A workout in computational finance / Michael Aichinger and Andreas Binder.
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...
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Chichester, West Sussex, United Kingdom :
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[2013]
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MARC
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| 100 | 1 | |a Aichinger, Michael, |d 1979- | |
| 245 | 1 | 2 | |a A workout in computational finance / |c Michael Aichinger and Andreas Binder. |
| 264 | 1 | |a Chichester, West Sussex, United Kingdom : |b Wiley, |c [2013] | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Finance |x Mathematical models. | |
| 650 | 7 | |a Finance |x Mathematical models |2 fast | |
| 700 | 1 | |a Binder, Andreas, |d 1964- | |
| 776 | 0 | 8 | |i Print version: |a Aichinger, Michael, 1979- |t Workout in computational finance. |d Hoboken, N.J. : John Wiley & Sons, Inc., [2013] |z 9781119971917 |w (DLC) 2013017386 |
| 856 | 4 | 0 | |u https://go.oreilly.com/UniOfColoradoBoulder/library/view/~/9781119971917/?ar |z Full Text (via O'Reilly/Safari) |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Introduction and Reading Guide -- |g 2. |t Binomial Trees -- |g 2.1. |t Equities and Basic Options -- |g 2.2. |t One Period Model -- |g 2.3. |t Multiperiod Binomial Model -- |g 2.4. |t Black-Scholes and Trees -- |g 2.5. |t Strengths and Weaknesses of Binomial Trees -- |g 2.5.1. |t Ease of Implementation -- |g 2.5.2. |t Oscillations -- |g 2.5.3. |t Non-recombining Trees -- |g 2.5.4. |t Exotic Options and Trees -- |g 2.5.5. |t Greeks and Binomial Trees -- |g 2.5.6. |t Grid Adaptivity and Trees -- |g 2.6. |t Conclusion -- |g 3. |t Finite Differences and the Black-Scholes PDE -- |g 3.1. |t Continuous Time Model for Equity Prices -- |g 3.2. |t Black-Scholes Model: From the SDE to the PDE -- |g 3.3. |t Finite Differences -- |g 3.4. |t Time Discretization -- |g 3.5. |t Stability Considerations -- |g 3.6. |t Finite Differences and the Heat Equation -- |g 3.6.1. |t Numerical Results -- |g 3.7. |t Appendix: Error Analysis -- |g 4. |t Mean Reversion and Trinomial Trees -- |g 4.1. |t Some Fixed Income Terms -- |g 4.1.1. |t Interest Rates and Compounding -- |g 4.1.2. |t Libor Rates and Vanilla Interest Rate Swaps -- |g 4.2. |t Black76 for Caps and Swaptions -- |g 4.3. |t One-Factor Short Rate Models -- |g 4.3.1. |t Prominent Short Rate Models -- |g 4.4. |t Hull-White Model in More Detail -- |g 4.5. |t Trinomial Trees -- |g 5. |t Upwinding Techniques for Short Rate Models -- |g 5.1. |t Derivation of a PDE for Short Rate Models -- |g 5.2. |t Upwind Schemes -- |g 5.2.1. |t Model Equation -- |g 5.3. |t Puttable Fixed Rate Bond under the Hull-White One Factor Model -- |g 5.3.1. |t Bond Details -- |g 5.3.2. |t Model Details -- |g 5.3.3. |t Numerical Method -- |g 5.3.4. |t Algorithm in Pseudocode -- |g 5.3.5. |t Results -- |g 6. |t Boundary, Terminal and Interface Conditions and their Influence -- |g 6.1. |t Terminal Conditions for Equity Options -- |g 6.2. |t Terminal Conditions for Fixed Income Instruments -- |g 6.3. |t Callability and Bermudan Options -- |g 6.4. |t Dividends -- |g 6.5. |t Snowballs and TARNs -- |g 6.6. |t Boundary Conditions -- |g 6.6.1. |t Double Barrier Options and Dirichlet Boundary Conditions -- |g 6.6.2. |t Artificial Boundary Conditions and the Neumann Case -- |g 7. |t Finite Element Methods -- |g 7.1. |t Introduction -- |g 7.1.1. |t Weighted Residual Methods -- |g 7.1.2. |t Basic Steps -- |g 7.2. |t Grid Generation -- |g 7.3. |t Elements -- |g 7.3.1. |t 1D Elements -- |g 7.3.2. |t 2D Elements -- |g 7.4. |t Assembling Process -- |g 7.4.1. |t Element Matrices -- |g 7.4.2. |t Time Discretization -- |g 7.4.3. |t Global Matrices -- |g 7.4.4. |t Boundary Conditions -- |g 7.4.5. |t Application of the Finite Element Method to Convection-Diffusion-Reaction Problems -- |g 7.5. |t Zero Coupon Bond Under the Two Factor Hull-White Model -- |g 7.6. |t Appendix: Higher Order Elements -- |g 7.6.1. |t 3D Elements -- |g 7.6.2. |t Local and Natural Coordinates -- |g 8. |t Solving Systems of Linear Equations -- |g 8.1. |t Direct Methods -- |g 8.1.1. |t Gaussian Elimination -- |g 8.1.2. |t Thomas Algorithm -- |g 8.1.3. |t LU Decomposition -- |g 8.1.4. |t Cholesky Decomposition -- |g 8.2. |t Iterative Solvers -- |g 8.2.1. |t Matrix Decomposition -- |g 8.2.2. |t Krylov Methods -- |g 8.2.3. |t Multigrid Solvers -- |g 8.2.4. |t Preconditioning -- |g 9. |t Monte Carlo Simulation -- |g 9.1. |t Principles of Monte Carlo Integration -- |g 9.2. |t Pricing Derivatives with Monte Carlo Methods -- |g 9.2.1. |t Discretizing the Stochastic