The terminology of mathematical finance is in fact quite a hodgepodge, being derived from several different sources. Partly it originates from the somewhat elevated parlance of mathematical economics, where people like to speak for instance of the elasticity of intertemporal substitution, sometimes abbreviated EIS to make it more snappy. Another part comes from the juicy lingo of the trading floor; would you like a plain vanilla option, or would you prefer a rainbow lookback? With little respect for mathematical tradition, the term “derivative” is used in finance for a contract that is derived from an underlying quantity, such as a stock price or an exchange rate. However, derivatives in the mathematical sense are used as well, including partial derivatives of option prices with respect to various parameters. These partial derivatives are referred to in the field as “Greeks”, because the most important among them are denoted by Greek letters. For instance, “delta” is the name that is used for the sensitivity of the option value with respect to the present level of the underlying.
Delta is a bona fide member of the Greek alphabet, and so are gamma (used for the second derivative of the option price with respect to the current level of the underlying) and theta (the partial derivative with respect to the time parameter). Vega is not a Greek letter, however. The story about its origin that I find most believable is the following. Soon after the publication of the Black-Scholes formula, smart entrepreneurs grabbed the opportunity to produce and sell computational software, first for the function value produced by the formula itself, but soon also for its derivatives. One of the basic lessons of marketing is that when you want to sell something, you have to give it an attractive name. Therefore, it may have been a marketeer for a software vendor who invented the term “vega”, for use in sales talk: “Is your current software capable of computing vega, Sir? Our product can do it.” It would take a rather self-assured manager to admit that he does not even know what vega is.
If the story is true, it constitutes an example of a piece of marketing savvy that has become entrenched in scientific terminology. This is not commercial use of science; it is scientific use of commerce.
Text by: Hans Schumacher