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High-order methods for parabolic equations in multiple space dimensions for option[...]
4 Application to Financial Engineering
4.1 Grid Transformation
Foreword
1 Introduction
1.1 Mathematical Models
1.2 Partial Differential Equation Methods in Computational Finance
1.3 Literature Overview and Outline of this Thesis
2 Spatial Discretization
2.1 Standard Finite Difference Methods
2.2 High-Order-Compact Finite Difference Methods
2.3 Pseudo-Spectral Methods
2.4 The Curse of Dimensionality and the Sparse Grid Combination Technique
3 Time Discretization - Alternating Direction Implicit Schemes
3.1 Stability Considerations
3.2 High-Order Finite Difference ADI Schemes
3.3 Stability of HO-ADI Schemes
3.4 (Hybrid) Pseudo-Spectral ADI Schemes
3.5 Stability of Hybrid Finite Difference/Pseudo-Spectral ADI Schemes
4 Application to Financial Engineering
4.1 Grid Transformation
4.2 Non-Smooth Initial Data
4.3 Basket Options
4.4 Stochastic Volatility Models
5 Conclusions and Outlook
5.1 Conclusions
5.2 Outlook
References
Dissertation
High-order methods for parabolic equations in multiple space dimensions for option pricing problems / vorgelegt von Christian Hendricks, geboren in Recklinghausen
Entstehung
Wuppertal
Dezember 2016
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