Title: Second-order numerical Fourier methods for option pricing
Authors: Jinhui Han - The Chinese University of Hong Kong (China) [presenting]
Abstract: A Fourier method will be applied to numerically simulate the option prices of various types, based on the second-order stochastic Taylor discretization of the underlying SDE dynamics. Particularly, we focus on high-dimensional SDEs, where the stochastic Levy area will be involved in the second-order expansion. The theoretical one-step conditional characteristic function is derived. To better simulate the characteristic function, a neural network is adopted and served as an interpolation function. The method differs from traditional Monte-Carlo simulations where each step requires an independent sampling process. Instead, the efficient Fourier method enables us to sample the characteristic function values on the grids for only once and it can be settled as an online library which is fully determined by the coefficients of the corresponding SDE. In this way, a higher weak convergence order is achieved and not much additional computational efforts will be required. The error analysis is conducted in detail as well. Finally, numerical experiments for computing different options prices are provided, including European options as well as path-dependent ones such as Bermuda options.