The Mathematics of Derivatives : Tools for Designing Numerical Algorithms

In the dynamic field of finance, where mathematics is playing an ever greater role in decision making, understanding the mathematical underpinnings and implications of derivatives is an important endeavor. 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.