option pricing

Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

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KAUST

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.

New publication in Quantitative Finance Journal

1 min read ·
At the end of October, the paper Numerical smoothing with hierarchical adaptive sparse grids and quasi-Monte Carlo methods for efficient option pricing by Christian Bayer ( Weierstrass Institute for Applied Analysis and Stochastics - WIAS) , Chiheb Ben Hammouda ( RWTH Aachen University ) , and Raul Tempone ( King Abdullah University of Science and Technology - KAUST; RWTH Aachen University ), was published in the Quantitative Finance Journal and is available at Taylor & Francis Online. Abstract: When approximating the expectations of a functional of a solution to a stochastic differential