Listed Volatility and Variance Derivatives

A Python-based Guide
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(368 Seiten)
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ISBN-13:
9781119167921
Einband:
E-Book
Seiten:
368
Autor:
Yves Hilpisch
Serie:
1, Wiley Finance Editions
eBook Typ:
PDF
eBook Format:
E-Book
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:

Leverage Python for expert-level volatility and variance derivative trading
Listed Volatility and Variance Derivatives is a comprehensive treatment of all aspects of these increasingly popular derivatives products, and has the distinction of being both the first to cover European volatility and variance products provided by Eurex and the first to offer Python code for implementing comprehensive quantitative analyses of these financial products. For those who want to get started right away, the book is accompanied by a dedicated Web page and a Github repository that includes all the code from the book for easy replication and use, as well as a hosted version of all the code for immediate execution.

Python is fast making inroads into financial modelling and derivatives analytics, and recent developments allow Python to be as fast as pure C++ or C while consisting generally of only 10% of the code lines associated with the compiled languages. This complete guide offers rare insight into the use of Python to undertake complex quantitative analyses of listed volatility and variance derivatives.
* Learn how to use Python for data and financial analysis, and reproduce stylised facts on volatility and variance markets
* Gain an understanding of the fundamental techniques of modelling volatility and variance and the model-free replication of variance
* Familiarise yourself with micro structure elements of the markets for listed volatility and variance derivatives
* Reproduce all results and graphics with IPython/Jupyter Notebooks and Python codes that accompany the book

Listed Volatility and Variance Derivatives is the complete guide to Python-based quantitative analysis of these Eurex derivatives products.

