Derivatives Analytics with Python

Supercharge options analytics and hedging using the power of Python

Derivatives Analytics with Python shows you how to implement market-consistent valuation and hedging approaches using advanced financial models, efficient numerical techniques, and the powerful capabilities of the Python programming language. This unique guide offers detailed explanations of all theory, methods, and processes, giving you the background and tools necessary to value stock index options from a sound foundation. You'll find and use self-contained Python scripts and modules and learn how to apply Python to advanced data and derivatives analytics as you benefit from the 5,000+ lines of code that are provided to help you reproduce the results and graphics presented. Coverage includes market data analysis, risk-neutral valuation, Monte Carlo simulation, model calibration, valuation, and dynamic hedging, with models that exhibit stochastic volatility, jump components, stochastic short rates, and more. The companion website features all code and IPython Notebooks for immediate execution and automation.

Python is gaining ground in the derivatives analytics space, allowing institutions to quickly and efficiently deliver portfolio, trading, and risk management results. This book is the finance professional's guide to exploiting Python's capabilities for efficient and performing derivatives analytics.

• Reproduce major stylized facts of equity and options markets yourself
• Apply Fourier transform techniques and advanced Monte Carlo pricing
• Calibrate advanced option pricing models to market data
• Integrate advanced models and numeric methods to dynamically hedge options

Recent developments in the Python ecosystem enable analysts to implement analytics tasks as performing as with C or C++, but using only about one-tenth of the code or even less. Derivatives Analytics with Python -- Data Analysis, Models, Simulation, Calibration and Hedging shows you what you need to know to supercharge your derivatives and risk analytics efforts.

Auteur

YVES HILPISCH is founder and Managing Partner of The Python Quants, a group that focuses on Python & Open Source Software for Quantitative Finance. Yves is also a Computational Finance Lecturer on the CQF Program. He works with clients in the financial industry around the globe and has ten years of experience with Python. Yves is the organizer of Python and Open Source for Quant Finance conferences and meetup groups in Frankfurt, London and New York City.

Texte du rabat

Supercharge options analytics and hedging using the power of Python Derivatives Analytics with Python shows you how to implement market-consistent valuation and hedging approaches using advanced financial models, efficient numerical techniques, and the powerful capabilities of the Python programming language. This unique guide offers detailed explanations of all theory, methods, and processes, giving you the background and tools necessary to value stock index options from a sound foundation. You'll find and use self-contained Python scripts and modules and learn how to apply Python to advanced data and derivatives analytics as you benefit from the 5,000+ lines of code that are provided to help you reproduce the results and graphics presented. Coverage includes market data analysis, risk-neutral valuation, Monte Carlo simulation, model calibration, valuation, and dynamic hedging, with models that exhibit stochastic volatility, jump components, stochastic short rates, and more. The companion website features all code and IPython Notebooks for immediate execution and automation. Python is gaining ground in the derivatives analytics space, allowing institutions to quickly and efficiently deliver portfolio, trading, and risk management results. This book is the finance professional's guide to exploiting Python's capabilities for efficient and performing derivatives analytics. Reproduce major stylized facts of equity and options markets yourself Apply Fourier transform techniques and advanced Monte Carlo pricing Calibrate advanced option pricing models to market data Integrate advanced models and numeric methods to dynamically hedge options Recent developments in the Python ecosystem enable analysts to implement analytics tasks as performing as with C or C++, but using only about one-tenth of the code or even less. Derivatives Analytics with Python -- Data Analysis, Models, Simulation, Calibration and Hedging shows you what you need to know to supercharge your derivatives and risk analytics efforts.

