Financial Modelling : Theory, Implementation and Practice (With MATLAB Source).

By: Kienitz, JoergContributor(s): Wetterau, Daniel | Wetterau, DanielSeries: The Wiley Finance SerPublisher: Somerset : John Wiley & Sons, Incorporated, 2013Copyright date: ©2012Edition: 1st edDescription: 1 online resource (735 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118413319Subject(s): MATLAB.;Finance -- Mathematical models.;Numerical analysis.;Finance -- Mathematical models -- Computer programs.;Numerical analysis -- Computer programsGenre/Form: Electronic books. Additional physical formats: Print version:: Financial Modelling : Theory, Implementation and Practice (With MATLAB Source)DDC classification: 332.0285/53 LOC classification: HG106.K53 2012Online resources: Click to View
Contents:
Intro -- Financial Modelling -- Contents -- Introduction -- 1 Introduction and Management Summary -- 2 Why We Have Written this Book -- 3 Why You Should Read this Book -- 4 The Audience -- 5 The Structure of this Book -- 6 What this Book Does Not Cover -- 7 Credits -- 8 Code -- PART I FINANCIAL MARKETS AND POPULAR MODELS -- 1 Financial Markets - Data, Basics and Derivatives -- 1.1 Introduction and Objectives -- 1.2 Financial Time-Series, Statistical Properties of Market Data and Invariants -- 1.2.1 Real World Distribution -- 1.3 Implied Volatility Surfaces and Volatility Dynamics -- 1.3.1 Is There More than just a Volatility? -- 1.3.2 Implied Volatility -- 1.3.3 Time-Dependent Volatility -- 1.3.4 Stochastic Volatility -- 1.3.5 Volatility from Jumps -- 1.3.6 Traders' Rule of Thumb -- 1.3.7 The Risk Neutral Density -- 1.4 Applications -- 1.4.1 Asset Allocation -- 1.4.2 Pricing, Hedging and Risk Management -- 1.5 General Remarks on Notation -- 1.6 Summary and Conclusions -- 1.7 Appendix - Quotes -- 2 Diffusion Models -- 2.1 Introduction and Objectives -- 2.2 Local Volatility Models -- 2.2.1 The Bachelier and the Black-Scholes Model -- 2.2.2 The Hull-White Model -- 2.2.3 The Constant Elasticity of Variance Model -- 2.2.4 The Displaced Diffusion Model -- 2.2.5 CEV and DD Models -- 2.3 Stochastic Volatility Models -- 2.3.1 Pricing European Options -- 2.3.2 Risk Neutral Density -- 2.3.3 The Heston Model (and Extensions) -- 2.3.4 The SABR Model -- 2.3.5 SABR - Further Remarks -- 2.4 Stochastic Volatility and Stochastic Rates Models -- 2.4.1 The Heston-Hull-White Model -- 2.5 Summary and Conclusions -- 3 Models with Jumps -- 3.1 Introduction and Objectives -- 3.2 Poisson Processes and Jump Diffusions -- 3.2.1 Poisson Processes -- 3.2.2 The Merton Model -- 3.2.3 The Bates Model -- 3.2.4 The Bates-Hull-White Model -- 3.3 Exponential Lévy Models.