Preface 1

I Introduction to Volatility and Variance 3

1 Derivatives, Volatility and Variance 5

1.1 Option Pricing and Hedging 5

1.2 Notions of Volatility and Variance 7

1.3 Listed Volatility and Variance Derivatives 8

1.3.1 The US History 8

1.3.2 The European History 10

1.3.3 Volatility of Volatility Indexes 11

1.3.4 Products Covered in this Book 12

1.4 Volatility and Variance Trading 12

1.4.1 Volatility Trading 13

1.4.2 Variance Trading 14

1.5 Python as Our Tool of Choice 15

1.6 Quick Guide Through Rest of the Book 15

2 Introduction to Python 19

2.1 Python Basics 19

2.1.1 Data Types 19

2.1.2 Data Structures 21

2.1.3 Control Structures 23

2.1.4 Special Python Idioms 24

2.2 NumPy 27

2.3 matplotlib 32

2.4 pandas 36

2.4.1 pandas Data Frame class 36

2.4.2 Input-Output Operations 40

2.4.3 Financial Analytics Examples 43

2.5 Conclusions 48

3 Model-Free Replication of Variance 49

3.1 Introduction 49

3.2 Spanning with Options 49

3.3 Log Contracts 50

3.4 Static Replication of Realized Variance and Variance Swaps 51

3.5 Constant Dollar Gamma Derivatives and Portfolios 51

3.6 Practical Replication of Realized Variance 52

3.7 VSTOXX as Volatility Index 57

3.8 Conclusions 59

II Listed Volatility Derivatives 61

4 Data Analysis and Strategies 63

4.1 Introduction 63

4.2 Retrieving Base Data 63

4.2.1 EURO STOXX 50 Data 63

4.2.2 VSTOXX Data 65

4.2.3 Combining the Data Sets 67

4.2.4 Saving the Data 68

4.3 Basic Data Analysis 69

4.4 Correlation Analysis 72

4.5 Constant Proportion Investment Strategies 77

4.6 Conclusions 82

5 VSTOXX Index 83

5.1 Introduction 83

5.2 Collecting Option Data 84

5.3 Calculating the Sub-Indexes 91

5.3.1 The Algorithm 91

5.4 Calculating the VSTOXX Index 98

5.5 Conclusions 101

5.6 Python Scripts 103

5.6.1 index_collect_option_data.py 103

5.6.2 index_subindex_calculation.py 107

5.6.3 index_vstoxx_calculation.py 110

6 Valuing Volatility Derivatives 113

6.1 Introduction 113

6.2 The Valuation Framework 113

6.3 The Futures Pricing Formula 114

6.4 The Option Pricing Formula 115

6.5 Monte Carlo Simulation 118

6.6 Automated Monte Carlo Tests 123

6.6.1 The Automated Testing 123

6.6.2 The Storage Functions 126

6.6.3 The Results 128

6.7 Model Calibration 133

6.7.1 The Option Quotes 133

6.7.2 The Calibration Procedure 134

6.7.3 The Calibration Results 138

6.8 Conclusions 141

6.9 Python Scripts 141

6.9.1 srd_functions.py 141

6.9.2 srd_simulation_analysis.py 145

6.9.3 srd_simulation_results.py 148

6.9.4 srd_model_calibration.py 151

7 Advanced Modeling of the VSTOXX Index 155

7.1 Introduction 155

7.2 Market Quotes for Call Options 155

7.3 The SRJD Model 158

7.4 Term Structure Calibration 159

7.4.1 Futures Term Structure 159

7.4.2 Shifted Volatility Process 163

7.5 Option Valuation by Monte Carlo Simulation 164

7.5.1 Monte Carlo Valuation 165

7.5.2 Technical Implementation 165

7.6 Model Calibration 169

7.6.1 The Python Code 169

7.6.2 Short Maturity 171

7.6.3 Two Maturities 173

7.6.4 Four Maturities 175

7.6.5 All Maturities 176

7.7 Conclusions 181

7.8 Python Scripts 181

7.8.1 srjd_fwd_calibration.py 181

7.8.2 srjd_simulation.py 183

7.8.3 srjd_model_calibration.py 185

8 Terms of the VSTOXX and its Derivatives 191

8.1 The EURO STOXX 50 Index 191

8.2 The VSTOXX Index 192

8.3 VSTOXX Futures Contracts 192

8.4 VSTOXX Options Contracts 193

8.5 Conclusions 195

III Listed Variance Derivatives 197

9 Realized Variance and Variance Swaps 199

9.1 Introdution 199

9.2 Realized Variance 199

9.3 Variance Swaps 204

9.3.1 Definition of a Variance Swap 204

9.3.2 Numerical Example 205

9.3.3 Mark-to-Market 208

9.3.4 Vega Sensitivity 209

9.3.5 Variance Swap on the EURO STOXX 50 211

9.4 Variance vs. Volatility 216

9.4.1 Squared Variations 216

9.4.2 Additivity in Time 216

9.4.3 Static Hedges 218

9.4.4 Broad Measure of Risk 218

9.5 Conclusions 218

10 Variance Futures at Eurex 219

10.1 Introduction 219

10.2 Variance Futures Concepts 220

10.2.1 Realized Variance 220

10.2.2 Net Present Value Concepts 220

10.2.3 Traded Variance Strike 224

10.2.4 Traded Futures Price 224

10.2.5 Number of Futures 225

10.2.6 Par Variance Strike 225

10.2.7 Futures Settlement Price 225

10.3 Example Calculation for a Variance Future 225

10.4 Comparison of Variance Swap and Future 230

10.5 Conclusions 233

11 Trading and Settlement 235

11.1 Introduction 235

11.2 Overview of Variance Futures Terms 235

11.3 Intraday Trading 236

11.4 Trade Matching 239

11.5 Different Traded Volatilities 239

11.6 After the Trade Matching 241

11.7 Further Details 243

11.7.1 Interest Rate Calculation 243

11.7.2 Market Disruption Events 243

11.8 Conclusions 244

IV DX Analytics 245

12 DX Analytics An Overview 247

12.1 Introduction 247

12.2 Modeling Risk Factors 248

12.3 Modeling Derivatives 250

12.4 Derivatives Portfolios 253

12.4.1 Modeling Portfolios 253

12.4.2 Simulation and Valuation 255

12.4.3 Risk Reports 256

12.5 Conclusions 257

13 DX Analytics Square-Root Diffusion 259

13.1 Introduction 259

13.2 Data Import and Selection 259

13.3 Modeling the VSTOXX Options 262

13.4 Calibration of the VSTOXX Model 264

13.5 Conclusions 269

13.6 Python Scripts 269

13.6.1 dx_srd_calibration.py 269

14 DX Analytics Square-Root Jump Diffusion 275

14.1 Introduction 275

14.2 Modeling the VSTOXX Options 275

14.3 Calibration of the VSTOXX Model 279

14.4 Calibration Results 283

14.4.1 Calibration to 1 Maturity 283

14.4.2 Calibration to 2 Maturities 283

14.4.3 Calibration to 5 Maturities 285

14.4.4 Calibration without Penalties 285

14.5 Conclusions 288

14.6 Python Scripts 288

14.6.1 dx_srjd_calibration.py 288

Bibliography 303

Index 305

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