Definition of Omega


What is Omega?

Omega is a measure of the price of options, similar to the Greek option that measures various characteristics of the option itself. Omega measures the percentage change in the value of an option relative to the percentage change in the underlying price. In this way, it measures the leverage of an options position.

Key takeaways

  • The third derivative of the option price, Omega measures the effect of an option’s leverage.
  • Omega is not always referred to among option Greeks.
  • This variable is most often used by option market makers or other sophisticated, high-volume option traders.

Understanding Omega

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 higher dollar value of the underlying security. In other words, a call option trading at $ 25 per contract 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 the obligation, to buy those 100 shares at a specified price (the strike price) before a specified date.

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

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

The formula is as follows:

Ω

=

Percentage change in

V

Percentage change in

S

where:

V

=

Option price

S

=

Underlying price

begin {align} & Omega = frac { text {Percentage change in} V} { text {Percentage change in} S} \ & textbf {where:} \ & V = text {Price of option} \ & S = text {Underlying price} \ end {aligned}

Ω=Percentage change in SPercentage change in Vwhere:V=Option priceS= Underlying price

Greek options

Omega is calculated based on two of the standard Greek options, delta and gamma. This set of metrics provides insight into the risk and reward of an options contract with respect to different variables. The most common option of the Greeks are:

  • Delta (Δ): Change in the value of the option with respect to the change in the underlying price.
  • Gamma (Γ): The derivative of delta, measures the change in delta with respect to the change in the underlying price.
  • Omega (Ω): percentage change in the option price with respect to the percentage change in the underlying price.
  • Theta (Θ): Change in the value of the option with respect to the change in time to expiration.
  • Rho (ρ): Variation of the value of the option with respect to the variation of the risk-free interest rate.
  • Vega (v): Change in the value of the option with respect to the change in the underlying volatility. (Vega is not the name of a Greek letter).

Relationship with Delta

The gamma of an option is also the rate of change (ROC) in its delta and can be called the delta delta.

The omega equation can also be expressed:

Ω

=


V


S

×

S

V

Omega = frac { partial V} { partial S} times frac {S} {V}

Ω=SV×VS

Since the equation for delta is:

Δ

=


V


S

Delta = frac { partial V} { partial S}

Δ=SV

omega can be expressed in delta terms as:

Ω

=

Δ

×

S

V

Omega = Delta times frac {S} {V}

Ω=Δ×VS

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