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A Workout in Computational Finance.
A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability t...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- A Workout in Computational Finance; Contents; Acknowledgements; About the Authors; 1 Introduction and Reading Guide; 2 Binomial Trees; 2.1 Equities and Basic Options; 2.2 The One Period Model; 2.3 The Multiperiod Binomial Model; 2.4 Black-Scholes and Trees; 2.5 Strengths and Weaknesses of Binomial Trees; 2.5.1 Ease of Implementation; 2.5.2 Oscillations; 2.5.3 Non-recombining Trees; 2.5.4 Exotic Options and Trees; 2.5.5 Greeks and Binomial Trees; 2.5.6 Grid Adaptivity and Trees; 2.6 Conclusion; 3 Finite Differences and the Black-Scholes PDE; 3.1 A Continuous Time Model for Equity Prices.
- 3.2 Black-Scholes Model: From the SDE to the PDE3.3 Finite Differences; 3.4 Time Discretization; 3.5 Stability Considerations; 3.6 Finite Differences and the Heat Equation; 3.6.1 Numerical Results; 3.7 Appendix: Error Analysis; 4 Mean Reversion and Trinomial Trees; 4.1 Some Fixed Income Terms; 4.1.1 Interest Rates and Compounding; 4.1.2 Libor Rates and Vanilla Interest Rate Swaps; 4.2 Black76 for Caps and Swaptions; 4.3 One-Factor Short Rate Models; 4.3.1 Prominent Short Rate Models; 4.4 The Hull-White Model in More Detail; 4.5 Trinomial Trees; 5 Upwinding Techniques for Short Rate Models.
- 5.1 Derivation of a PDE for Short Rate Models5.2 Upwind Schemes; 5.2.1 Model Equation; 5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model; 5.3.1 Bond Details; 5.3.2 Model Details; 5.3.3 Numerical Method; 5.3.4 An Algorithm in Pseudocode; 5.3.5 Results; 6 Boundary, Terminal and Interface Conditions and their Influence; 6.1 Terminal Conditions for Equity Options; 6.2 Terminal Conditions for Fixed Income Instruments; 6.3 Callability and Bermudan Options; 6.4 Dividends; 6.5 Snowballs and TARNs; 6.6 Boundary Conditions.
- 6.6.1 Double Barrier Options and Dirichlet Boundary Conditions6.6.2 Artificial Boundary Conditions and the Neumann Case; 7 Finite Element Methods; 7.1 Introduction; 7.1.1 Weighted Residual Methods; 7.1.2 Basic Steps; 7.2 Grid Generation; 7.3 Elements; 7.3.1 1D Elements; 7.3.2 2D Elements; 7.4 The Assembling Process; 7.4.1 Element Matrices; 7.4.2 Time Discretization; 7.4.3 Global Matrices; 7.4.4 Boundary Conditions; 7.4.5 Application of the Finite Element Method to Convection-Diffusion-Reaction Problems; 7.5 A Zero Coupon Bond Under the Two Factor Hull-White Model.
- 7.6 Appendix: Higher Order Elements7.6.1 3D Elements; 7.6.2 Local and Natural Coordinates; 8 Solving Systems of Linear Equations; 8.1 Direct Methods; 8.1.1 Gaussian Elimination; 8.1.2 Thomas Algorithm; 8.1.3 LU Decomposition; 8.1.4 Cholesky Decomposition; 8.2 Iterative Solvers; 8.2.1 Matrix Decomposition; 8.2.2 Krylov Methods; 8.2.3 Multigrid Solvers; 8.2.4 Preconditioning; 9 Monte Carlo Simulation; 9.1 The Principles of Monte Carlo Integration; 9.2 Pricing Derivatives with Monte Carlo Methods; 9.2.1 Discretizing the Stochastic Differential Equation; 9.2.2 Pricing Formalism.