CHAPTER 1
Introduction and Overview

Finance is the study of money, something commonly used as a medium of exchange. It involves the measurement and management of money: how much we had, how much we have, and how much we expect to have in the future. Much of what we study and do in finance, however, is about making money, so its focus tends to be on the future. Yet, the future is unknown, and the unknown is about risk. People take risks in order to earn money. Finance is essentially the study of the risk and return of money.

In order to do what we do in finance, we must measure money. In fact, measurement in terms of monetary units, such as US dollars, is a core activity of finance, and there is considerably more to measuring money than just counting it. The challenge in finance is in measuring the value of assets that are not cash but can be expressed in terms of cash. An instrument is a generic term that refers to a tool that measures something. A financial instrument is a type of instrument defined as a tool that measures something in dollars or other currency units. In our context, positive-valued financial instruments are called assets and negative-valued financial instruments are called liabilities. In general, assets and liabilities are both categorized as instruments or financial instruments because our focus is on finance. Thus, an instrument can reference either assets or liabilities.

Some instruments trade in a market where we can observe their prices, but does that mean that we do not question whether these prices are good prices, in the sense of fairly and accurately reflecting what something should be worth? If you need to buy a used car and you find a 10-year-old car with 150,000 miles on it selling for $50,000, does that mean you would pay that price? No, it is likely you would believe that price to be too high. Perhaps $5,000 is a better price. What we have just done is a valuation of the car. We may have gotten it from some service, observed the prices of similar cars, or simply said that $5,000 is the amount we would pay, meaning that we would willingly part with the consumption of $5,000 of other goods and services to obtain the car.

Likewise, securities that trade in markets have prices that are observable, but that does not mean that we accept those prices as fair. These securities need to be valued, meaning to assign a number to them that represents what one thinks is a fair price. If the value assigned by the investor exceeds the price at which the security is trading in the market, the security is attractively priced and would suggest that the investor should buy the security. If the value assigned by the investor is below the price at which the security is trading in the market, the security is unattractively priced and would suggest that the investor should sell the security if they own it, short sell it if they do not own it, or simply not trade it at all.

We now explain our motivation for writing Foundations of the Pricing of Financial Derivatives.

1.1 MOTIVATION FOR THIS BOOK

Many finance courses focus on valuing stocks and bonds. Yet, there is also another family of financial instruments known as derivatives, and valuing derivatives is one of the most technical subjects in finance. It requires not only setting up a model of the prices of assets that trade in the market but also establishing a means by which one can connect the derivative to the asset on which the derivative is based. There is a great deal of technical knowledge that must transfer from instructor to student. Much of that knowledge can seem cryptic and inaccessible, though that could be a bit of an overreaction from the fear of learning something new. However, those who know this subject reasonably well can easily fall into the trap of assuming that those who do not know this subject well should find the subject easy. That is the pitfall of being a scholar. A scholar thinks that material in which they have expertise in is not that difficult, when in fact, it really is quite challenging. What a scholar should do in conveying knowledge, however, is to recall how it was when they were learning it. In other words, putting oneself in the student's shoes and empathizing with the student will result in the most successful learning environment. That is indeed one of the overriding objectives of this book: to teach some seemingly complex material in a very user-friendly way.

For without a doubt, teaching and learning advanced material in finance is challenging to the instructor and to the student. Indeed, one of the greatest challenges for instructors in advanced graduate courses in finance is to cover a large body of highly technical information in a relatively short course of study. Well-prepared students make it a lot easier, but student preparation is often not at the desired level, and classes are frequently filled with students with varying degrees of preparation. In an ideal world, such students would have previously had courses in probability, calculus, linear algebra, coding, stochastic processes, econometrics, numerical analysis, non-parametric statistics, differential equations, microeconomics and macroeconomics, and last but certainly not least, finance. It is common for faculty members and students alike to complain that students are inadequately prepared for the technical rigors of advanced graduate study in finance. This book is an effort to address this problem by leveling the base of preparation.

The degree of preparation of finance students is typically a function of the program in which the student is enrolled. Graduate study in finance can generally be done in one of three types of programs. One is an MBA, which usually comprises two years of study, the first consisting of a core set of business courses, of which a broad survey of finance is typically one component. The second year of an MBA is composed of a few required courses in general business but largely permits students to tailor their programs toward their specialized interests. Many students choose to take second-year courses in finance. The MBA is usually the marquee program at top-tier universities, a large money-maker, and is designed to draw students with degrees from all undergraduate disciplines. Hence, the first-year finance course starts at the very foundations of the subject with such topics as time value of money and discounted cash flow valuation, ultimately moving on to understanding financial markets, the relationship between risk and return, market efficiency, and corporate capital structure and dividend policy. Though some MBA students have technical backgrounds, most do not. Hence, MBA students will often struggle with advanced finance courses that are particularly quantitative.

A second form of masters' level study in finance is the specialized master's degree in finance, often called an MS or master of science, and sometimes MSF for master of science in finance. Such a program provides concentrated graduate study in finance, typically over a period of one to two academic years. There may be certain core or required courses, and students are usually allowed to take electives in their preferred areas of finance. Students in this type of program will almost always have previously studied finance and will tend to have more technical backgrounds than the average MBA student.

The third type of program in finance is the doctor of philosophy or PhD. This degree, requiring a minimum of four years, is an intensive research-oriented program that requires all students to achieve a high level of understanding of theoretical models and empirical research methods.1 It is here that the greatest problem lies in giving students a sufficient level of technical knowledge without sacrificing the time they need to devote to seminars in the various areas of finance. When students are accepted into PhD programs in finance, they are typically required to have a solid foundation in math. But, the definition of a "solid foundation in math" can vary, and merely taking some math courses and making good grades is not necessarily enough. Most finance PhD students, even those with strong math backgrounds, learn something new about math while in their PhD programs. Students who have been accepted into PhD programs are often advised to take more math courses before starting the program. They usually do, but it does not often help nearly as much as one might think.

Let us be clear. Finance is not mathematics. Mathematics is a set of tools used in finance. But just as one cannot build furniture efficiently without knowledge of how to use tools, one cannot understand finance without having the necessary tools of mathematics.

And, as noted, one of the most technical subjects in finance is derivative pricing theory. Sometimes it can be even difficult to keep terms straight because terms can mean different things in different settings. Throughout this book, we will use price and value interchangeably as is financial industry custom. Technically, the concept of price refers to the monetary amount that is exchanged when something is traded, irrespective of what one thinks the item is worth. Value refers to an instrument's non-observed monetary amount as assigned by a market participant. The individual may or may not be using a formal mathematical model. Thus, technically, formal models in finance, such as the capital asset pricing model (CAPM) and the Black-Scholes-Merton option pricing model (BSMOPM), should have been termed the capital asset valuation model...