Mathematical Models of Financial Derivatives

Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of ?nancial derivatives and structured products in the ?nancial markets around the globe and the surge in research on derivative pricing theory. Leading ?nancial ins- tutions are hiring graduates with a science background who can use advanced a- lytical and numerical techniques to price ?nancial derivatives and manage portfolio risks, a phenomenon coined as Rocket Science on Wall Street. There are now more than a hundred Master level degreed programs in Financial Engineering/Quantitative Finance/Computational Finance in different continents. This book is written as an - troductory textbook on derivative pricing theory for students enrolled in these degree programs. Another audience of the book may include practitioners in quantitative teams in ?nancial institutions who would like to acquire the knowledge of option pricing techniques and explore the new development in pricing models of exotic structured derivatives. The level of mathematics in this book is tailored to readers with preparation at the advanced undergraduate level of science and engineering - jors, in particular, basic pro?ciencies in probability and statistics, differential eq- tions, numerical methods, and mathematical analysis. Advance knowledge in s- chastic processes that are relevant to the martingale pricing theory, like stochastic differential calculus and theory of martingale, are introduced in this book. The cornerstones of derivative pricing theory are the Black-Scholes-Merton pricing model and the martingale pricing theory of ?nancial derivatives.