hierarchical approximation methods

Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

Chiheb Ben Hammouda, Ph.D., Applied Mathematics and Computational Sciences

Jul 2, 14:00 - 16:00

KAUST

hierarchical approximation methods option pricing Computational biology

In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques, based on multilevel Monte Carlo methods and importance sampling, for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks (SRNs). In the second part of this thesis, we design novel numerical methods for pricing financial derivatives. Option pricing is usually challenging due to a combination of two complications: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by using different techniques for smoothing the integrand to uncover the available regularity and improve quadrature methods' convergence behavior. We develop different ways of smoothing that depend on the characteristics of the problem at hand. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation.