Chapter 1
This book is written for those physicists who want to work on Wall
Street but have not bothered to read anything about Finance. This is
a crash course that the author, a physicist himself, needed when he
landed a financial data analyst job and became fascinated with the
huge data sets at his disposal. More broadly, this book addresses the
reader with some background in science or engineering (college-level
math helps) who is willing to learn the basic concepts and quantitative
methods used in modern finance.
The book loosely consists of two parts: the ‘‘applied’’ part and the
‘‘academic’’ one. Two major fields, Econometrics and Mathematical
Finance, constitute the applied part of the book. Econometrics can be
broadly defined as the methods of model-based statistical inference in
financial economics [1]. This book follows the traditional definition
of Econometrics that focuses primarily on the statistical analysis of
economic and financial time series [2]. The other field is Mathematical
Finance [3, 4]. This term implies that finance has given a rise to
several new mathematical theories. The leading directions in
Mathematical Finance include portfolio theory, option-pricing
theory, and risk measurement.
The ‘‘academic’’ part of this book demonstrates that financial data
can be an area of exciting theoretical research, which might be of
interest to physicists regardless of their career motivation. This part
includes the Econophysics topics and the agent-based modeling of
financial markets.
Physicists use the term Econophysics to emphasize
the concepts of theoretical physics (e.g., scaling, fractals, and chaos)
that are applied to the analysis of economic and financial data. This
field was formed in the early 1990s, and it has been growing rapidly
ever since. Several books on Econophysics have been published to date
[5–11] as well as numerous articles in the scientific periodical journals
such as Physica A and Quantitative Finance.
The agent-based model-
ing of financial markets was introduced by mathematically inclined
economists (see [12] for a review). Not surprisingly, physicists, being
accustomed to the modeling of ‘‘anything,’’ have contributed into this
field, too [7, 10].
Although physicists are the primary audience for this book, two
other reader groups may also benefit from it. The first group includes
computer science and mathematics majors who are willing to work (or
have recently started a career) in the finance industry. In addition, this
book may be of interest to majors in economics and finance who are
curious about Econophysics and agent-based modeling of financial
markets. This book can be used for self-education or in an elective
course on Quantitative Finance for science and engineering majors.
The book is organized as follows. Chapter 2 describes the basics of
financial markets. Its topics include market price formation, returns
and dividends, and market efficiency. The next five chapters outline
the theoretical framework of Quantitative Finance: elements of math-
ematical statistics (Chapter 3), stochastic processes (Chapter 4), time
series analysis (Chapter 5), fractals (Chapter 6), and nonlinear dy-
namical systems (Chapter 7). Although all of these subjects have been
exhaustively covered in many excellent sources, we offer this material
for self-contained presentation.
In Chapter 3, the basic notions of mathematical statistics are
introduced and several popular probability distributions are listed.
In particular, the stable distributions that are used in analysis of
financial time series are discussed.
Chapter 4 begins with an introduction to the Wiener process, which
is the basis for description of the stochastic financial processes. Three
methodological approaches are outlined: one is rooted in the generic
Markov process, the second one is based on the Langevin equation,
and the last one stems from the discrete random walk. Then the basics
of stochastic calculus are described. They include the Ito’s lemma and
2 Introduction

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