3.3.1 The Variance Gamma Model -- 3.3.2 The Normal Inverse Gaussian Model -- 3.4 Other Models -- 3.4.1 Exponential Lévy Models with Stochastic Volatility -- 3.4.2 Stochastic Clocks -- 3.5 Martingale Correction -- 3.6 Summary and Conclusions -- 4 Multi-Dimensional Models -- 4.1 Introduction and Objectives -- 4.2 Multi-Dimensional Diffusions -- 4.2.1 GBM Baskets -- 4.2.2 Libor Market Models -- 4.3 Multi-Dimensional Heston and SABR Models -- 4.3.1 Stochastic Volatility Models -- 4.4 Parameter Averaging -- 4.4.1 Applications to CMS Spread Options -- 4.5 Markovian Projection -- 4.5.1 Baskets with Local Volatility -- 4.5.2 Markovian Projection on Local Volatility and Heston Models -- 4.5.3 Markovian Projection onto DD SABR Models -- 4.6 Copulae -- 4.6.1 Measures of Concordance and Dependency -- 4.6.2 Examples -- 4.6.3 Elliptical Copulae -- 4.6.4 Archimedean Copulae -- 4.6.5 Building New Copulae from Given Copulae -- 4.6.6 Asymmetric Copulae -- 4.6.7 Applying Copulae to Option Pricing -- 4.6.8 Applying Copulae to Asset Allocation -- 4.7 Multi-Dimensional Variance Gamma Processes -- 4.8 Summary and Conclusions -- PART II NUMERICAL METHODS AND RECIPES -- 5 Option Pricing by Transform Techniques and Direct Integration -- 5.1 Introduction and Objectives -- 5.2 Fourier Transform -- 5.2.1 Discrete Fourier Transform -- 5.2.2 Fast Fourier Transform -- 5.3 The Carr-Madan Method -- 5.3.1 The Optimal α -- 5.4 The Lewis Method -- 5.4.1 Application to Other Payoffs -- 5.5 The Attari Method -- 5.6 The Convolution Method -- 5.7 The Cosine Method -- 5.8 Comparison, Stability and Performance -- 5.8.1 Other Issues -- 5.9 Extending the Methods to Forward Start Options -- 5.9.1 Forward Characteristic Function for Lévy Processes and CIR Time Change -- 5.9.2 Forward Characteristic Function for Lévy Processes and Gamma-OU Time Change -- 5.9.3 Results -- 5.10 Density Recovery.
5.11 Summary and Conclusions -- 6 Advanced Topics Using Transform Techniques -- 6.1 Introduction and Objectives -- 6.2 Pricing Non-Standard Vanilla Options -- 6.2.1 FFT with Lewis Method -- 6.3 Bermudan and American Options -- 6.3.1 The Convolution Method -- 6.3.2 The Cosine Method -- 6.3.3 Numerical Results -- 6.3.4 The Fourier Space Time-Stepping -- 6.4 The Cosine Method and Barrier Options -- 6.5 Greeks -- 6.6 Summary and Conclusions -- 7 Monte Carlo Simulation and Applications -- 7.1 Introduction and Objectives -- 7.2 Sampling Diffusion Processes -- 7.2.1 The Exact Scheme -- 7.2.2 The Euler Scheme -- 7.2.3 The Predictor-Corrector Scheme -- 7.2.4 The Milstein Scheme -- 7.2.5 Implementation and Results -- 7.3 Special Purpose Schemes -- 7.3.1 Schemes for the Heston Model -- 7.3.2 Unbiased Scheme for the SABR Model -- 7.4 Adding Jumps -- 7.4.1 Jump Models - Poisson Processes -- 7.4.2 Fixed Grid Sampling (FGS) -- 7.4.3 Stochastic Grid Sampling (SGS) -- 7.4.4 Simulation - Lévy Models -- 7.4.5 Schemes for Lévy Models with Stochastic Volatility -- 7.5 Bridge Sampling -- 7.6 Libor Market Model -- 7.7 Multi-Dimensional Lévy Models -- 7.8 Copulae -- 7.8.1 Distributional Sampling Approach (DSA) -- 7.8.2 Conditional Sampling Approach (CSA) -- 7.8.3 Simulation from Other Copulae -- 7.9 Summary and Conclusions -- 8 Monte Carlo Simulation - Advanced Issues -- 8.1 Introduction and Objectives -- 8.2 Monte Carlo and Early Exercise -- 8.2.1 Longstaff-Schwarz Regression -- 8.2.2 Policy Iteration Methods -- 8.2.3 Upper Bounds -- 8.2.4 Problems of the Method -- 8.2.5 Financial Examples and Numerical Results -- 8.3 Greeks with Monte Carlo -- 8.3.1 The Finite Difference Method (FDM) -- 8.3.2 The Pathwise Method -- 8.3.3 The Affine Recursion Problem (ARP) -- 8.3.4 Adjoint Method -- 8.3.5 Bermudan ARPs -- 8.4 Euler Schemes and General Greeks -- 8.4.1 SDE of Diffusions.
