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Listed Volatility and Variance Derivatives: A Python-based Guide

ISBN: 978-1-119-16793-8
368 pages
November 2016
Listed Volatility and Variance Derivatives: A Python-based Guide (1119167930) cover image

Description

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.

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Table of Contents

Preface xi

PART ONE Introduction to Volatility and Variance

CHAPTER 1 Derivatives, Volatility and Variance 3

1.1 Option Pricing and Hedging 3

1.2 Notions of Volatility and Variance 6

1.3 Listed Volatility and Variance Derivatives 7

1.3.1 The US History 7

1.3.2 The European History 8

1.3.3 Volatility of Volatility Indexes 9

1.3.4 Products Covered in this Book 10

1.4 Volatility and Variance Trading 11

1.4.1 Volatility Trading 11

1.4.2 Variance Trading 13

1.5 Python as Our Tool of Choice 14

1.6 Quick Guide Through the Rest of the Book 14

CHAPTER 2 Introduction to Python 17

2.1 Python Basics 17

2.1.1 Data Types 17

2.1.2 Data Structures 20

2.1.3 Control Structures 22

2.1.4 Special Python Idioms 23

2.2 NumPy 28

2.3 matplotlib 34

2.4 pandas 38

2.4.1 pandas DataFrame class 39

2.4.2 Input-Output Operations 45

2.4.3 Financial Analytics Examples 47

2.5 Conclusions 53

CHAPTER 3 Model-Free Replication of Variance 55

3.1 Introduction 55

3.2 Spanning with Options 56

3.3 Log Contracts 57

3.4 Static Replication of Realized Variance and Variance Swaps 57

3.5 Constant Dollar Gamma Derivatives and Portfolios 58

3.6 Practical Replication of Realized Variance 59

3.7 VSTOXX as Volatility Index 65

3.8 Conclusions 67

PART TWO Listed Volatility Derivatives

CHAPTER 4 Data Analysis and Strategies 71

4.1 Introduction 71

4.2 Retrieving Base Data 71

4.2.1 EURO STOXX 50 Data 71

4.2.2 VSTOXX Data 74

4.2.3 Combining the Data Sets 76

4.2.4 Saving the Data 78

4.3 Basic Data Analysis 78

4.4 Correlation Analysis 83

4.5 Constant Proportion Investment Strategies 87

4.6 Conclusions 93

CHAPTER 5 VSTOXX Index 95

5.1 Introduction 95

5.2 Collecting Option Data 95

5.3 Calculating the Sub-Indexes 105

5.3.1 The Algorithm 106

5.4 Calculating the VSTOXX Index 114

5.5 Conclusions 118

5.6 Python Scripts 118

5.6.1 index collect option_data.py 118

5.6.2 index_subindex_calculation.py 123

5.6.3 index_vstoxx_calculation.py 127

CHAPTER 6 Valuing Volatility Derivatives 129

6.1 Introduction 129

6.2 The Valuation Framework 129

6.3 The Futures Pricing Formula 130

6.4 The Option Pricing Formula 132

6.5 Monte Carlo Simulation 135

6.6 Automated Monte Carlo Tests 141

6.6.1 The Automated Testing 141

6.6.2 The Storage Functions 145

6.6.3 The Results 146

6.7 Model Calibration 153

6.7.1 The Option Quotes 154

6.7.2 The Calibration Procedure 155

6.7.3 The Calibration Results 160

6.8 Conclusions 163

6.9 Python Scripts 163

6.9.1 srd_functions.py 163

6.9.2 srd simulation analysis.py 167

6.9.3 srd simulation results.py 171

6.9.4 srd model calibration.py 174

CHAPTER 7 Advanced Modeling of the VSTOXX Index 179

7.1 Introduction 179

7.2 Market Quotes for Call Options 179

7.3 The SRJD Model 182

7.4 Term Structure Calibration 183

7.4.1 Futures Term Structure 184

7.4.2 Shifted Volatility Process 190

7.5 Option Valuation by Monte Carlo Simulation 191

7.5.1 Monte Carlo Valuation 191

7.5.2 Technical Implementation 192

7.6 Model Calibration 195

7.6.1 The Python Code 196

7.6.2 Short Maturity 199

7.6.3 Two Maturities 201

7.6.4 Four Maturities 203

