Yves Hilpisch

Derivatives Analytics with Python (eBook, PDF)

Data Analysis, Models, Simulation, Calibration and Hedging

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 376
• Erscheinungstermin: 15. Juni 2015
• Englisch
• ISBN-13: 9781119037934
• Artikelnr.: 43126485

Autorenporträt

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.

Inhaltsangabe

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 It^o'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 Valuation CHAPTER 8 A First Example of Market-Based Valuation
147 8.1 Introduction 147 8.2 Market Model 147 8.3 Valuation 148 8.4
Calibration 149 8.5 Simulation 149 8.6 Conclusions 155 8.7 Python Scripts
155 8.7.1 Valuation by Numerical Integration 155 8.7.2 Valuation by FFT 157
8.7.3 Calibration to Three Maturities 160 8.7.4 Calibration to Short
Maturity 163 8.7.5 Valuation by MCS 165 CHAPTER 9 General Model Framework
169 9.1 Introduction 169 9.2 The Framework 169 9.3 Features of the
Framework 170 9.4 Zero-Coupon Bond Valuation 172 9.5 European Option
Valuation 173 9.5.1 PDE Approach 173 9.5.2 Transform Methods 175 9.5.3
Monte Carlo Simulation 176 9.6 Conclusions 177 9.7 Proofs and Python
Scripts 177 9.7.1 It^o's Lemma 177 9.7.2 Python Script for Bond Valuation
178 9.7.3 Python Script for European Call Valuation 180 CHAPTER 10 Monte
Carlo Simulation 187 10.1 Introduction 187 10.2 Valuation of Zero-Coupon
Bonds 188 10.3 Valuation of European Options 192 10.4 Valuation of American
Options 196 10.4.1 Numerical Results 198 10.4.2 Higher Accuracy vs. Lower
Speed 201 10.5 Conclusions 203 10.6 Python Scripts 204 10.6.1 General
Zero-Coupon Bond Valuation 204 10.6.2 CIR85 Simulation and Valuation 205
10.6.3 Automated Valuation of European Options by Monte Carlo Simulation
209 10.6.4 Automated Valuation of American Put Options by Monte Carlo
Simulation 215 CHAPTER 11 Model Calibration 223 11.1 Introduction 223 11.2
General Considerations 223 11.2.1 Why Calibration at All? 224 11.2.2 Which
Role Do Different Model Components Play? 226 11.2.3 What Objective
Function? 227 11.2.4 What Market Data? 228 11.2.5 What Optimization
Algorithm? 229 11.3 Calibration of Short Rate Component 230 11.3.1
Theoretical Foundations 230 11.3.2 Calibration to Euribor Rates 231 11.4
Calibration of Equity Component 233 11.4.1 Valuation via Fourier Transform
Method 235 11.4.2 Calibration to EURO STOXX 50 Option Quotes 236 11.4.3
Calibration of H93 Model 236 11.4.4 Calibration of Jump Component 237
11.4.5 Complete Calibration of BCC97 Model 239 11.4.6 Calibration to
Implied Volatilities 240 11.5 Conclusions 243 11.6 Python Scripts for
Cox-Ingersoll-Ross Model 243 11.6.1 Calibration of CIR85 243 11.6.2
Calibration of H93 Stochastic Volatility Model 248 11.6.3 Comparison of
Implied Volatilities 251 11.6.4 Calibration of Jump-Diffusion Part of BCC97
252 11.6.5 Calibration of Complete Model of BCC97 256 11.6.6 Calibration of
BCC97 Model to Implied Volatilities 258 CHAPTER 12 Simulation and Valuation
in the General Model Framework 263 12.1 Introduction 263 12.2 Simulation of
BCC97 Model 263 12.3 Valuation of Equity Options 266 12.3.1 European
Options 266 12.3.2 American Options 268 12.4 Conclusions 268 12.5 Python
Scripts 269 12.5.1 Simulating the BCC97 Model 269 12.5.2 Valuation of
European Call Options by MCS 274 12.5.3 Valuation of American Call Options
by MCS 275 CHAPTER 13 Dynamic Hedging 279 13.1 Introduction 279 13.2
Hedging Study for BSM Model 280 13.3 Hedging Study for BCC97 Model 285 13.4
Conclusions 289 13.5 Python Scripts 289 13.5.1 LSM Delta Hedging in BSM
(Single Path) 289 13.5.2 LSM Delta Hedging in BSM (Multiple Paths) 293
13.5.3 LSM Algorithm for American Put in BCC97 295 13.5.4 LSM Delta Hedging
in BCC97 (Single Path) 300 CHAPTER 14 Executive Summary 303 APPENDIX A
Python in a Nutshell 305 A.1 Python Fundamentals 305 A.1.1 Installing
Python Packages 305 A.1.2 First Steps with Python 306 A.1.3 Array
Operations 310 A.1.4 Random Numbers 313 A.1.5 Plotting 314 A.2 European
Option Pricing 316 A.2.1 Black-Scholes-Merton Approach 316 A.2.2
Cox-Ross-Rubinstein Approach 318 A.2.3 Monte Carlo Approach 323 A.3
Selected Financial Topics 325 A.3.1 Approximation 325 A.3.2 Optimization
328 A.3.3 Numerical Integration 329 A.4 Advanced Python Topics 330 A.4.1
Classes and Objects 330 A.4.2 Basic Input-Output Operations 332 A.4.3
Interacting with Spreadsheets 334 A.5 Rapid Financial Engineering 336
Bibliography 341 Index 347