Download or read book Robust Barrier Option Pricing by Frame Projection Under Exponential Levy Dynamics written by Justin Kirkby and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an efficient method for robustly pricing discretely monitored barrier and occupation time derivatives under exponential Levy models. This includes ordinary barrier options, as well as (resetting) Parisian options, delayed barrier options (also known as cumulative Parisian or Parasian options), fader options, and step options (soft-barriers), all with single and double barriers, which have yet to be priced with more general Levy processes, including KoBoL (CGMY), Merton's jump diffusion and NIG. The method's efficiency is derived in part from the use of frame projected transition densities, which transform the problem into the Fourier domain, and accelerate the convergence of intermediate expectations. Moreover, these expectations are approximated by Toeplitz matrix-vector multiplications, resulting in a fast implementation. We devise an augmentation approach that contributes to the method's robustness, adding protection against mis-specifying a proper truncation support of the transition density. Theoretical convergence is verified by a series of numerical experiments which demonstrate the method's efficiency and accuracy.