Few specialties within the financial world are as technical and highly developed as mathematical finance. As old as finance itself, the mathematical side of the profession has long tried to turn financial risk and decision-making into a practice that is driven by theorems, probabilities, and practical numerical output that makes sense of what can appear to outsiders to be a relatively “random” practice. Financial professionals who are interested in the mathematical aspects of the profession often pursue multiple advanced degrees in this academic area, helping them to fully understand each theorem and its applications. While related to computational finance, it’s important to understand that the mathematic approach does not center on algorithms and algorithmic decision-making. Instead, its goal is to account for the probability of various financial outcomes using established formulas.
Derivatives: Not Just a Concept in Calculus
Most people outside of the financial industry probably view derivatives as something that they learned about in a basic calculus class. After that class ended, they likely forgot almost everything they learned about derivatives unless it was professionally required of them. In finance, derivatives are central to modern trading. In fact, derivatives themselves are financial mechanisms that can be used to greatly enhance the value of a portfolio or of a company’s stock.
Their name isn’t an accident: The structure of financial derivatives ties directly into calculus, and mathematical professionals within the financial world use stochastic calculus to compute the expected value of such derivatives on a routine basis. In this way, professionals in this field are actually helping large financial corporations determine the risks, benefits, and necessity of trading such derivatives on a routine basis. Their mathematical analysis can make or break certain trades or financial behaviors as well.
P vs. Q: Two Different Sides of Finance
Mathematically, financial professionals have split themselves into two distinct groups, sometimes called “schools.” The first of these is the Q school, which is primarily focused on derivatives pricing, expected value, modeling, and trading. The “Q School” of practice is used to determine the fair price of a derivatives-based security and then to make a market on that security. The goal of this sell-side practice is said to be to “extrapolate the present.” Essentially, the goal of the “Q School” principles is to use present data to determine expected value. Inherently, this practice is aimed at judging the risk or benefit of trading various derivative options.
The “P School” of practice is quite different. Professionals who work in this capacity are focused on a broad portfolio of financial tools and options, with the typical goal being to maximize the value and profit of that portfolio over both the long-term and short-term. This means that “P” finance is buy-side, assessing the risk and return for an entire portfolio of bonds, stocks, and other investment choices. Typically, this type of numerical finance is applied to massive investment mechanisms like 401(k) investment portfolios, invested pension funds, mutual funds, and similar tools.
A Major Area of Study and Practice Within Finance
Finance is a highly technical profession that relies much more on math and modeling than most people realize. Professional traders and financial analysts who work within mathematical finance spend a great deal of time quantifying financial decisions based on several major theorems and schools of thought, ultimately in an effort to maximize future value while minimizing both the present and future risk of each financial decision.
