What Is Omega?
Let me explain Omega to you directly: it's a key measure in options pricing, much like the other option Greeks that assess different aspects of the option. Specifically, Omega tracks the percentage change in an option's value compared to the percentage change in the underlying asset's price, which essentially shows you the leverage in an options position.
Key Takeaways
As the third derivative of the option price, Omega directly measures the impact of leverage on an option. You won't always hear about Omega among the standard option Greeks, but it's a tool I see used most by option market makers or those handling high-volume, sophisticated trades.
Understanding Omega
You know traders turn to options for various reasons, but leverage stands out as crucial. Consider this: a small outlay on a call option lets you control a much larger value in the underlying security. For instance, a call option at $25 per contract might give you command over 100 shares of a stock priced at $50 each, totaling $5,000 in value. You hold the right, without obligation, to buy those shares at the strike price by a set date.
Omega, being the third derivative of the option price and the derivative of gamma, is also termed elasticity. To illustrate leverage, suppose Ford Motor Co. shares rise 7% in a period, and a Ford call option rises 3% in the same timeframe. The omega here is 3 divided by 7, or 0.43, meaning for every 1% move in Ford's stock, the call option moves 0.43%.
The formula for Omega is straightforward: it's the percent change in V (the option's price) divided by the percent change in S (the underlying price).
Options Greeks
Omega builds on two core option Greeks: delta and gamma. These metrics help you gauge the risk and reward of an options contract across various factors. Delta shows the change in option value relative to the underlying price change. Gamma, as the derivative of delta, tracks how delta shifts with underlying price movements. Omega itself measures the percent change in option price against the percent change in underlying price. Theta indicates how the option value changes with time to expiration. Rho covers changes due to the risk-free interest rate. Vega, though not a Greek letter, reflects changes from underlying volatility.
Relationship to Delta
Gamma for an option is the rate of change in its delta, essentially the delta of the delta. You can express Omega as the partial derivative of V with respect to S, multiplied by S over V. Since delta is the partial derivative of V over S, Omega simplifies to delta times S over V.
