Introduction

This book aims to lay a solid mathematical foundation for understanding quantitative models in financial engineering [1, 5]. As a reference book or self-study text, it contains a large number of exercises, many of which are commonly asked questions in financial quantitative interviews [1].

The main mathematical techniques and applications in finance covered in this book include: calculus (differentials, integrals, multivariable functions), numerical integration, probability theory (discrete and continuous probabilities, variances, covariances, correlations, standard normal variables), options (ordinary European calls and puts, put-call parity), forward and futures contracts, interest rates, bonds (yields) , duration, convexity), Black-Scholes formula and calculation and hedging of Greek letters (Greeks), lognormal variables and risk-neutral pricing, Taylor formula and Taylor series, finite differences and Black-Scholes partial differential equations (PDE), multivariable calculus (chain rule, integral substitution, extreme values), Lagrange multiplier method and Newton's method [2, 4, 5, 7, 10]. In addition, the book also covers numerical methods such as solving nonlinear problems, calculating bond yields and implied volatilities, and yield curve bootstrapping [1, 4]. The book also discusses portfolio optimization (maximum return portfolio, minimum variance portfolio) and the numerical accuracy of Greek letter finite difference approximations [6, 7]. The book provides pseudocode of numerical methods to help readers understand and implement them [5, 10].

Main features

• Solid theoretical foundation
• Rich practical cases
• Clear operating instructions
• Suitable for practical applications

Suitable for the crowd

• Quantitative Analyst
• Algorithmic Trader
• Financial Engineer
• Data Scientist