7. Option Greeks

Option Greeks are financial measures of the sensitivity of an option’s price to its underlying determining parameters, such as volatility or the price of the underlying asset
Delta, Gamma, Vega, Theta, and Rho are the key option Greeks. However, there are many other option Greeks that can be derived from those mentioned above.
| Name | Dependent Variable | Independent Variable |
| ----- | ------------------ | ------------------------- |
| Delta | Option price | Value of underlying asset |
| Gamma | Delta | Value of underlying asset |
| Vega | Option price | Volatility |
| Theta | Option price | Time to maturity |
| Rho | Option price | Interest rate |

Change in option price with respect worth change in the underlying price
Change on option price for every $1 change in the underlying
For example if a call's delta is .8, the underlying going higher by $2.00 represents an increase in its call price of $1.60
It is also an approximation of the probability of expiring ITM, using the absolute value of delta
Since option contracts cover 100 shares/units, the delta is often expressed without the decimal point. The .30 delta strike can be referred as the 30 delta strike
Delta is not static, it also changes as the underlying moves, these changes are quantified by another Greek: gamma
The total exposure for a multilegged position can be calculated by adding up the deltas for every individual leg of some underlying, long stock would contribute to 100 deltas and short stock -100 deltas

Theta is a measure of time decay in dollars per day
For example, if the value of an option is 7.50 and the option has a theta of .02. After one day, the option’s value will be 7.48, 2 days 7.46. etc.
Tends to be grater at ATM options
Inversely proportional to time
Tends to be positive for traders that sell options and negative for traders that sell options

Gamma is how much delta changes as the underlying price changes
It is a measure of acceleration of profit
Gamma is positive for long options and negative for short options
| Gamma | Calls | Puts |
| ----- | ----- | ---- |
| Long | + | + |
| Short | - | - |
The second most important factor that influences an option’s gamma is the amount of time left until the option expires, As illustrated here, at-the-money options with little time until expiration have the most gamma exposure. Conversely, in-the-money and out-of-the-money options with fewer days until expiration have less gamma exposure
Why is this? When the stock price moves up or down by $1, at-the-money options with little time until expiration will experience the greatest change in the probability of expiring in-the-money (delta)