1. Finance and Python
A Brief History of Finance
Major Trends in Finance
A Four-Languages World
The Approach of This Book
Getting Started with Python
Conclusions
References
2. Two-State Economy
Economy
Real Assets
Agents
Time
Money
Cash Flow
Return
Interest
Present Value
Net Present Value
Uncertainty
Financial Assets
Risk
Probability Measure
Expectation
Expected Return
Volatility
Contingent Claims
Replication
Arbitrage Pricing
Market Completeness
Arrow-Debreu Securities
Martingale Pricing
First Fundamental Theorem of Asset Pricing
Pricing by Expectation
Second Fundamental Theorem of Asset Pricing
Mean-Variance Portfolios
Conclusions
Further Resources
3. Three-State Economy
Uncertainty
Financial Assets
Attainable Contingent Claims
Martingale Pricing
Martingale Measures
Risk-Neutral Pricing
Super-Replication
Approximate Replication
Capital Market Line
Capital Asset Pricing Model
Conclusions
Further Resources
4. Optimality and Equilibrium
Utility Maximization
Indifference Curves
Appropriate Utility Functions
Logarithmic Utility
Time-Additive Utility
Expected Utility
Optimal Investment Portfolio
Time-Additive Expected Utility
Pricing in Complete Markets
Arbitrage Pricing
Martingale Pricing
Risk-Less Interest Rate
A Numerical Example (I)
Pricing in Incomplete Markets
Martingale Measures
Equilibrium Pricing
A Numerical Example (II)
Conclusions
Further Resources
5. Static Economy
Uncertainty
Random Variables
Numerical Examples
Financial Assets
Contingent Claims
Market Completeness
Fundamental Theorems of Asset Pricing
Black-Scholes-Merton Option Pricing
Completeness of Black-Scholes-Merton
Merton Jump-Diffusion Option Pricing
Representative Agent Pricing
Conclusions
Further Resources
6. Dynamic Economy
Binomial Option Pricing
Simulation and Valuation Based on Python Loops
Simulation and Valuation Based on Vectorized Code
Speed Comparison
Black-Scholes-Merton Option Pricing
Monte Carlo Simulation of Stock Price Paths
Monte Carlo Valuation of the European Put Option
Monte Carlo Valuation of the American Put Option
Conclusions
Further Resources
7. Where to Go from Here?
Mathematics
Financial Theory
Python Programming
Python for Finance
Financial Data Science
Algorithmic Trading
Computational Finance
Artificial Intelligence
Other Resources
Final Words
Index

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