control parameters." Even greater improvement is observed for the method's extension to arithmetic Asian option pricing, as well as for Bermudan and barrier options, and credit default swaps, which will appear in follow up papers that expand on the foundations developed in this work.