Partial Differential Equations in Quantitative Finance

Reactive Publishing
Partial Differential Equations (PDEs) are at the core of modern quantitative finance. From the Black-Scholes equation to advanced multi-factor models, PDEs provide the mathematical foundation for option pricing, risk management, and hedging strategies across global markets.
This book delivers a clear, practical introduction to PDEs in finance, bridging rigorous theory with real-world application. Readers will learn not only the mathematics behind PDE-based models but also how to implement and apply them directly to derivatives trading, risk modeling, and quantitative research.
What You’ll Learn

• The fundamentals of parabolic, elliptic, and hyperbolic PDEs in financial contexts
• Step-by-step construction of the Black-Scholes PDE and its solutions
• Applications of PDEs to European, American, and exotic options
• Numerical methods: finite difference schemes, Crank-Nicolson, implicit/explicit solvers
• PDE approaches to interest rate models, volatility surfaces, and multi-asset derivatives
• Python implementations of PDE solvers for practical trading and research

Who This Book Is For

• Quantitative analysts and traders working with derivatives
• Financial engineers and risk managers
• Graduate students in quantitative finance, applied math, or financial engineering
• Python developers applying numerical methods in finance