8.4.2 Approximation by Euler Schemes -- 8.4.3 Approximating General Greeks Using ARP -- 8.4.4 Greeks -- 8.5 Application to Trigger Swap -- 8.5.1 Mathematical Modelling -- 8.5.2 Numerical Results -- 8.5.3 The Likelihood Ratio Method (LRM) -- 8.5.4 Likelihood Ratio for Finite Differences - Proxy Simulation -- 8.5.5 Numerical Results -- 8.6 Summary and Conclusions -- 8.7 Appendix - Trees -- 9 Calibration and Optimization -- 9.1 Introduction and Objectives -- 9.2 The Nelder-Mead Method -- 9.2.1 Implementation -- 9.2.2 Calibration Examples -- 9.3 The Levenberg-Marquardt Method -- 9.3.1 Implementation -- 9.3.2 Calibration Examples -- 9.4 The L-BFGS Method -- 9.4.1 Implementation -- 9.4.2 Calibration Examples -- 9.5 The SQP Method -- 9.5.1 The Modified and Globally Convergent SQP Iteration -- 9.5.2 Implementation -- 9.5.3 Calibration Examples -- 9.6 Differential Evolution -- 9.6.1 Implementation -- 9.6.2 Calibration Examples -- 9.7 Simulated Annealing -- 9.7.1 Implementation -- 9.7.2 Calibration Examples -- 9.8 Summary and Conclusions -- 10 Model Risk - Calibration, Pricing and Hedging -- 10.1 Introduction and Objectives -- 10.2 Calibration -- 10.2.1 Similarities - Heston and Bates Models -- 10.2.2 Parameter Stability -- 10.3 Pricing Exotic Options -- 10.3.1 Exotic Options and Different Models -- 10.4 Hedging -- 10.4.1 Hedging - The Basics -- 10.4.2 Hedging in Incomplete Markets -- 10.4.3 Discrete Time Hedging -- 10.4.4 Numerical Examples -- 10.5 Summary and Conclusions -- PART III IMPLEMENTATION, SOFTWARE DESIGN AND MATHEMATICS -- 11 Matlab - Basics -- 11.1 Introduction and Objectives -- 11.2 General Remarks -- 11.3 Matrices, Vectors and Cell Arrays -- 11.3.1 Matrices and Vectors -- 11.3.2 Cell Arrays -- 11.4 Functions and Function Handles -- 11.4.1 Functions -- 11.4.2 Function Handles -- 11.5 Toolboxes -- 11.5.1 Financial -- 11.5.2 Financial Derivatives.
11.5.3 Fixed-Income -- 11.5.4 Optimization -- 11.5.5 Global Optimization -- 11.5.6 Statistics -- 11.5.7 Portfolio Optimization -- 11.6 Useful Functions and Methods -- 11.6.1 FFT -- 11.6.2 Solving Equations and ODE -- 11.6.3 Useful Functions -- 11.7 Plotting -- 11.7.1 Two-Dimensional Plots -- 11.7.2 Three-Dimensional Plots - Surfaces -- 11.8 Summary and Conclusions -- 12 Matlab - Object Oriented Development -- 12.1 Introduction and Objectives -- 12.2 The Matlab OO Model -- 12.2.1 Classes -- 12.2.2 Handling Classes in Matlab -- 12.2.3 Inheritance, Base Classes and Superclasses -- 12.2.4 Handle and Value Classes -- 12.2.5 Overloading -- 12.3 A Model Class Hierarchy -- 12.4 A Pricer Class Hierarchy -- 12.5 An Optimizer Class Hierarchy -- 12.6 Design Patterns -- 12.6.1 The Builder Pattern -- 12.6.2 The Visitor Pattern -- 12.6.3 The Strategy Pattern -- 12.7 Example - Calibration Engine -- 12.7.1 Calibrating a Data Set or a History -- 12.8 Example - The Libor Market Model and Greeks -- 12.8.1 An Abstract Class for LMM Derivatives -- 12.8.2 A Class for Bermudan Swaptions -- 12.8.3 A Class for Trigger Swaps -- 12.9 Summary and Conclusions -- 13 Math Fundamentals -- 13.1 Introduction and Objectives -- 13.2 Probability Theory and Stochastic Processes -- 13.2.1 Probability Spaces -- 13.2.2 Random Variables -- 13.2.3 Important Results -- 13.2.4 Distributions -- 13.2.5 Stochastic Processes -- 13.2.6 Lévy Processes -- 13.2.7 Stochastic Differential Equations -- 13.3 Numerical Methods for Stochastic Processes -- 13.3.1 Random Number Generation -- 13.3.2 Methods for Computing Variates -- 13.4 Basics on Complex Analysis -- 13.4.1 Complex Numbers -- 13.4.2 Complex Differentiation and Integration along Paths -- 13.4.3 The Complex Exponential and Logarithm -- 13.4.4 The Residual Theorem -- 13.5 The Characteristic Function and Fourier Transform.
