Financial theory with Python : a gentle introduction

Nowadays, finance, mathematics, and programming are intrinsically linked. This book provides the relevant foundations of each discipline to give you the major tools you need to get started in the world of computational finance. Using an approach where mathematical concepts provide the common background against which financial ideas and programming techniques are learned, this practical guide teaches you the basics of financial economics. Written by the best-selling author of __Python for Finance__, Yves Hilpisch, __Financial Theory with Python__ explains financial, mathematical, and Python programming concepts in an integrative manner so that the interdisciplinary concepts reinforce each other. * Draw upon mathematics to learn the foundations of financial theory and Python programming * Learn about financial theory, financial data modeling, and the use of Python for computational finance * Leverage simple economic models to better understand basic notions of finance and Python programming concepts * Use both static and dynamic financial modeling to address fundamental problems in finance, such as pricing, decision-making, equilibrium, and asset allocation * Learn the basics of Python packages useful for financial modeling, such as NumPy, pandas, Matplotlib, and SymPy Cover 1 Copyright 4 Table of Contents 5 Preface 9 Why This Book? 9 Target Audience 10 Overview of the Book 11 Conventions Used in This Book 12 Using Code Examples 13 O’Reilly Online Learning 14 How to Contact Us 14 Acknowledgments 15 Chapter 1. Finance and Python 17 A Brief History of Finance 18 Major Trends in Finance 19 A Four-Languages World 20 The Approach of This Book 21 Getting Started with Python 24 Conclusions 31 References 32 Chapter 2. Two-State Economy 33 Economy 34 Real Assets 34 Agents 34 Time 35 Money 36 Cash Flow 37 Return 39 Interest 39 Present Value 40 Net Present Value 41 Uncertainty 42 Financial Assets 44 Risk 45 Probability Measure 45 Expectation 47 Expected Return 48 Volatility 49 Contingent Claims 51 Replication 53 Arbitrage Pricing 56 Market Completeness 58 Arrow-Debreu Securities 63 Martingale Pricing 65 First Fundamental Theorem of Asset Pricing 66 Pricing by Expectation 67 Second Fundamental Theorem of Asset Pricing 67 Mean-Variance Portfolios 68 Conclusions 73 Further Resources 73 Chapter 3. Three-State Economy 75 Uncertainty 76 Financial Assets 76 Attainable Contingent Claims 77 Martingale Pricing 80 Martingale Measures 80 Risk-Neutral Pricing 83 Super-Replication 83 Approximate Replication 87 Capital Market Line 89 Capital Asset Pricing Model 91 Conclusions 96 Further Resources 97 Chapter 4. Optimality and Equilibrium 99 Utility Maximization 100 Indifference Curves 102 Appropriate Utility Functions 104 Logarithmic Utility 105 Time-Additive Utility 106 Expected Utility 109 Optimal Investment Portfolio 111 Time-Additive Expected Utility 114 Pricing in Complete Markets 115 Arbitrage Pricing 117 Martingale Pricing 118 Risk-Less Interest Rate 118 A Numerical Example (I) 119 Pricing in Incomplete Markets 122 Martingale Measures 124 Equilibrium Pricing 125 A Numerical Example (II) 127 Conclusions 131 Further Resources 132 Chapter 5. Static Economy 133 Uncertainty 134 Random Variables 135 Numerical Examples 136 Financial Assets 138 Contingent Claims 140 Market Completeness 141 Fundamental Theorems of Asset Pricing 145 Black-Scholes-Merton Option Pricing 149 Completeness of Black-Scholes-Merton 153 Merton Jump-Diffusion Option Pricing 154 Representative Agent Pricing 159 Conclusions 160 Further Resources 161 Chapter 6. Dynamic Economy 163 Binomial Option Pricing 164 Simulation and Valuation Based on Python Loops 167 Simulation and Valuation Based on Vectorized Code 170 Speed Comparison 173 Black-Scholes-Merton Option Pricing 175 Monte Carlo Simulation of Stock Price Paths 175 Monte Carlo Valuation of the European Put Option 179 Monte Carlo Valuation of the American Put Option 180 Conclusions 182 Further Resources 182 Chapter 7. Where to Go from Here? 185 Mathematics 185 Financial Theory 186 Python Programming 189 Python for Finance 189 Financial Data Science 190 Algorithmic Trading 190 Computational Finance 191 Artificial Intelligence 192 Other Resources 192 Final Words 193 Index 195 About the Author 202 Colophon 203 Nowadays, finance, mathematics, and programming are intrinsically linked. Financial Theory with Python provides relevant foundations of each discipline to give you the major tools you need to get started in the world of computational finance. Using an approach where mathematical concepts provide the common background against which financial ideas and programming techniques are learned, Financial Theory with Python teaches you the basics of financial economics. Written by the bestselling author of Python for Finance, Yves Hilpisch, this practical guide explains financial, mathematical, and Python programming concepts in an integrative manner so that the interdisciplinary concepts reinforce each other. Draw upon mathematics to learn the foundations of financial theory and Python programming Learn about financial theory, financial data modeling, and the use of Python for computational finance Leverage simple economic models to better understand basic notions of finance and Python programming concepts Utilize both static and dynamic financial modeling to address fundamental problems in finance, such as pricing, decision making, equilibrium, and asset allocation Learn the basics of Python packages useful for financial modeling, such as NumPy, pandas, matplotlib, and SymPy Written by the best-selling author of Python for Finance, Yves Hilpisch, this new book explains financial, mathematical, and Python programming concepts in an integrative manner so that the interdisciplinary concepts reinforce each other.