Learn the Lingo (Optionality and Greeks)

Derivatives are a booming business these days, and I figured I've yet to talk about options and the ways we describe them. It's been a while since I've done a real "learn the lingo" post.

People talk about the greeks all the time (not referring to their frat/sorority buddies), but it seems precious few outside the derivatives world understand what they're talking about. Actually, precious few IN the derivatives world understand what they're talking about. Try to avoid being one of those people. Do note that I use the term "derivative" both in referring to derivative contracts and in referring to the mathematical derivative. I'm sure you'll figure out when I'm using it in each way, but do ask if my writing is confusing.

Call Option - a contract to enter into the right to buy something at a set price.

Put Option - a contract to enter into the right to sell something at a set price.

Future - a contract, usually on an exchange, allowing one to buy X units of something at the price the contract was transacted.

OTC - Over-the-Counter, refering to transactions done as deals between entities as opposed to exchange traded, thus making the market for such transactions more opaque.

Forward - a contract, usually OTC, to buy X units of something at a set price.

Delta - the sensitivity of a derivative to a small move in the underlying reference material. Sometimes delta is used to refer to the trading of the reference material itself. The reference material can be an underlying security, a commodity, a rate, even some economic variable. Delta is also the first derivative of the price of a contract with respect to the underlying reference material (remember from Calculus that the first derivative is the slope of a curve? Notice how a the slope approximates a small move in the y coordinate due to a small move in the x coordinate?).

Gamma - the second derivative of a contract with respect to the underlying reference. This shows the sensitivity of the price of a contract to large moves in the underlying. It is the curvature of the price sensitivity graph. Do you remember doing Taylor approximations in Calculus? Delta and gamma (the first and second derivative of the price of a contract with respect to it's underlying) are often used to find the price of a contract after a move in the underlying via Taylor approximation. The important concept, however, is that gamma refers to the sensitivity of a contract to large moves in the underlying.

Theta - option decay. Options are worth more when there is a lot of time before they expire. It shouldn't be surprising that the longer you have the option, the more it's worth.

Vega - the sensitivity of a contract to the volatility of the underlying reference. This is often a parameter in pricing models, but conceptually it refers to how much more a contract is worth when the underlying reference material becomes more volatile. Most options are worth more with volatility. In fact, option traders are often referred to as vega or vol traders.

Rho - the sensitivity of a contract to the underlying interest rate assumption. This is important because the interest rate changes the discount factor of value over time.

Black-Scholes - The Black-Scholes model has been the benchmark option pricing model since it's inception. It incorporates all the greeks above. In fact, it pretty much gave birth to the greeks.