Omega

Omega is one of the options Greeks that measure various characteristics of the option itself. Omega measures the percentage change in an option's value with respect to the percentage change in the underlying price. In this way, it measures the leverage of an options position.

The formula is as follows:

• Ω = percent change in V ÷ percent change in S

where:

• V = price of the option
• S = underlying price

Omega is the third derivative of the option price, and the derivative of gamma. It is also known as elasticity or the delta of delta.

Traders use options for many reasons, but one of the most important is leverage. A small investment in a call option, for example, allows the trader to control a larger dollar value of the underlying security. In other words, a call option trading at $25.00 per contract, or $250, could control 100 shares of a stock trading at $50 per share with a value of $5,000. The holder has the right, but not obligation, to purchase those 100 shares at a specific price (the strike price) by a certain date.

To see leverage in action, assume Ford Motor Co. shares increase 7% in a given period and a Ford call option increases 3% in that same period. The omega of the call option is 3 ÷ 7, or 0.43. This would imply that for every 1% Ford stock moves, the call option will move 0.43%.

Omega is one of the Greeks, a set of metrics that give a sense of an options contract's risk and reward with respect to different variables. While there are many Greeks, omega is one of a limited number of first-order Greeks, meaning that it relates directly to the value of an options contract, rather than to another Greek. The most common first-order Greeks are:

Delta (Δ) – change in option value with respect to change in underlying price.

Theta (Θ) – change in option value with respect to change in time to expiration.

Rho (ρ) – change in option value with respect to change in risk-free interest rate.

Omega (Ω) – percent change in option price with respect to percent change in underlying price.

Vega (v) – change in option value with respect to change in underlying volatility. (Vega is not the name of a Greek letter.)

Another common Greek is a second-order variable, gamma (Γ): the derivative of delta, it measures the change in delta with respect to the change in the underlying price. 

An option's gamma is also the rate of change in its delta and may be called the delta of the delta.

The equation for omega can also be expressed:

Given that the equation for delta is:

omega can be expressed in terms of delta as: