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...

Descripción completa

Detalles Bibliográficos
Autor principal:	Aichinger, Michael, 1979- (-)
Otros Autores:	Binder, Andreas, 1964-
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	Hoboken, N.J. : John Wiley & Sons, Inc 2013.
Edición:	1st edition
Colección:	Wiley finance series Wiley finance series.
Materias:	Finance > Mathematical models.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009629580806719

Tabla de Contenidos:

Intro
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 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 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 Models
5.2 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 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 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 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 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
9.2.3 Valuation of a Steepener under a Two Factor Hull-White Model
9.3 An 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 A 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 A 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 A Bermudan Callable Floater under Different Short-rate Models
11.3.2 A Bermudan Callable Steepener Swap under a Two Factor Hull-White Model
11.3.3 A 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 A 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 A 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 ρ
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 A 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 A 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
Bibliography
Index.

A workout in computational finance

Ejemplares similares