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Spectral Element Method for Pricing European Options and Their Greeks

dc.contributor.advisor Liu, Qing H. Yue, Tianyao 2013-01-16T20:28:52Z 2013-01-16T20:28:52Z 2012
dc.description.abstract <p>Numerical methods such as Monte Carlo method (MCM), finite difference method (FDM) and finite element method (FEM) have been successfully implemented to solve financial partial differential equations (PDEs). Sophisticated computational algorithms are strongly desired to further improve accuracy and efficiency.</p><p>The relatively new spectral element method (SEM) combines the exponential convergence of spectral method and the geometric flexibility of FEM. This dissertation carefully investigates SEM on the pricing of European options and their Greeks (Delta, Gamma and Theta). The essential techniques, Gauss quadrature rules, are thoroughly discussed and developed. The spectral element method and its error analysis are briefly introduced first and expanded in details afterwards.</p><p>Multi-element spectral element method (ME-SEM) for the Black-Scholes PDE is derived on European put options with and without dividend and on a condor option with a more complicated payoff. Under the same Crank-Nicolson approach for the time integration, the SEM shows significant accuracy increase and time cost reduction over the FDM. A novel discontinuous payoff spectral element method (DP-SEM) is invented and numerically validated on a European binary put option. The SEM is also applied to the constant elasticity of variance (CEV) model and verified with the MCM and the valuation formula. The Stochastic Alpha Beta Rho (SABR) model is solved with multi-dimensional spectral element method (MD-SEM) on a European put option. Error convergence for option prices and Greeks with respect to the number of grid points and the time step is analyzed and illustrated.</p>
dc.subject Electrical engineering
dc.subject Applied mathematics
dc.subject Finance
dc.subject Binary Options
dc.subject Black-Scholes
dc.subject Gauss Quadrature
dc.subject Option Greeks
dc.subject Spectral Element Method
dc.subject Stochastic Volatility
dc.title Spectral Element Method for Pricing European Options and Their Greeks
dc.type Dissertation
dc.department Electrical and Computer Engineering
dcterms.provenance PDF updated on 26 January 2022 by request of the author. The final page of the original PDF was removed, since it contained a biographical statement with sensitive information that should not be shown publicly.

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