Quantitative Finance (PDF)

A rigorous, yet accessible, introduction to essential topics in
mathematical finance

Presented as a course on the topic, Quantitative Finance traces
the evolution of financial theory and provides an overview of core
topics associated with financial investments. With its thorough
explanations and use of real-world examples, this book carefully
outlines instructions and techniques for working with essential
topics found within quantitative finance including portfolio
theory, pricing of derivatives, decision theory, and the empirical
behavior of prices.

The author begins with introductory chapters on mathematical
analysis and probability theory, which provide the needed tools for
modeling portfolio choice and pricing in discrete time. Next, a
review of the basic arithmetic of compounding as well as the
relationships that exist among bond prices and spot and forward
interest rates is presented.? Additional topics covered
include:

* Dividend discount models

* Markowitz mean-variance theory

* The Capital Asset Pricing Model

* Static?portfolio theory based on the expected-utility
paradigm

* Familiar probability models for marginal distributions of
returns and the dynamic behavior of security prices

The final chapters of the book delve into the paradigms of
pricing and present the application of martingale pricing in
advanced models of price dynamics. Also included is a step-by-step
discussion on the use of Fourier methods to solve for
arbitrage-free prices when underlying price dynamics are modeled in
realistic, but complex ways.

Throughout the book, the author presents insight on current
approaches along with comments on the unique difficulties that
exist in the study of financial markets. These reflections
illustrate the evolving nature of the financial field and help
readers develop analytical techniques and tools to apply in their
everyday work. Exercises at the end of most chapters progress in
difficulty, and selected worked-out solutions are available in the
appendix. In addition, numerous empirical projects utilize
MATLAB® and Minitab® to demonstrate the mathematical
tools of finance for modeling the behavior of prices and markets.
Data sets that accompany these projects can be found via the book's
FTP site.

Quantitative Finance is an excellent book for courses in
quantitative finance or financial engineering at the
upper-undergraduate and graduate levels. It is also a valuable
resource for practitioners in related fields including engineering,
finance, and economics.