Rocket Science and Business

A few months ago, I had just finished a lecture on Optimal Control and Investment when a student from the class caught up with me in the corridor and said, "I never thought one could price a firm by solving a differential equation!" I was about to ask him if he could think of some other way to price an enterprise, but I smiled tactfully instead. His question made me think – and then realize – that, even when stories about "rocket scientists" getting jobs on Wall Street are no longer news items, the use of high-end mathematics in everyday financial practice is seen as a fad by many who could actually benefit from such technology. That the realm of stock-options is the least important use of mathematical finance has yet to become public knowledge. Yes, the mathematics of Black-Scholes' equation was first engineered to explain the mechanics of trades on the Chicago Board of Options Exchange and was of little concern to the rest of the crowd. In the last decade, however – as if all that happened during the century was not enough – the world of business switched gears. It went global in a way that was unimaginable at the time when Fisher Black, Myron Scholes and Robert Merton established the principals for pricing options and corporate liabilities. The globalization phenomenon produced an avalanche of new financial instruments whose level of complexity required a radical new technology. Fortunately, the new technology was already at hand, fast computers became affordable, and the internet made instantaneous communication and access to information possible. After all, the mathematics of placing an order for an airplane is no different from that of placing an order on CBOE. In both cases, someone makes an investment, with some degree of risk involved, in exchange for rewards in the future. Yet the price quotes for airplane orders are not published daily in WSJ, and in most cases come as a result of lengthy negotiations and – yes – calculations. In this respect, investing in research for a new product, or signing an insurance policy is no different. Mathematical Finance, sometimes called Financial Engineering or Computational Finance, allows one to assess and hedge the risk involved in such contracts (the so-called "real options") and consequently to determine their value. It turns into concrete numbers vague concepts like "the price of risk" and "the value of waiting" – something which was never possible under the good old rule, "Invest as soon as the present value exceeds the market value." Also, it provides a rigorous quantitative approach to the control over production levels and timing, or a way for policy makers to determine whether intervention in a particular industry is needed. A point can be made that the current unprecedented period of economic growth and relatively stable markets is partly due to the multitude of financial instruments and the use of quantitative methods in investing – market's version of "the law of large numbers," perhaps.

       Helpful as it certainly is, mathematical finance is not easy to grasp. It goes well beyond the basic algebra and calculus one usually learns in college and requires solid knowledge of at least one computer programming language, in addition to the ability to simulate and analyze enormous amounts of financial data. This explains why mathematicians, physicists and computer scientists are welcomed on Wall Street. In its Investment Banking section, the web-site careers-in-finance.com recommends: "Some jobs in investment banking call for very strong ma­the­matical ability. If you are good at math think about getting an advanced degree in a technical field (studying areas such as stochastic calculus and differential equations), then take some advanced finance courses in options pricing or bond valuation and apply to a research department on Wall Street."  Goldman Sachs, Citibank, Merrill Lynch, J. P. Morgan, State Street and John Hancock are all known to have people with such skills on their research teams and a number of universities are already offering graduate programs dedicated exclusively to this type of training and leading to a degree in mathematical finance. Microsoft, American Electric Power, Columbia Energy Group, Louisville Gas & Electric Power Marketing also are known to have hired graduates from such programs. Many firms – Daniel H. Wagner Associates is a good example – offer consulting services in all areas of mathematical finance.

       In spite of these developments, a large number of investment specialists and policy makers remain unaware of existing advanced computational tools in finance and prefer to rely on their "gut feelings." If Wall Street and its neighborhood is any gauge for what comes next in the world of finance, this might be set to change. Insight and intuition are, of course, indispensable in the world of business and investing and will always be, but there is a limit to how large an aircraft one can fly without instruments. Investment and academic institutions concentrated in New York City seem to be attending to mathematical finance more than those in other financial centers. In addition to a formidable amount of joint research, lectures and other events, fellows from Goldman, Sachs, J. P. Morgan and Merrill Lynch are actively involved in graduate-level mathematical finance programs offered by Columbia and NYU. Carnegie Mellon's program in computational finance has even extended one of its classrooms by way of web-casting to a convenient location in Manhattan.