7.6.5 All Maturities 205

7.7 Conclusions 209

7.8 Python Scripts 210

7.8.1 srjd fwd calibration.py 210

7.8.2 srjd_simulation.py 212

7.8.3 srjd_model_calibration.py 215

CHAPTER 8 Terms of the VSTOXX and its Derivatives 221

8.1 The EURO STOXX 50 Index 221

8.2 The VSTOXX Index 221

8.3 VSTOXX Futures Contracts 223

8.4 VSTOXX Options Contracts 224

8.5 Conclusions 225

PART THREE Listed Variance Derivatives

CHAPTER 9 Realized Variance and Variance Swaps 229

9.1 Introduction 229

9.2 Realized Variance 229

9.3 Variance Swaps 235

9.3.1 Definition of a Variance Swap 235

9.3.2 Numerical Example 235

9.3.3 Mark-to-Market 239

9.3.4 Vega Sensitivity 241

9.3.5 Variance Swap on the EURO STOXX 50 242

9.4 Variance vs. Volatility 247

9.4.1 Squared Variations 247

9.4.2 Additivity in Time 247

9.4.3 Static Hedges 250

9.4.4 Broad Measure of Risk 250

9.5 Conclusions 250

CHAPTER 10 Variance Futures at Eurex 251

10.1 Introduction 251

10.2 Variance Futures Concepts 252

10.2.1 Realized Variance 252

10.2.2 Net Present Value Concepts 252

10.2.3 Traded Variance Strike 257

10.2.4 Traded Futures Price 257

10.2.5 Number of Futures 258

10.2.6 Par Variance Strike 258

10.2.7 Futures Settlement Price 258

10.3 Example Calculation for a Variance Future 258

10.4 Comparison of Variance Swap and Future 265

10.5 Conclusions 268

CHAPTER 11 Trading and Settlement 269

11.1 Introduction 269

11.2 Overview of Variance Futures Terms 269

11.3 Intraday Trading 270

11.4 Trade Matching 274

11.5 Different Traded Volatilities 275

11.6 After the Trade Matching 277

11.7 Further Details 279

11.7.1 Interest Rate Calculation 279

11.7.2 Market Disruption Events 280

11.8 Conclusions 280

PART FOUR DX Analytics

CHAPTER 12 DX Analytics – An Overview 283

12.1 Introduction 283

12.2 Modeling Risk Factors 284

12.3 Modeling Derivatives 287

12.4 Derivatives Portfolios 290

12.4.1 Modeling Portfolios 292

12.4.2 Simulation and Valuation 293

12.4.3 Risk Reports 294

12.5 Conclusions 296

CHAPTER 13 DX Analytics – Square-Root Diffusion 297

13.1 Introduction 297

13.2 Data Import and Selection 297

13.3 Modeling the VSTOXX Options 301

13.4 Calibration of the VSTOXX Model 303

13.5 Conclusions 308

13.6 Python Scripts 308

13.6.1 dx srd calibration.py 308

CHAPTER 14 DX Analytics – Square-Root Jump Diffusion 315

14.1 Introduction 315

14.2 Modeling the VSTOXX Options 315

14.3 Calibration of the VSTOXX Model 320

14.4 Calibration Results 325

14.4.1 Calibration to One Maturity 325

14.4.2 Calibration to Two Maturities 325

14.4.3 Calibration to Five Maturities 325

14.4.4 Calibration without Penalties 331

14.5 Conclusions 332

14.6 Python Scripts 334

14.6.1 dx srjd calibration.py 334

Bibliography 345

Index 347

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Author Information

DR. YVES HILPISCH is founder and managing partner of The Python Quants (http://tpq.io), a group focusing on the use of open source technologies for financial data science, algorithmic trading and computational finance. He is the author of Python for Finance, and Derivatives Analytics with Python. Yves lectures on computational finance on the CQF Program as well as on data science at htw saar University of Applied Sciences. He has written the financial analytics library DX Analytics (http://dx-analytics.com) and organizes meetup groups and conferences about Python for quantitative finance in Frankfurt, London and New York.

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