High-order methods for parabolic equations in multiple space dimensions for option pricing problems / vorgelegt von Christian Hendricks, geboren in Recklinghausen. Wuppertal, Dezember 2016
Content
- 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
- References