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Towards efficient nonlinear option pricing

Towards efficient nonlinear option pricing

Tan, Shih-Hau (2018) Towards efficient nonlinear option pricing. PhD thesis, University of Greenwich.

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Abstract

This thesis describes the development of efficient numerical solvers for a wide range of nonlinear option pricing problems, including European options, Asian options and a multi-asset case. The chosen research methodology is the numerical PDE approach which essentially is to solve the nonlinear Black-Scholes equations with the relevant nonlinear volatility functions. The emphasis is on obtaining the numerical solution with reasonable accuracy and using high-performance computation.

The first approach applies the Newton-Raphson method to solve the nonlinear system resulting from the finite difference spatial discretisation. Several adjustments for improving accuracy are examined. These Newton-based solvers are combined with a semi-Lagrangian scheme to deal with the Asian option case, and one Alternative Direction Implicit (ADI) method for pricing options on multiple assets. An approach to solving large-scale problems with nonlinear volatilities with a GPU-based parallelisation framework is also proposed. Implementations on different software platforms are explained and compared. Case studies including large-scale Europe option pricing problems computed using single and multiple GPUs are discussed to demonstrate their performance compared with using sequential algorithms. These constructed solvers with parallel computing implementations essentially contribute to solving nonlinear problems in finance.

Item Type: Thesis (PhD)
Uncontrolled Keywords: Nonlinear option pricing models; Newton-based solvers; GPU computing; multi-asset problems; mathematical modelling;
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 17 Apr 2019 14:51
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/23634

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