13.6 Summary and Conclusions.
Summary: Financial Modelling - Theory, Implementation and Practice is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving  prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes.Summary: Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk.  The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor Market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.
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Intro -- Financial Modelling -- Contents -- Introduction -- 1 Introduction and Management Summary -- 2 Why We Have Written this Book -- 3 Why You Should Read this Book -- 4 The Audience -- 5 The Structure of this Book -- 6 What this Book Does Not Cover -- 7 Credits -- 8 Code -- PART I FINANCIAL MARKETS AND POPULAR MODELS -- 1 Financial Markets - Data, Basics and Derivatives -- 1.1 Introduction and Objectives -- 1.2 Financial Time-Series, Statistical Properties of Market Data and Invariants -- 1.2.1 Real World Distribution -- 1.3 Implied Volatility Surfaces and Volatility Dynamics -- 1.3.1 Is There More than just a Volatility? -- 1.3.2 Implied Volatility -- 1.3.3 Time-Dependent Volatility -- 1.3.4 Stochastic Volatility -- 1.3.5 Volatility from Jumps -- 1.3.6 Traders' Rule of Thumb -- 1.3.7 The Risk Neutral Density -- 1.4 Applications -- 1.4.1 Asset Allocation -- 1.4.2 Pricing, Hedging and Risk Management -- 1.5 General Remarks on Notation -- 1.6 Summary and Conclusions -- 1.7 Appendix - Quotes -- 2 Diffusion Models -- 2.1 Introduction and Objectives -- 2.2 Local Volatility Models -- 2.2.1 The Bachelier and the Black-Scholes Model -- 2.2.2 The Hull-White Model -- 2.2.3 The Constant Elasticity of Variance Model -- 2.2.4 The Displaced Diffusion Model -- 2.2.5 CEV and DD Models -- 2.3 Stochastic Volatility Models -- 2.3.1 Pricing European Options -- 2.3.2 Risk Neutral Density -- 2.3.3 The Heston Model (and Extensions) -- 2.3.4 The SABR Model -- 2.3.5 SABR - Further Remarks -- 2.4 Stochastic Volatility and Stochastic Rates Models -- 2.4.1 The Heston-Hull-White Model -- 2.5 Summary and Conclusions -- 3 Models with Jumps -- 3.1 Introduction and Objectives -- 3.2 Poisson Processes and Jump Diffusions -- 3.2.1 Poisson Processes -- 3.2.2 The Merton Model -- 3.2.3 The Bates Model -- 3.2.4 The Bates-Hull-White Model -- 3.3 Exponential Lévy Models.

3.3.1 The Variance Gamma Model -- 3.3.2 The Normal Inverse Gaussian Model -- 3.4 Other Models -- 3.4.1 Exponential Lévy Models with Stochastic Volatility -- 3.4.2 Stochastic Clocks -- 3.5 Martingale Correction -- 3.6 Summary and Conclusions -- 4 Multi-Dimensional Models -- 4.1 Introduction and Objectives -- 4.2 Multi-Dimensional Diffusions -- 4.2.1 GBM Baskets -- 4.2.2 Libor Market Models -- 4.3 Multi-Dimensional Heston and SABR Models -- 4.3.1 Stochastic Volatility Models -- 4.4 Parameter Averaging -- 4.4.1 Applications to CMS Spread Options -- 4.5 Markovian Projection -- 4.5.1 Baskets with Local Volatility -- 4.5.2 Markovian Projection on Local Volatility and Heston Models -- 4.5.3 Markovian Projection onto DD SABR Models -- 4.6 Copulae -- 4.6.1 Measures of Concordance and Dependency -- 4.6.2 Examples -- 4.6.3 Elliptical Copulae -- 4.6.4 Archimedean Copulae -- 4.6.5 Building New Copulae from Given Copulae -- 4.6.6 Asymmetric Copulae -- 4.6.7 Applying Copulae to Option Pricing -- 4.6.8 Applying Copulae to Asset Allocation -- 4.7 Multi-Dimensional Variance Gamma Processes -- 4.8 Summary and Conclusions -- PART II NUMERICAL METHODS AND RECIPES -- 5 Option Pricing by Transform Techniques and Direct Integration -- 5.1 Introduction and Objectives -- 5.2 Fourier Transform -- 5.2.1 Discrete Fourier Transform -- 5.2.2 Fast Fourier Transform -- 5.3 The Carr-Madan Method -- 5.3.1 The Optimal α -- 5.4 The Lewis Method -- 5.4.1 Application to Other Payoffs -- 5.5 The Attari Method -- 5.6 The Convolution Method -- 5.7 The Cosine Method -- 5.8 Comparison, Stability and Performance -- 5.8.1 Other Issues -- 5.9 Extending the Methods to Forward Start Options -- 5.9.1 Forward Characteristic Function for Lévy Processes and CIR Time Change -- 5.9.2 Forward Characteristic Function for Lévy Processes and Gamma-OU Time Change -- 5.9.3 Results -- 5.10 Density Recovery.

