| Description |
1 online resource |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
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. |
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Machine generated contents note: 1. Introduction and Reading Guide -- 2. Binomial Trees -- 2.1. Equities and Basic Options -- 2.2. One Period Model -- 2.3. 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. Continuous Time Model for Equity Prices -- 3.2. Black-Scholes Model: From the SDE to the PDE -- 3.3. 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. 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 Models -- 5.2. Upwind Schemes -- 5.2.1. Model Equation -- 5.3. 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. 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 Conditions -- 6.6.2. 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. 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. Zero Coupon Bond Under the Two Factor Hull-White Model -- 7.6. Appendix: Higher Order Elements -- 7.6.1. 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. 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 -- 9.2.3. Valuation of a Steepener under a Two Factor Hull-White Model -- 9.3. Introduction to the Libor Market Model -- 9.4. Random Number Generation -- 9.4.1. Properties of a Random Number Generator -- 9.4.2. Uniform Variates -- 9.4.3. Random Vectors -- 9.4.4. Recent Developments in Random Number Generation -- 9.4.5. Transforming Variables -- 9.4.6. Random Number Generation for Commonly Used Distributions -- 10. Advanced Monte Carlo Techniques -- 10.1. Variance Reduction Techniques -- 10.1.1. Antithetic Variates -- 10.1.2. Control Variates -- 10.1.3. Conditioning -- 10.1.4. Additional Techniques for Variance Reduction -- 10.2. Quasi Monte Carlo Method -- 10.2.1. Low-Discrepancy Sequences -- 10.2.2. Randomizing QMC -- 10.3. Brownian Bridge Technique -- 10.3.1. Steepener under a Libor Market Model -- 11. Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks -- 11.1. Pricing American options using the Longstaff and Schwartz algorithm -- 11.2. Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments -- 11.2.1. Algorithm: Extended LSMC Method for Bermudan Options -- 11.2.2. Notes on Basis Functions and Regression -- 11.3. Examples -- 11.3.1. Bermudan Callable Floater under Different Short-rate Models -- 11.3.2. Bermudan Callable Steepener Swap under a Two Factor Hull-White Model -- 11.3.3. Bermudan Callable Steepener Cross Currency Swap in a 3D IR/FX Model Framework -- 12. Characteristic Function Methods for Option Pricing -- 12.1. Equity Models -- 12.1.1. Heston Model -- 12.1.2. Jump Diffusion Models -- 12.1.3. Infinite Activity Models -- 12.1.4. Bates Model -- 12.2. Fourier Techniques -- 12.2.1. Fast Fourier Transform Methods -- 12.2.2. Fourier-Cosine Expansion Methods -- 13. Numerical Methods for the Solution of PIDEs -- 13.1. PIDE for Jump Models -- 13.2. Numerical Solution of the PIDE -- 13.2.1. Discretization of the Spatial Domain -- 13.2.2. Discretization of the Time Domain -- 13.2.3. European Option under the Kou Jump Diffusion Model -- 13.3. Appendix: Numerical Integration via Newton-Cotes Formulae -- 14. Copulas and the Pitfalls of Correlation -- 14.1. Correlation -- 14.1.1. Pearson's/ρ -- 14.1.2. Spearman's ρ -- 14.1.3. Kendall's τ -- 14.1.4. Other Measures -- 14.2. Copulas -- 14.2.1. Basic Concepts -- 14.2.2. Important Copula Functions -- 14.2.3. Parameter estimation and sampling -- 14.2.4. Default Probabilities for Credit Derivatives -- 15. Parameter Calibration and Inverse Problems -- 15.1. Implied Black-Scholes Volatilities -- 15.2. Calibration Problems for Yield Curves -- 15.3. Reversion Speed and Volatility -- 15.4. Local Volatility -- 15.4.1. Dupire's Inversion Formula -- 15.4.2. Identifying Local Volatility -- 15.4.3. Results -- 15.5. Identifying Parameters in Volatility Models -- 15.5.1. Model Calibration for the FTSE-100 -- 16. Optimization Techniques -- 16.1. Model Calibration and Optimization -- 16.1.1. Gradient-Based Algorithms for Nonlinear Least Squares Problems -- 16.2. Heuristically Inspired Algorithms -- 16.2.1. Simulated Annealing -- 16.2.2. Differential Evolution -- 16.3. Hybrid Algorithm for Heston Model Calibration -- 16.4. Portfolio Optimization -- 17. Risk Management -- 17.1. Value at Risk and Expected Shortfall -- 17.1.1. Parametric VaR -- 17.1.2. Historical VaR -- 17.1.3. Monte Carlo VaR -- 17.1.4. Individual and Contribution VaR -- 17.2. Principal Component Analysis -- 17.2.1. Principal Component Analysis for Non-scalar Risk Factors -- 17.2.2. Principal Components for Fast Valuation -- 17.3. Extreme Value Theory -- 18. Quantitative Finance on Parallel Architectures -- 18.1. Short Introduction to Parallel Computing -- 18.2. Different Levels of Parallelization -- 18.3. GPU Programming -- 18.3.1. CUDA and OpenCL -- 18.3.2. Memory -- 18.4. Parallelization of Single Instrument Valuations using (Q)MC -- 18.5. Parallelization of Hybrid Calibration Algorithms -- 18.5.1. Implementation Details -- 18.5.2. Results -- 19. Building Large Software Systems for the Financial Industry. |
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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. |
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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. |
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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. |
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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. |
| Summary |
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 to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and ca. |
| Subject |
Finance -- Mathematical models.
|
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Finances -- Modèles mathématiques. |
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Finance -- Mathematical models |
| Added Author |
Binder, Andreas, 1964-
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| Other Form: |
Print version: Aichinger, Michael, 1979- Workout in computational finance. Hoboken, N.J. : John Wiley & Sons, Inc., [2013] 9781119971917 (DLC) 2013017386 |
| ISBN |
9781119973492 (epub) |
|
111997349X (epub) |
|
9781119973485 (pdf) |
|
1119973481 (pdf) |
|
9781119973508 (mobipocket) |
|
1119973503 (mobipocket) |
|
9781119973515 (electronic bk.) |
|
1119973511 (electronic bk.) |
|
1299804853 |
|
9781299804852 |
|
1119971918 |
|
9781119971917 |
|
(cloth/website) |
|
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