Analytical and numerical approximative methods for solving multifactor models for pricing of financial derivatives / Mgr. Zuzana Bučková. Wuppertal, 2016
Inhalt
- Leere Seite
- Acknowledgement
- Abstract
- Contents
- Abbreviations
- Foreword
- 1 Outline of the thesis and related scientific works
- I Analytical Approximations of Interest Short Rate Models
- 2 Introduction: Pricing of financial derivatives
- 3 Convergence model of interest rates of CKLS type
- 3.1 Convergence models
- 3.1.1 The convergence model of Vasicek type
- 3.1.2 Convergence model of CIR type
- 3.1.3 Convergence model of CKLS type
- 3.2 Approximation of the domestic bond price solution
- 3.3 Numerical results for CIR model with zero correlation
- 3.4 Formulation of the optimization problems in the calibration algorithm
- 3.5 The algorithm for estimating parameters in the CIR model with zero correlation
- 3.5.1 Simulated data
- 3.5.2 Estimation of the European parameters
- 3.5.3 Estimation of the domestic parameters
- 3.5.4 Simulation analysis
- 3.6 Generalization for CKLS model with zero correlation and the known e, d
- 3.7 Estimation of correlation a parameters e, d
- 3.8 Calibration of the model using real market data
- 4 Estimating the short rate from the term structures
- 5 Short rate as a sum of two CKLS-type processes
- 5.1 Model
- 5.2 Two-factor Vasicek model: singularity and transformation
- 5.3 Application to real market data
- 5.4 Robustness of the short rate estimates
- 5.5 Approximation of the bond prices in the CKLS model
- 6 A three-factor convergence model of interest rates
- II Alternating direction explicit methods, Fichera theory and Trefftz methods
- 7 Intro to numerical solutions, ADE schemes, Fichera theory, option pricing
- 7.1 Proper treatment of boundary conditions, using Fichera theory
- 7.2 Option pricing with Black-Scholes model
- 7.3 Alternating Direction Explicit Schemes
- 8 Fichera theory and its application to finance
- 8.1 The Boundary Value Problem for the Elliptic PDE
- 8.2 Application to one-factor interest rate Models of CKLS type
- 8.3 A two-factor interest rate Model
- 8.4 Numerical Results
- 9 ADE methods for convection-diffusion-reactions Equations
- 9.0.1 The modified difference quotients for the ADE method
- 9.1 Stability of the ADE method
- 9.1.1 Stability analysis using the Matrix approach
- 9.1.2 Von Neumann stability analysis for the convection-diffusion-reaction equation
- 9.2 Consistency Analysis of the ADE methods
- 10 ADE method for higher dimensional Black-Scholes model
- 10.1 ADE Schemes for Multi-Dimensional Models
- 10.1.1 ADE Schemes for Two-dimensional Models
- 10.1.2 ADE Schemes for Three and Higher Dimensional Models
- 10.1.3 Boundary Conditions
- 10.2 Numerical Scheme
- 10.2.1 Algorithm of the Scheme
- 10.2.2 Upward Finite Difference Quotients and Its Numerical Scheme
- 10.2.3 Difference Quotients and Numerical Scheme for the Downward Sweep
- 10.3 Numerical Results and Experimental Study of Convergence
- 10.4 Influence of dimensionality on computational complexity of the scheme
- 11 Trefftz methods for the Black-Scholes equation, FLAME
- 11.1 How Trefftz methods work?
- 11.2 Numerical results with Six-Point FLAME Scheme
- 11.3 Comparison of FLAME and Crank-Nicolson scheme
- 11.4 Further potential of the Trefftz schemes
- Conclusion and Outlook