Greeks

Options are dynamic financial instruments whose values are influenced by a variety of factors that fluctuate throughout the trading day. The Greeks are a set of metrics that quantify how sensitive an option’s price is to changes in these factors—such as the price of the underlying asset, time until expiration, and implied volatility. By understanding how each Greek responds to market movements, traders can better assess risk and manage their positions effectively.

Among the Greeks, the first-order measures—Delta, Theta, and Vega—play a fundamental role. They capture how an option’s price is influenced by key variables:

• Delta – Sensitivity to changes in the underlying asset’s price.
• Theta – Sensitivity to the passage of time (time decay).
• Vega – Sensitivity to changes in implied volatility.
• Rho, which measures sensitivity to interest rate changes, falls outside the scope of this course.

The following sections explore Delta, Theta, and Vega in greater detail.

1. Delta

Delta is a measure of how much an option’s price changes in response to a $1 change in the underlying asset’s price. It represents the first derivative of the option price with respect to the underlying.
For example, a call option with a Delta of 0.60 would increase in value by approximately $0.60 for every $1 increase in the underlying price. Put options have negative Delta values, ranging from -1 to 0, indicating that they gain value as the underlying price falls.

The relationship between Delta and the underlying asset's price is nonlinear:

• Call options: Delta increases gradually when out-of-the-money (OTM), accelerates near at-the-money (ATM), and stabilizes near 1 when deep in-the-money (ITM).
• Put options: The pattern is reversed—Delta starts near -1 when deep ITM, moves toward -0.5 near ATM, and approaches 0 when far OTM.

This behavior reflects the probability that the option will expire in the money. ATM options tend to have a Delta close to 0.5, suggesting an equal chance of finishing ITM or OTM at expiration.

Understanding Delta is essential for managing directional exposure. It helps traders gauge how their positions will respond to changes in the underlying asset and serves as a foundation for more complex hedging strategies.

2. Theta

Options lose value as time passes, even if the underlying asset remains unchanged. This erosion in value is captured by Theta, which measures the rate of time decay.
Theta is usually negative, signifying that the option’s extrinsic value diminishes with each passing day.

For instance, a Theta of -0.05 implies the option would lose about $0.05 in value daily, assuming all other variables remain constant. This time decay accelerates as expiration nears, especially for ATM options.

The rate of decay depends on the option’s moneyness:

• Deep ITM options: Decay more slowly, as most of their value comes from intrinsic value.
• ATM options: Experience the fastest decay due to maximum uncertainty and highest extrinsic value.
• OTM options: Decay gradually until expiration nears, at which point they may rapidly lose all remaining value.

Theta is particularly important for strategies involving the sale of options, where time decay can be harvested as profit. Conversely, buyers of options must be aware of the erosive effect of time, especially when holding positions near expiration.

3. Vega

Vega measures how sensitive an option’s price is to changes in implied volatility (IV). It indicates the expected change in the option’s value for a 1% change in IV.
For example, a Vega of 0.10 suggests the option’s price will increase by $0.10 if implied volatility rises by 1%.

Unlike Delta and Theta, Vega is always positive for both calls and puts. When volatility increases, options become more valuable because there is a greater chance that the underlying price will move favorably before expiration.

Vega is most impactful for ATM options. These options have the highest extrinsic value and are the most responsive to changes in volatility. As the strike moves further ITM or OTM, Vega declines, since the outcome of the option becomes more certain and less influenced by volatility.

This distribution of Vega means that:

• Traders anticipating volatility spikes often target ATM options to maximize exposure.
• A decline in volatility disproportionately affects high-Vega options, reducing their value more sharply.

Conclusion

Mastering the first-order Greeks—Delta, Theta, and Vega—is essential for anyone navigating the options market. Each captures a different dimension of risk and provides insight into how an option’s price will behave under changing conditions:

• Delta helps evaluate directional exposure to the underlying.
• Theta reflects the cost of time decay.
• Vega highlights the sensitivity to market uncertainty through implied volatility.

By understanding how these Greeks interact and affect option pricing, traders can craft more effective strategies and manage risk with greater confidence.

‍