From the June 01, 2012 issue of Futures Magazine • Subscribe!

Greeks: The what, why and how of options pricing

Γ (Gamma)

At its simplest, gamma measures the change in delta. While delta tells how much an option’s value will change based on any move in the underlying asset, gamma measures the rate of that change. If a stock goes from $100 to $101, the delta may go from 50 to 56. Then as the stock goes from $101 to $102, delta may rise from 56 to 61. Gamma measures that change.

This often is referred to as the curvature of an option. “[Gamma is] the number of deltas that are gained or lost per a one-point move in the underlying security. It’s basically how long I am getting or how short I am getting for every one-point move in that underlying,” Grigoletto says.

Bittman advises that gamma tends to be more important to professional traders managing a portfolio of deltas. “Retail traders should be most concerned with delta and second with theta,” he says. “All the mathematical relationships hold and apply whether you are large or small, but typically the small guy is worried about making money and not about how fast his gamma is changing.” 


Vega, or kappa because vega is not really a Greek symbol, is used in options pricing models to measure the rate of change relative to a change in volatility. There are two types of volatility: Historical and implied. Historical volatility is a mathematical measurement of price movements through time and basically is a standard deviation. Implied volatility, the one used in the options pricing model, essentially is the measure of supply and demand for the options.

For most retail traders, vega is not a big factor except around times of increased volatility. “Volatility will change around earnings announcements if there is an unexpected announcement from the Federal Reserve, or an unanticipated economic report,” Bittman says. “For the typical retail trader, other than earnings periods, volatility of stocks tends not to change so dramatically that a 10- or 20-contract position will be impacted severely.”

Vega typically becomes more negligible the closer the option moves to expiration; longer-dated options feel a greater effect than shorter-dated ones. Grigoletto explains that this is because more volatility further out from expiration equals more possibilities before expiration.

Ρ (Rho)

In the current market environment, rho is not nearly as important as it has been in the past. Rho is the rate the model predicts an option price will change when the expected risk-free interest rate changes. 

With the Federal Reserve’s intention transmitted to keep interest rates low until late 2014, Grigoletto says rho is the least important of the five values at the moment. “You can look back to the 1980s where rho was very important because interest rates were hovering around 16%-17% and that affected the cost of carry. But that’s not the case today, so we’ll put that on the bottom of the most important for the current market environment.”

Ω (Omega)

Options are an investment tool that allows you to hedge your exposure, exploit changes in volatility and price, take advantage of where a market is not going as well as where it may go and, most importantly, allows you to define your risk clearly. Every trade is a balance of risk and reward, and options allow you to calibrate that risk/reward to your own specifications. Although option pricing can seem chaotic to the uninitiated, an understanding of the Greeks can bring order. “It’s not theoretical,” Bittman says. “It’s a mathematical relationship and this the way the option market works 95%-99% of the time.”

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