Contenu

List of Tables xi

List of Figures xiii

Preface xvii

Chapter 1 A Quick Tour 1

1.1 Market-Based Valuation 1

1.2 Structure of the Book 2

1.3 Why Python? 3

1.4 Further Reading 4

Part One The Market

Chapter 2 What is Market-Based Valuation? 9

2.1 Options and their Value 9

2.2 Vanilla vs. Exotic Instruments 13

2.3 Risks Affecting Equity Derivatives 14

2.3.1 Market Risks 14

2.3.2 Other Risks 15

2.4 Hedging 16

2.5 Market-Based Valuation as a Process 17

Chapter 3 Market Stylized Facts 19

3.1 Introduction 19

3.2 Volatility, Correlation and Co. 19

3.3 Normal Returns as the Benchmark Case 21

3.4 Indices and Stocks 25

3.4.1 Stylized Facts 25

3.4.2 DAX Index Returns 26

3.5 Option Markets 30

3.5.1 Bid/Ask Spreads 31

3.5.2 Implied Volatility Surface 31

3.6 Short Rates 33

3.7 Conclusions 36

3.8 Python Scripts 37

3.8.1 GBM Analysis 37

3.8.2 DAX Analysis 40

3.8.3 BSM Implied Volatilities 41

3.8.4 EURO STOXX 50 Implied Volatilities 43

3.8.5 Euribor Analysis 45

Part Two Theoretical Valuation

Chapter 4 Risk-Neutral Valuation 49

4.1 Introduction 49

4.2 Discrete-Time Uncertainty 50

4.3 Discrete Market Model 54

4.3.1 Primitives 54

4.3.2 Basic Definitions 55

4.4 Central Results in Discrete Time 57

4.5 Continuous-Time Case 61

4.6 Conclusions 66

4.7 Proofs 66

4.7.1 Proof of Lemma 1 66

4.7.2 Proof of Proposition 1 67

4.7.3 Proof of Theorem 1 68

Chapter 5 Complete Market Models 71

5.1 Introduction 71

5.2 Black-Scholes-Merton Model 72

5.2.1 Market Model 72

5.2.2 The Fundamental PDE 72

5.2.3 European Options 74

5.3 Greeks in the BSM Model 76

5.4 Cox-Ross-Rubinstein Model 81

5.5 Conclustions 84

5.6 Proofs and Python Scripts 84

5.6.1 Itô's Lemma 84

5.6.2 Script for BSM Option Valuation 85

5.6.3 Script for BSM Call Greeks 88

5.6.4 Script for CRR Option Valuation 92

Chapter 6 Fourier-Based Option Pricing 95

6.1 Introduction 95

6.2 The Pricing Problem 96

6.3 Fourier Transforms 97

6.4 Fourier-Based Option Pricing 98

6.4.1 Lewis (2001) Approach 98

6.4.2 Carr-Madan (1999) Approach 101

6.5 Numerical Evaluation 103

6.5.1 Fourier Series 103

6.5.2 Fast Fourier Transform 105

6.6 Applications 107

6.6.1 Black-Scholes-Merton (1973) Model 107

6.6.2 Merton (1976) Model 108

6.6.3 Discrete Market Model 110

6.7 Conclusions 114

6.8 Python Scripts 114

6.8.1 BSM Call Valuation via Fourier Approach 114

6.8.2 Fourier Series 119

6.8.3 Roots of Unity 120

6.8.4 Convolution 121

6.8.5 Module with Parameters 122

6.8.6 Call Value by Convolution 123

6.8.7 Option Pricing by Convolution 123

6.8.8 Option Pricing by DFT 124

6.8.9 Speed Test of DFT 125

Chapter 7 Valuation of American Options by Simulation 127

7.1 Introduction 127

7.2 Financial Model 128

7.3 American Option Valuation 128

7.3.1 Problem Formulations 128

7.3.2 Valuation Algorithms 130

7.4 Numerical Results 132

7.4.1 American Put Option 132

7.4.2 American Short Condor Spread 135

7.5 Conclusions 136

7.6 Python Scripts 137

7.6.1 Binomial Valuation 137

7.6.2 Monte Carlo Valuation with LSM 139

7.6.3 Primal and Dual LSM Algorithms 140

**Part Three Market-Based Valua…