General Background for Financial Engineering

Some theories, originated from a very technical area, because of their deep insight and analytical power, become the foundation of much broader fields. Modern astronomy, founded by Copernicus, Kepler, Newton and others, was originally developed to understand the movements of several planets. Rational mechanics, the physical foundation of modern astronomy, later became the foundation of all modern science. Starting from 1870, Jevons, Walras and others applied the principle of rational mechanics to establish neoclassical economic theory. Today the philosophy and techniques originated from modern astronomy become the foundation of both natural science and social science.

In this notes, we will examine the parallels between finance and astronomy to understand why the progress in financial research will revolutionize the whole foundation of social science.

We will discuss several common properties of finance and astronomy that make them the pioneer subjects that trigger much deeper changes in the foundation of sciences.

First, both the study of astronomy and finance are heavily data driven. Astronomy is the oldest precise science. Data of celestial observation have been accumulated over thousand of years. As observation became more accurate over time, it became easier to test alternative theories. Financial data are the most frequently and abundantly recorded data set. For each stock, each transaction price, bid-ask price, the size of the trade, and many other information are recorded on computerized systems. The abundance of real time financial data makes financial theories much easier to test than economic theories, since economic data are less frequent, less reliable and often subject to different interpretation.

The second is the simplicity of astronomy and finance. Astronomy, which Wiener termed as “an ideally simple science”, studied the orbits of isolated planets with little disturbance from other sources. Finance studies cash flows under uncertainty or price innovation of market securities, abstracted from all the intrigues of social and organizational complexities. Although many complicated forces are at work in the financial market, the low transaction costs determines that prices alone already reflect most of the interaction of these forces.

The simplicity of astronomy and finance makes the alternative theories easy to test. In astronomy, two alternative theories at the time were the earth centered universe and the sun centered universe. As the data became very accurate and sophisticated mathematical tools were developed, the alternative theories became easy to test. In finance, the default theories are the irrelevance of financial structure in corporate finance and efficient market theory in investment. Both theories are empirically testable. This is in sharp contrast to the general economic theory, where utility function can be defined in many different ways. It is difficult to test whether economic agents maximize “utility” because it cannot be precisely defined.

Third, it is usually in simple subjects where sophisticated mathematical theories are developed and applied with great effectiveness. Calculus was invented by Newton to calculate the planet orbits. Before the invention of calculus, the calculation of nonlinear curves was almost impossible. After calculus was invented, the same calculation can be performed by any competent person with proper training. In social sciences, the complex relationship often prevents the development of sophisticated mathematical tools that are relevant and effective. In finance, however, the simplicity of research subjects enables people to develop mathematical models with deep analytical power and far reaching consequences. While calculus was first invented to calculate nonlinear planet orbits, stochastic calculus was successfully applied to solve the nonlinear payoff problems in options by Black and Scholes.

Fourth, both astronomy and finance are of immense practical value. A new theory doesn’t grow from vacuum. Before a new theory germinates, there always exists an established paradigm in any area of research. Before Copernican theory, theology was the foundation of the cosmology. Currently, general equilibrium theory is the foundation of economics and finance. Given the dominant status of theology then and the neoclassical economics today, why Copernican theory in astronomy and new theories in finance, such as behavioral finance, got established. This is because both astronomy in Copernicus’ day and finance today have tremendous practical values. People tend to neglect the ideological differences on issues of practical values. For example, in general economic theory, dissident opinions rarely surface in major economic journals, although the problems of neoclassical economics are apparent to many people. In finance, however, papers on alternative theories, such as behavioral finance, have already occupied top tier finance journals for a long time.

Fifth, both astronomy and finance were pure mathematical theories initially but gradually turned to physics. Astronomy was a part of mathematical science in the ancient time. But starting from Kepler, people looked for physical causes to offer a unified understanding of celestial movements. Eventually, Newton established the universal gravitational laws to unify the understanding of not only celestial bodies but also objects on earth. Financial theories are predominantly mathematical today. However it has been shown recently that the analytical thermodynamic theory of social sciences can be developed based on the techniques similar to those of Black-Scholes option pricing theory.

The simplicity of research subjects, the objectivity of research methodologies and powerful mathematics enabled the researchers in astronomy to break into the dominant paradigms of the time: the earth centered universe. In the process, a physical theory, rational mechanics, was developed to understand much broader phenomena. Since then, rational mechanics has become the dominant paradigm in natural science and social science. These same qualities in financial research help us establish a new paradigm: the analytical thermodynamic theory in social science and life science.