Mathematical Models of Financial Derivatives

This book contains a comprehensive account of pricing models of financial derivatives. It covers risk neutral valuation theory, martingale measure, and tools in stochastic calculus required for the understanding of option pricing theory.

Objectives and Audience In the past three decades, we have witnessed the phenomenal growth in the trading of financial derivatives and structured products in the financial markets around the globe and the surge in research on derivative pricing theory. Leading financial ins- tutions are hiring graduates with a science background who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks, a phenomenon coined as Rocket Science on Wall Street. There are now more than a hundred Master level degree programs in Financial Engineering/Quantitative Finance/Computational Finance on different continents. This book is written as an introductory textbook on derivative pricing theory for students enrolled in these degree programs. Another audience of the book may include practitioners in quantitative teams in financial 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 majors, in particular, basic profiiencies in probability and statistics, differential equations, numerical methods, and mathematical analysis. Advance knowledge in stochastic 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 BlackScholesMerton pricing model and the martingale pricing theory of financial derivatives.

Was one of the earliest introductory textbooks in mathematical finance Good reputation established by the 1st edition Includes supplementary material: sn.pub/extras

Autorentext

Yue-Kuen Kwok is Professor and Program Director of MSc in Mathematics (Financial Mathematics and Statistics) at the Department of Mathematics of Hong Kong University of Science and Technology

Klappentext

Mathematical Models of Financial Derivatives is a textbook on the theory behind modeling derivatives using the financial engineering approach, focussing on the martingale pricing principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are

analyzed, emphasizing on the aspects of pricing, hedging and their risk management. Starting from the renowned Black-Scholes-Merton formulation of option pricing model, readers are guided through the text on the new advances on the state-of-the-art derivative pricing models and interest rate models. Both analytic techniques and numerical methods for solving various types of derivative pricing models are emphasized.

The second edition presents a substantial revision of the first edition. The continuous-time martingale pricing theory is motivated through analysis of the underlying financial economics principles within a discrete-timeframework. A large collection of closed-form formulas of various forms of exotic equity and fixed income derivatives are documented. The most recent research results and methodologies are made accessible to readers through the extensive set of exercises at the end of each chapter.

Yue-Kuen Kwok is Professor of Mathematics at Hong Kong University of Science and Technology. He is the author of over 80 research papers and several books, including Applied Complex Variables. He is an associate editor of Journal of Economic Dynamics and Control and Asia-Pacific Financial Markets.

Inhalt
to Derivative Instruments.- Financial Economics and Stochastic Calculus.- Option Pricing Models: BlackScholesMerton Formulation and Martingale Pricing Theory.- Path Dependent Options.- American Options.- Numerical Schemes for Pricing Options.- Interest Rate Models and Bond Pricing.- Interest Rate Derivatives: Bond Options, LIBOR and Swap Products.