5.11 Summary and Conclusions -- 6 Advanced Topics Using Transform Techniques -- 6.1 Introduction and Objectives -- 6.2 Pricing Non-Standard Vanilla Options -- 6.2.1 FFT with Lewis Method -- 6.3 Bermudan and American Options -- 6.3.1 The Convolution Method -- 6.3.2 The Cosine Method -- 6.3.3 Numerical Results -- 6.3.4 The Fourier Space Time-Stepping -- 6.4 The Cosine Method and Barrier Options -- 6.5 Greeks -- 6.6 Summary and Conclusions -- 7 Monte Carlo Simulation and Applications -- 7.1 Introduction and Objectives -- 7.2 Sampling Diffusion Processes -- 7.2.1 The Exact Scheme -- 7.2.2 The Euler Scheme -- 7.2.3 The Predictor-Corrector Scheme -- 7.2.4 The Milstein Scheme -- 7.2.5 Implementation and Results -- 7.3 Special Purpose Schemes -- 7.3.1 Schemes for the Heston Model -- 7.3.2 Unbiased Scheme for the SABR Model -- 7.4 Adding Jumps -- 7.4.1 Jump Models - Poisson Processes -- 7.4.2 Fixed Grid Sampling (FGS) -- 7.4.3 Stochastic Grid Sampling (SGS) -- 7.4.4 Simulation - Lévy Models -- 7.4.5 Schemes for Lévy Models with Stochastic Volatility -- 7.5 Bridge Sampling -- 7.6 Libor Market Model -- 7.7 Multi-Dimensional Lévy Models -- 7.8 Copulae -- 7.8.1 Distributional Sampling Approach (DSA) -- 7.8.2 Conditional Sampling Approach (CSA) -- 7.8.3 Simulation from Other Copulae -- 7.9 Summary and Conclusions -- 8 Monte Carlo Simulation - Advanced Issues -- 8.1 Introduction and Objectives -- 8.2 Monte Carlo and Early Exercise -- 8.2.1 Longstaff-Schwarz Regression -- 8.2.2 Policy Iteration Methods -- 8.2.3 Upper Bounds -- 8.2.4 Problems of the Method -- 8.2.5 Financial Examples and Numerical Results -- 8.3 Greeks with Monte Carlo -- 8.3.1 The Finite Difference Method (FDM) -- 8.3.2 The Pathwise Method -- 8.3.3 The Affine Recursion Problem (ARP) -- 8.3.4 Adjoint Method -- 8.3.5 Bermudan ARPs -- 8.4 Euler Schemes and General Greeks -- 8.4.1 SDE of Diffusions.