Differential Equation -- |g 9.2.2. |t Pricing Formalism -- |g 9.2.3. |t Valuation of a Steepener under a Two Factor Hull-White Model -- |g 9.3. |t Introduction to the Libor Market Model -- |g 9.4. |t Random Number Generation -- |g 9.4.1. |t Properties of a Random Number Generator -- |g 9.4.2. |t Uniform Variates -- |g 9.4.3. |t Random Vectors -- |g 9.4.4. |t Recent Developments in Random Number Generation -- |g 9.4.5. |t Transforming Variables -- |g 9.4.6. |t Random Number Generation for Commonly Used Distributions -- |g 10. |t Advanced Monte Carlo Techniques -- |g 10.1. |t Variance Reduction Techniques -- |g 10.1.1. |t Antithetic Variates -- |g 10.1.2. |t Control Variates -- |g 10.1.3. |t Conditioning -- |g 10.1.4. |t Additional Techniques for Variance Reduction -- |g 10.2. |t Quasi Monte Carlo Method -- |g 10.2.1. |t Low-Discrepancy Sequences -- |g 10.2.2. |t Randomizing QMC -- |g 10.3. |t Brownian Bridge Technique -- |g 10.3.1. |t Steepener under a Libor Market Model -- |g 11. |t Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks -- |g 11.1. |t Pricing American options using the Longstaff and Schwartz algorithm -- |g 11.2. |t Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments -- |g 11.2.1. |t Algorithm: Extended LSMC Method for Bermudan Options -- |g 11.2.2. |t Notes on Basis Functions and Regression -- |g 11.3. |t Examples -- |g 11.3.1. |t Bermudan Callable Floater under Different Short-rate Models -- |g 11.3.2. |t Bermudan Callable Steepener Swap under a Two Factor Hull-White Model -- |g 11.3.3. |t Bermudan Callable Steepener Cross Currency Swap in a 3D IR/FX Model Framework -- |g 12. |t Characteristic Function Methods for Option Pricing -- |g 12.1. |t Equity Models -- |g 12.1.1. |t Heston Model -- |g 12.1.2. |t Jump Diffusion Models -- |g 12.1.3. |t Infinite Activity Models -- |g 12.1.4. |t Bates Model -- |g 12.2. |t Fourier Techniques -- |g 12.2.1. |t Fast Fourier Transform Methods -- |g 12.2.2. |t Fourier-Cosine Expansion Methods -- |g 13. |t Numerical Methods for the Solution of PIDEs -- |g 13.1. |t PIDE for Jump Models -- |g 13.2. |t Numerical Solution of the PIDE -- |g 13.2.1. |t Discretization of the Spatial Domain -- |g 13.2.2. |t Discretization of the Time Domain -- |g 13.2.3. |t European Option under the Kou Jump Diffusion Model -- |g 13.3. |t Appendix: Numerical Integration via Newton-Cotes Formulae -- |g 14. |t Copulas and the Pitfalls of Correlation -- |g 14.1. |t Correlation -- |g 14.1.1. |t Pearson's/ρ -- |g 14.1.2. |t Spearman's ρ -- |g 14.1.3. |t Kendall's τ -- |g 14.1.4. |t Other Measures -- |g 14.2. |t Copulas -- |g 14.2.1. |t Basic Concepts -- |g 14.2.2. |t Important Copula Functions -- |g 14.2.3. |t Parameter estimation and sampling -- |g 14.2.4. |t Default Probabilities for Credit Derivatives -- |g 15. |t Parameter Calibration and Inverse Problems -- |g 15.1. |t Implied Black-Scholes Volatilities -- |g 15.2. |t Calibration Problems for Yield Curves -- |g 15.3. |t Reversion Speed and Volatility -- |g 15.4. |t Local Volatility -- |g 15.4.1. |t Dupire's Inversion Formula -- |g 15.4.2. |t Identifying Local Volatility -- |g 15.4.3. |t Results -- |g 15.5. |t Identifying Parameters in Volatility Models -- |g 15.5.1. |t Model Calibration for the FTSE-100 -- |g 16. |t Optimization Techniques -- |g 16.1. |t Model Calibration and Optimization -- |g 16.1.1. |t Gradient-Based Algorithms for Nonlinear Least Squares Problems -- |g 16.2. |t Heuristically Inspired Algorithms -- |g 16.2.1. |t Simulated Annealing -- |g 16.2.2. |t Differential Evolution -- |g 16.3. |t Hybrid Algorithm for Heston Model Calibration -- |g 16.4. |t Portfolio Optimization -- |g 17. |t Risk Management -- |g 17.1. |t Value at Risk and Expected Shortfall -- |g 17.1.1. |t Parametric VaR -- |g 17.1.2. |t Historical VaR -- |g 17.1.3. |t Monte Carlo VaR -- |g 17.1.4. |t Individual and Contribution VaR -- |g 17.2. |t Principal Component Analysis -- |g 17.2.1. |t Principal Component Analysis for Non-scalar Risk Factors -- |g 17.2.2. |t Principal Components for Fast Valuation -- |g 17.3. |t Extreme Value Theory -- |g 18. |t Quantitative Finance on Parallel Architectures -- |g 18.1. |t Short Introduction to Parallel Computing -- |g 18.2. |t Different Levels of Parallelization -- |g 18.3. |t GPU Programming -- |g 18.3.1. |t CUDA and OpenCL -- |g 18.3.2. |t Memory -- |g 18.4. |t Parallelization of Single Instrument Valuations using (Q)MC -- |g 18.5. |t Parallelization of Hybrid Calibration Algorithms -- |g 18.5.1. |t Implementation Details -- |g 18.5.2. |t Results -- |g 19. |t Building Large Software Systems for the Financial Industry. |
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