The Mathematics of Derivatives: Tools for Designing Numerical Algorithms (Wiley Finance) [Hardcover]

"The Mathematics of Derivatives provides a concise pedagogical discussion of both fundamental and very recent developments in mathematical finance, and is particularly well suited for readers with a science or engineering background. It is written from the point of view of a physicist focused on providing an understanding of the methodology and the assumptions behind derivative pricing. Navin has a unique and elegant viewpoint, and will help mathematically sophisticated readers rapidly get up to speed in the latest Wall Street financial innovations."
—David Montano, Managing Director JPMorgan Securities

A stylish and practical introduction to the key concepts in financial mathematics, this book tackles key fundamentals in the subject in an intuitive and refreshing manner whilst also providing detailed analytical and numerical schema for solving interesting derivatives pricing problems. If Richard Feynman wrote an introduction to financial mathematics, it might look similar. The problem and solution sets are first rate."
—Barry Ryan, Partner Bhramavira Capital Partners, London

"This is a great book for anyone beginning (or contemplating), a career in financial research or analytic programming. Navin dissects a huge, complex topic into a series of discrete, concise, accessible lectures that combine the required mathematical theory with relevant applications to real–world markets. I wish this book was around when I started in finance. It would have saved me a lot of time and aggravation."
—Larry Magargal

Nobody knows this better than author Robert Navin, whose detailed knowledge of derivatives has allowed him to excel over the course of his financial career—as well as help those around him quickly grasp the mathematical techniques behind the modeling of derivatives. Now, in The Mathematics of Derivatives, he shares his expertise and experience with you.

Filled with in–depth insights and practical advice, The Mathematics of Derivatives provides individuals involved in this industry—whether you′re a quant–in–training with a background in economics or a software designer creating financial programs—with the information they need to succeed.

Divided into two comprehensive parts, this well–rounded resource outlines the models—and the math—used to analyze the trading and risks of derivatives in Part One and then challenges you to master these methods through a variety of exercises in Part Two.

An array of topics are covered, including:

• The Black–Scholes formula with modifications as well as more general ideas behind the derivation of the Black–Scholes formula
• Relevant mathematical tools—from distribution and integration definitions to n–Dimensional Jacobians, Path Integrals, and the Central Limit Theorem
• Stochastic processes and their applicationsto finance
• Numerical algorithmic methods for solving parabolic partial differential equations (PDEs)
• The simple default probability approach tocredit derivatives
• The Heath–Jarrow–Morton (HJM) model, as well as some specific examples of modeling derivatives, such as convertible bonds and collateralizeddebt obligations

With the information illustrated throughout these pages, you′ll be able to implement the risk–neutral pricing paradigm correctly, design models of real–world processes using stochastic calculus, convert such models into a risk–neutral pricing equation with boundary conditions, numerically solve these equations with great accuracy, and much more.

In order to fully understand the pricing, hedging, and risk management issues associated with derivatives, you must first become familiar with the mathematical formalism that underlies them. Written in a straightforward and accessible style, The Mathematics of Derivatives provides you with a solid foundation in this field—and an opportunity to succeed in today′s turbulent markets.