# Understanding the Greeks

The Greeks represent mathematical formulas used to calculate changes in an option’s pricing. The main four discussed below account for change in the underlying stock price, rate of said change, time, and volatility.

**Delta** – The expected rate of change based on a $1 move in the underlying.

- Calls have a positive delta between 0.0 and 1.0
- Calls that are ATM will have a delta of .5 and as they transition ITM that delta will increase closer to 1.0, conversely as they transition OTM this reduces delta towards 0.0
- Puts have a negative delta between -1.0 and 0.0
- Puts that are ATM have a delta of -.5 and as they transition ITM that delta will decrease closer to -1.0, conversely as they transition OTM this increases delta towards 0.0

**Gamma** – The expected rate of change in delta based on a $1 move in the underlying.

- Gamma is always represented as a positive number.
- Gamma is highest ATM and decreases as prices extends deeper ITM or OTM.
- If a call’s Delta is currently .5 and the Gamma is .05 a $1 increase in the underlying would result in a new Delta of .55 (this means that the next $1 increase in the underlying would result in a $.55 increase in the options price).
- If a put’s Delta is currently -.5 and the Gamma is .1 a $1 decrease in the underlying would result in a new delta of -.6 (this means that the next $1 decrease in the underlying would result in a $.60 increase in the option’s price).

**Theta** – The expected decline in extrinsic value based on the passage of time.

- Theta is always represented as a negative number.
- Theta is highest ATM and decreases as prices extends deeper ITM or OTM.
- Theta decreases as DTE increases, and really begins to take effect <55 days DTE.
- Theta is the friend of the option seller and enemy of the option buyer. This is because every second that the contract is being traded the premium is being eroded away until it eventually reaches $0.00 at expiration. At expiration, the only value left in the contract’s value is the intrinsic value (amount ITM).
- If a call option has a Theta of -.50 the options price will lose -$.50 per day.
- Theta increases exponentially as a contract nears expiration. Meaning a 30 DTE contract may have a Theta of -.10 however the same strike 7 DTE may have a Theta of -.75

**Vega** – The expected rate of change based on a 1% pt. change in implied volatility.

- Vega is always represented as a positive number.
- Vega is highest ATM and decreases as prices extends deeper ITM or OTM.
- If a call or put option has a Vega of .15 and IV increases from 25% to 26% (a 1% increase) the price of both the call and put option contract will increase by +$.15
- If a call or put option has a Vega of .20 and IV decreases from 25% to 23% (a 2% decline) the price of both the call and put option contract will decrease by -$.40

Understanding the Greeks – Delta, Gamma, Theta, and Vega – is critical to successful options trading. These mathematical measures provide insights into how changes in the underlying stock price, its rate of change, time decay, and volatility can impact an option’s price. Delta and Gamma help assess the rate of change in an option’s price based on movements in the underlying asset. Theta quantifies the effect of time decay on an option’s price, serving as a constant reminder of the ticking clock in options trading. Finally, Vega offers insights into how changes in implied volatility can impact an option’s price.

By mastering the Greeks, traders can more effectively navigate the dynamic, intricate world of options trading, better predict outcomes, and, ultimately, make more informed trading decisions. As such, the Greeks are not just abstract concepts, but practical tools in the arsenal of every successful options trader.