Joerg Kienitz, Daniel Wetterau

Financial Modelling

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Wiley Finance Series
• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 14574489000
• 1. Auflage
• Seitenzahl: 736
• Erscheinungstermin: 18. Februar 2013
• Englisch
• Abmessung: 251mm x 176mm x 45mm
• Gewicht: 1386g
• ISBN-13: 9780470744895
• ISBN-10: 0470744898
• Artikelnr.: 35259506

Autorenporträt

About the authors JÖRG KIENITZ is the head of Quantitative Analytics at Deutsche Postbank AG. He is primarily involved in developing and implementing models for pricing complex derivatives structures and for asset allocation. He also lectures at university level on advanced financial modelling and implementation including the University of Oxford's part-time Masters of Finance course. Jörg works as an independent consultant for model development and validation as well as giving seminars for finance professionals. He is a speaker at the major financial conferences including Global Derivatives, WBS Fixed Income and RISK. Jörg is a member of the editorial board of International Review of Applied Financial Issues and Economics and holds a Ph.D. in stochastic analysis from the University of Bielefeld. DANIEL WETTERAU is a 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.

Inhaltsangabe

Introduction 1

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