Introduction

Financial engineers bring their knowledge base and perspectives to serve the financial industry for applications including the development of high-speed hardware and software infrastructure in order to trade securities (financial assets) within microseconds or faster, the design and implementation of high-frequency trading algorithms and systems, and advanced trading and risk management solutions for large size investment portfolios. A well-equipped financial engineer understands how the markets work, seeks to explain the behavior of the markets, develops mathematical and stochastic models for various signals related to the financial assets (such as price, return, volatility, comovement) through analyzing available financial data as well as understanding the market microstructure (studies on modeling the limit order book activity), then builds trading and risk management strategies using those models, and develops execution strategies to get in and out of investment positions in an asset. The list of typical questions financial engineers strive to answer include

• “What is the arrival rate of market orders and its variation in the limit order book of a security?”

• “How can one partition a very large order into smaller orders such that it won’t be subject to significant market impact?”

• “How does the cross correlation of two financial instruments vary in time?”

• “Do high frequency traders have positive or negative impact on the markets and why?”

• “Can Flash Crash of May 6, 2010 happen again in the future? What was the reason behind it? How can we prevent similar incidents in the future?”

and many others. We emphasize that these and similar questions and problems have been historically addressed in overlapping fields such as finance, economics, econometrics, and mathematical finance (also known as quantitative finance). They all pursue a similar path of applied study. Mostly, the theoretical frameworks and tools of applied mathematics, statistics, signal processing, computer engineering, high-performance computing, information analytics, and computer communication networks are utilized to better understand and to address such important problems that frequently arise in finance. We note that financial engineers are sometimes called “quants” (experts in mathematical finance) since they practice quantitative finance with the heavy use of the state-of-the-art computing devices and systems for high-speed data processing and intelligent decision making in real-time.

Although the domain specifics of application is unique as expected, the interest and focus of a financial engineer is indeed quite similar to what a signal processing engineer does in professional life. Regardless of the application focus, the goal is to extract meaningful information out of observed and harvested signals (functions or vectors that convey information) with built-in noise otherwise seem random, to develop stochastic models that mathematically describe those signals, to utilize those models to estimate and predict certain information to make intelligent and actionable decisions to exploit price inefficiencies in the markets. Although there has been an increasing activity in the signal processing and engineering community for finance applications over the last few years (for example, see special issues of IEEE Signal Processing Magazine [2] and IEEE Journal of Selected Topics in Signal Processing [3], IEEE ICASSP and EURASIP EUSIPCO conference special sessions and tutorials on Financial Signal Processing and Electronic Trading, and the edited book Financial Signal Processing and Machine Learning [1]), inter-disciplinary academic research activity, industry-university collaborations, and the cross-fertilization are currently at their infancy. This is a typical phase in the inter-disciplinary knowledge generation process since the disciplines of interest go through their own learning processes themselves to understand and assess the common problem area from their perspectives and propose possible improvements. For example, speech, image, video, EEG, EKG, and price of a stock are all described as signals, but the information represented and conveyed by each signal is very different than the others by its very nature. In the foreword of Andrew Pole’s book on statistical arbitrage [4], Gregory van Kipnis states “A description with any meaningful detail at all quickly points to a series of experiments from which an alert listener can try to reverse-engineer the [trading] strategy. That is why quant practitioners talk in generalities that are only understandable by the mathematically trained.” Since one of the main goals of financial engineers is to profit from their findings of market inefficiencies complemented with expertise in trading, “talking in generalities” is understandable. However, we believe, as it is the case for every discipline, financial engineering has its own “dictionary” of terms coupled with a crowded toolbox, and anyone well equipped with necessary analytical and computational skill set can learn and practice them. We concur that a solid mathematical training and knowledge base is a must requirement to pursue financial engineering in the professional level. However, once a competent signal processing engineer armed with the theory of signals and transforms and computational skill set understands the terminology and the finance problems of interest, it then becomes quite natural to contribute to the field as expected. The main challenge has been to understand, translate, and describe finance problems from an engineering perspective. The book mainly attempts to fill that void by presenting, explaining, and discussing the fundamentals, the concepts and terms, and the problems of high interest in financial engineering rather than their mathematical treatment in detail. It should be considered as an entry point and guide, written by engineers, for engineers to explore and possibly move to the financial sector as the specialty area. The book provides mathematical principles with cited references and avoids rigor for the purpose. We provide simple examples and their MATLAB codes to fix the ideas for elaboration and further studies. We assume that the reader does not have any finance background and is familiar with signals and transforms, linear algebra, probability theory, and stochastic processes.

We start with a discussion on market structures in Chapter 2. We highlight the entities of the financial markets including exchanges, electronic communication networks (ECNs), brokers, traders, government agencies, and many others. We further elaborate their roles and interactions in the global financial ecosystem. Then, we delve into six most commonly traded financial instruments. Namely, they are stocks, options, futures contracts, exchange traded funds (ETFs), currency pairs (FX), and fixed income securities. Each one of these instruments has its unique financial structure and properties, and serves a different purpose. One needs to understand the purpose, financial structure, and properties of such a financial instrument in order to study and model its behavior in time, intelligently price it, and develop trading and risk management strategies to profit from its usually short lived inefficiencies in the market. In Chapter 2, we also provide the definitions of a wide range of financial terms including buy-side and sell-side firms, fundamental, technical, and quantitative finance and trading, traders, investors, and brokers, European and American options, initial public offering (IPO), and others.

We cover the fundamentals of quantitative finance in Chapter 3. Each topic discussed in this chapter could easily be extended in an entire chapter of its own. However, our goal in Chapter 3 is to introduce the very basic concepts and structures as well as to lay the framework for the following chapters. We start with the price models and present continuous- and...