Financial Modelling by Joerg Kienitz -- Read -- Imperial Library of Trantor

Index

Cover Series Title Page Copyright Dedication 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

Chapter 1: Financial Markets – Data, Basics and Derivatives

1.1 INTRODUCTION AND OBJECTIVES 1.2 FINANCIAL TIME-SERIES, STATISTICAL PROPERTIES OF MARKET DATA AND INVARIANTS 1.3 IMPLIED VOLATILITY SURFACES AND VOLATILITY DYNAMICS 1.4 APPLICATIONS 1.5 GENERAL REMARKS ON NOTATION 1.6 SUMMARY AND CONCLUSIONS 1.7 APPENDIX – QUOTES

Chapter 2: Diffusion Models

2.1 INTRODUCTION AND OBJECTIVES 2.2 LOCAL VOLATILITY MODELS 2.3 STOCHASTIC VOLATILITY MODELS 2.4 STOCHASTIC VOLATILITY AND STOCHASTIC RATES MODELS 2.5 SUMMARY AND CONCLUSIONS

Chapter 3: Models with Jumps

3.1 INTRODUCTION AND OBJECTIVES 3.2 POISSON PROCESSES AND JUMP DIFFUSIONS 3.3 EXPONENTIAL LéVY MODELS 3.4 OTHER MODELS 3.5 MARTINGALE CORRECTION 3.6 SUMMARY AND CONCLUSIONS

Chapter 4: Multi-Dimensional Models

4.1 INTRODUCTION AND OBJECTIVES 4.2 MULTI-DIMENSIONAL DIFFUSIONS 4.3 MULTI-DIMENSIONAL HESTON AND SABR MODELS 4.4 PARAMETER AVERAGING 4.5 MARKOVIAN PROJECTION 4.6 COPULAE 4.7 MULTI-DIMENSIONAL VARIANCE GAMMA PROCESSES 4.8 SUMMARY AND CONCLUSIONS

Part II: Numerical Methods and Recipes

5.1 INTRODUCTION AND OBJECTIVES 5.2 FOURIER TRANSFORM 5.3 THE CARR--MADAN METHOD 5.4 THE LEWIS METHOD 5.5 THE ATTARI METHOD 5.6 THE CONVOLUTION METHOD 5.7 THE COSINE METHOD 5.8 COMPARISON, STABILITY AND PERFORMANCE 5.9 EXTENDING THE METHODS TO FORWARD START OPTIONS 5.10 DENSITY RECOVERY 5.11 SUMMARY AND CONCLUSIONS

Chapter 6: Advanced Topics Using Transform Techniques

6.1 INTRODUCTION AND OBJECTIVES 6.2 PRICING NON-STANDARD VANILLA OPTIONS 6.3 BERMUDAN AND AMERICAN OPTIONS 6.4 THE COSINE METHOD AND BARRIER OPTIONS 6.5 GREEKS 6.6 SUMMARY AND CONCLUSIONS

Chapter 7: Monte Carlo Simulation and Applications

7.1 INTRODUCTION AND OBJECTIVES 7.2 SAMPLING DIFFUSION PROCESSES 7.3 SPECIAL PURPOSE SCHEMES 7.4 ADDING JUMPS 7.5 BRIDGE SAMPLING 7.6 LIBOR MARKET MODEL 7.7 MULTI-DIMENSIONAL LéVY MODELS 7.8 COPULAE 7.9 SUMMARY AND CONCLUSIONS

Chapter 8: Monte Carlo Simulation – Advanced Issues

8.1 INTRODUCTION AND OBJECTIVES 8.2 MONTE CARLO AND EARLY EXERCISE 8.3 GREEKS WITH MONTE CARLO 8.4 EULER SCHEMES AND GENERAL GREEKS 8.5 APPLICATION TO TRIGGER SWAP 8.6 SUMMARY AND CONCLUSIONS 8.7 APPENDIX – TREES

Chapter 9: Calibration and Optimization

9.1 INTRODUCTION AND OBJECTIVES 9.2 THE NELDER–MEAD METHOD 9.3 THE LEVENBERG–MARQUARDT METHOD 9.4 THE L-BFGS METHOD 9.5 THE SQP METHOD 9.6 DIFFERENTIAL EVOLUTION 9.7 SIMULATED ANNEALING 9.8 SUMMARY AND CONCLUSIONS

Chapter 10: Model Risk – Calibration, Pricing and Hedging

10.1 INTRODUCTION AND OBJECTIVES 10.2 CALIBRATION 10.3 PRICING EXOTIC OPTIONS 10.4 HEDGING 10.5 SUMMARY AND CONCLUSIONS

Part III: Implementation, Software Design and Mathematics

Chapter 11: Matlab – Basics

11.1 INTRODUCTION AND OBJECTIVES 11.2 GENERAL REMARKS 11.3 MATRICES, VECTORS AND CELL ARRAYS 11.4 FUNCTIONS AND FUNCTION HANDLES 11.5 TOOLBOXES 11.6 USEFUL FUNCTIONS AND METHODS 11.7 PLOTTING 11.8 SUMMARY AND CONCLUSIONS

Chapter 12: Matlab – Object Oriented Development

12.1 INTRODUCTION AND OBJECTIVES 12.2 THE MATLAB OO MODEL 12.3 A MODEL CLASS HIERARCHY 12.4 A PRICER CLASS HIERARCHY 12.5 AN OPTIMIZER CLASS HIERARCHY 12.6 DESIGN PATTERNS 12.7 EXAMPLE – CALIBRATION ENGINE 12.8 EXAMPLE – THE LIBOR MARKET MODEL AND GREEKS 12.9 SUMMARY AND CONCLUSIONS

Chapter 13: Math Fundamentals

13.1 INTRODUCTION AND OBJECTIVES 13.2 PROBABILITY THEORY AND STOCHASTIC PROCESSES 13.3 NUMERICAL METHODS FOR STOCHASTIC PROCESSES 13.4 BASICS ON COMPLEX ANALYSIS 13.5 THE CHARACTERISTIC FUNCTION AND FOURIER TRANSFORM 13.6 SUMMARY AND CONCLUSIONS

List of Figures List of Tables Bibliography Index