8.4.2 Approximation by Euler Schemes -- 8.4.3 Approximating General Greeks Using ARP -- 8.4.4 Greeks -- 8.5 Application to Trigger Swap -- 8.5.1 Mathematical Modelling -- 8.5.2 Numerical Results -- 8.5.3 The Likelihood Ratio Method (LRM) -- 8.5.4 Likelihood Ratio for Finite Differences - Proxy Simulation -- 8.5.5 Numerical Results -- 8.6 Summary and Conclusions -- 8.7 Appendix - Trees -- 9 Calibration and Optimization -- 9.1 Introduction and Objectives -- 9.2 The Nelder-Mead Method -- 9.2.1 Implementation -- 9.2.2 Calibration Examples -- 9.3 The Levenberg-Marquardt Method -- 9.3.1 Implementation -- 9.3.2 Calibration Examples -- 9.4 The L-BFGS Method -- 9.4.1 Implementation -- 9.4.2 Calibration Examples -- 9.5 The SQP Method -- 9.5.1 The Modified and Globally Convergent SQP Iteration -- 9.5.2 Implementation -- 9.5.3 Calibration Examples -- 9.6 Differential Evolution -- 9.6.1 Implementation -- 9.6.2 Calibration Examples -- 9.7 Simulated Annealing -- 9.7.1 Implementation -- 9.7.2 Calibration Examples -- 9.8 Summary and Conclusions -- 10 Model Risk - Calibration, Pricing and Hedging -- 10.1 Introduction and Objectives -- 10.2 Calibration -- 10.2.1 Similarities - Heston and Bates Models -- 10.2.2 Parameter Stability -- 10.3 Pricing Exotic Options -- 10.3.1 Exotic Options and Different Models -- 10.4 Hedging -- 10.4.1 Hedging - The Basics -- 10.4.2 Hedging in Incomplete Markets -- 10.4.3 Discrete Time Hedging -- 10.4.4 Numerical Examples -- 10.5 Summary and Conclusions -- PART III IMPLEMENTATION, SOFTWARE DESIGN AND MATHEMATICS -- 11 Matlab - Basics -- 11.1 Introduction and Objectives -- 11.2 General Remarks -- 11.3 Matrices, Vectors and Cell Arrays -- 11.3.1 Matrices and Vectors -- 11.3.2 Cell Arrays -- 11.4 Functions and Function Handles -- 11.4.1 Functions -- 11.4.2 Function Handles -- 11.5 Toolboxes -- 11.5.1 Financial -- 11.5.2 Financial Derivatives.

11.5.3 Fixed-Income -- 11.5.4 Optimization -- 11.5.5 Global Optimization -- 11.5.6 Statistics -- 11.5.7 Portfolio Optimization -- 11.6 Useful Functions and Methods -- 11.6.1 FFT -- 11.6.2 Solving Equations and ODE -- 11.6.3 Useful Functions -- 11.7 Plotting -- 11.7.1 Two-Dimensional Plots -- 11.7.2 Three-Dimensional Plots - Surfaces -- 11.8 Summary and Conclusions -- 12 Matlab - Object Oriented Development -- 12.1 Introduction and Objectives -- 12.2 The Matlab OO Model -- 12.2.1 Classes -- 12.2.2 Handling Classes in Matlab -- 12.2.3 Inheritance, Base Classes and Superclasses -- 12.2.4 Handle and Value Classes -- 12.2.5 Overloading -- 12.3 A Model Class Hierarchy -- 12.4 A Pricer Class Hierarchy -- 12.5 An Optimizer Class Hierarchy -- 12.6 Design Patterns -- 12.6.1 The Builder Pattern -- 12.6.2 The Visitor Pattern -- 12.6.3 The Strategy Pattern -- 12.7 Example - Calibration Engine -- 12.7.1 Calibrating a Data Set or a History -- 12.8 Example - The Libor Market Model and Greeks -- 12.8.1 An Abstract Class for LMM Derivatives -- 12.8.2 A Class for Bermudan Swaptions -- 12.8.3 A Class for Trigger Swaps -- 12.9 Summary and Conclusions -- 13 Math Fundamentals -- 13.1 Introduction and Objectives -- 13.2 Probability Theory and Stochastic Processes -- 13.2.1 Probability Spaces -- 13.2.2 Random Variables -- 13.2.3 Important Results -- 13.2.4 Distributions -- 13.2.5 Stochastic Processes -- 13.2.6 Lévy Processes -- 13.2.7 Stochastic Differential Equations -- 13.3 Numerical Methods for Stochastic Processes -- 13.3.1 Random Number Generation -- 13.3.2 Methods for Computing Variates -- 13.4 Basics on Complex Analysis -- 13.4.1 Complex Numbers -- 13.4.2 Complex Differentiation and Integration along Paths -- 13.4.3 The Complex Exponential and Logarithm -- 13.4.4 The Residual Theorem -- 13.5 The Characteristic Function and Fourier Transform.

13.6 Summary and Conclusions.

Financial Modelling - Theory, Implementation and Practice is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving  prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes.

Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk.  The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor Market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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