Calculate Delta, Gamma, Theta, Vega, and Rho using the Black-Scholes model.
Delta measures how much an option's price changes for every $1 move in the underlying stock. A call with Delta 0.50 gains about $0.50 if the stock rises $1. Delta also approximates the probability that the option expires in-the-money — a Delta-50 option has roughly a 50% chance of expiring ITM.
Theta is the daily time decay of an option — the amount of value lost each day purely from the passage of time, all else equal. Theta accelerates as expiration approaches, especially in the final 30 days. Options buyers lose value from Theta daily; options sellers collect it. A Theta of -0.05 means the option loses about $5 per day per contract.
A high Vega means the option's price is very sensitive to changes in implied volatility. High-Vega options (typically longer-dated or near-the-money) gain value when IV rises and lose value when IV falls. Buying high-Vega options ahead of earnings can be profitable if the resulting IV crush doesn't overwhelm the move.
Options sellers primarily care about Theta (time decay working in their favor), Delta (directional risk), and Vega (volatility risk). Selling options with high Theta and low Vega is generally preferable — you collect time value quickly without excessive exposure to IV spikes. Gamma risk becomes critical near expiration.
Delta is a snapshot of how much the option moves with the stock right now. Gamma measures how fast Delta itself changes. A high-Gamma option has a Delta that shifts rapidly with every $1 move in the stock, making it harder to hedge and more sensitive to price swings — particularly dangerous for short options near expiration.