Exotic Options: A Unified Mathematical Framework for Pricing, Hedging, and Risk Management

Exotic options are among the most sophisticated instruments in modern finance. This monograph provides a comprehensive mathematical framework for the pricing, hedging, and risk management of these complex derivatives. Covering a broad range of path-dependent and non-standard options, the book brings together the theoretical foundations, mathematical models, and practical techniques used in modern quantitative finance. It examines key pricing methods-including stochastic processes, risk-neutral valuation, partial differential equations (PDEs), Monte Carlo simulation, lattice methods, and numerical techniques-alongside hedging strategies, model assumptions, and practical challenges encountered in financial markets. Designed as a comprehensive review, this book serves as a valuable reference for graduate students, researchers, quantitative analysts, financial engineers, and finance professionals seeking a deeper understanding of exotic options and advanced derivative pricing. By combining mathematical rigor with practical financial applications, it offers a clear and structured overview of one of the most advanced areas of quantitative finance.