Financial Modelling
Theory, Implementation and Practice with MATLAB Source
Wiley Finance Series
1. Auflage September 2012
734 Seiten, Hardcover
Fachbuch
This book will enable the reader to model, design and implement a range of financial models for derivatives pricing and asset allocation. The book will provide practitioners with the complete financial modeling workflow, from model choice, deriving (semi-) analytic approximate prices and Greeks even for exotic options. Such methods can be used for calibration to market data. Furthermore, Monte Carlo simulation techniques are covered which can be applied to multi-dimensional and path dependent options or some asset allocation problems.
Equity/Equity-Interest Rate Hybrid models, Interest Rate models and Asset Allocation are used as examples showing specific models with analysis of their features. The authors then go on to show how to price simple options and how to calibrate the models to real life market data and finally they discuss the pricing of exotic options. At the end of these sections the reader will be able to use the techniques discussed for equity derivatives and interest rate models in other areas of finance such as foreign exchange and inflation.
The models discussed for derivatives pricing are:
* Heston / Bates Model
* Local/Stochastic Volatility Models (DD, CEV, DDHeston)
* Lévy Models (Variance-Gamma, Normal Inverse Gaussian)
* Heston -- Hull -- White Model
* Libor Market Model
* SABR Model
* Lévy Models with Stochastic Volatility
The methods which are discusses
* Direct Integration methods+
* Methods based on Fourier Transform
* Monte Carlo Simulation
* Local and Global Optimization
The models discussed for asset allocation are:
* Markowitz Model
* Black-Litterman Model
* Copula Models
* CVaR numerical optimization
Source code for all the examples is provided with implementation in Matlab.
1 Introduction and Management Summary 1
2 Why We Have Written this Book 2
3 Why You Should Read this Book 3
4 The Audience 3
5 The Structure of this Book 4
6 What this Book Does Not Cover 5
7 Credits 6
8 Code 6
PART I FINANCIAL MARKETS AND POPULAR MODELS
1 Financial Markets - Data, Basics and Derivatives 9
1.1 Introduction and Objectives 9
1.2 Financial Time-Series, Statistical Properties of Market Data and Invariants 10
1.3 Implied Volatility Surfaces and Volatility Dynamics 17
1.4 Applications 26
1.5 General Remarks on Notation 30
1.6 Summary and Conclusions 31
1.7 Appendix - Quotes 32
2 Diffusion Models 35
2.1 Introduction and Objectives 35
2.2 Local Volatility Models 35
2.3 Stochastic Volatility Models 54
2.4 Stochastic Volatility and Stochastic Rates Models 81
2.5 Summary and Conclusions 90
3 Models with Jumps 93
3.1 Introduction and Objectives 93
3.2 Poisson Processes and Jump Diffusions 94
3.3 Exponential L´evy Models 105
3.4 Other Models 118
3.5 Martingale Correction 129
3.6 Summary and Conclusions 134
4 Multi-Dimensional Models 137
4.1 Introduction and Objectives 137
4.2 Multi-Dimensional Diffusions 137
4.3 Multi-Dimensional Heston and SABR Models 141
4.4 Parameter Averaging 143
4.5 Markovian Projection 159
4.6 Copulae 172
4.7 Multi-Dimensional Variance Gamma Processes 187
4.8 Summary and Conclusions 193
PART II NUMERICAL METHODS AND RECIPES
5 Option Pricing by Transform Techniques and Direct Integration 197
5.1 Introduction and Objectives 197
5.2 Fourier Transform 197
5.3 The Carr-Madan Method 202
5.4 The Lewis Method 210
5.5 The Attari Method 215
5.6 The Convolution Method 216
5.7 The Cosine Method 220
5.8 Comparison, Stability and Performance 228
5.9 Extending the Methods to Forward Start Options 235
Time Change 238
Time Change 239
5.10 Density Recovery 245
5.11 Summary and Conclusions 250
6 Advanced Topics Using Transform Techniques 253
6.1 Introduction and Objectives 253
6.2 Pricing Non-Standard Vanilla Options 253
6.3 Bermudan and American Options 254
6.4 The Cosine Method and Barrier Options 277
6.5 Greeks 278
6.6 Summary and Conclusions 287
7 Monte Carlo Simulation and Applications 289
7.1 Introduction and Objectives 289
7.2 Sampling Diffusion Processes 289
7.3 Special Purpose Schemes 292
7.4 Adding Jumps 313
7.5 Bridge Sampling 339
7.6 Libor Market Model 346
7.7 Multi-Dimensional L´evy Models 351
7.8 Copulae 352
7.9 Summary and Conclusions 359
8 Monte Carlo Simulation - Advanced Issues 361
8.1 Introduction and Objectives 361
8.2 Monte Carlo and Early Exercise 361
8.3 Greeks with Monte Carlo 382
8.4 Euler Schemes and General Greeks 396
8.5 Application to Trigger Swap 407
8.6 Summary and Conclusions 433
8.7 Appendix - Trees 434
9 Calibration and Optimization 435
9.1 Introduction and Objectives 435
9.2 The Nelder-Mead Method 437
9.3 The Levenberg-Marquardt Method 449
9.4 The L-BFGS Method 460
9.5 The SQP Method 468
9.6 Differential Evolution 482
9.7 Simulated Annealing 493
9.8 Summary and Conclusions 505
10 Model Risk - Calibration, Pricing and Hedging 507
10.1 Introduction and Objectives 507
10.2 Calibration 508
10.3 Pricing Exotic Options 521
10.4 Hedging 528
10.5 Summary and Conclusions 550
PART III IMPLEMENTATION, SOFTWARE DESIGN AND MATHEMATICS
11 Matlab - Basics 553
11.1 Introduction and Objectives 553
11.2 General Remarks 553
11.3 Matrices, Vectors and Cell Arrays 556
11.4 Functions and Function Handles 564
11.5 Toolboxes 570
11.6 Useful Functions and Methods 589
11.7 Plotting 593
11.8 Summary and Conclusions 597
12 Matlab - Object Oriented Development 599
12.1 Introduction and Objectives 599
12.2 The Matlab OO Model 599
12.3 A Model Class Hierarchy 611
12.4 A Pricer Class Hierarchy 613
12.5 An Optimizer Class Hierarchy 618
12.6 Design Patterns 620
12.7 Example - Calibration Engine 629
12.8 Example - The Libor Market Model and Greeks 634
12.9 Summary and Conclusions 641
13 Math Fundamentals 643
13.1 Introduction and Objectives 643
13.2 Probability Theory and Stochastic Processes 643
13.3 Numerical Methods for Stochastic Processes 665
13.4 Basics on Complex Analysis 671
13.5 The Characteristic Function and Fourier Transform 675
13.6 Summary and Conclusions 679
List of Figures 681
List of Tables 691
Bibliography 695
Index 705
Daniel Wetterau is senior specialist in the Quantitative Analytics team of Deutsche Postbank AG. He is responsible for the implementation of term structure models, advanced numerical methods, optimization algorithms and methods for advanced quantitative asset allocation. Further to his work he teaches finance courses for market professionals. Daniel received a Masters in financial mathematics from the University of Wuppertal and was awarded the Barmenia mathematics award for his thesis.
