Options Greeks Without the Mysticism

Options have a price called the premium. That premium changes based on five inputs: the underlying stock price, time remaining, implied volatility, interest rates, and dividends. The Greeks are sensitivity measures that quantify each of those relationships. You need three of them.

Options series, part 2 of 3: Options trading → Options Greeks → VIX and volatility. If the mechanics of calls and puts are unfamiliar, read part 1 first.

Delta: How Much the Option Moves With the Stock

Delta measures how much an option's premium changes when the underlying stock moves $1. A call with a delta of 0.50 gains approximately $0.50 for every $1 the stock rises.

• Call deltas range from 0 to 1.0. At-the-money calls are roughly 0.50.
• Put deltas range from -1.0 to 0. At-the-money puts are roughly -0.50.
• Deep in-the-money options approach delta 1.0 and move nearly dollar-for-dollar with the stock.
• Deep out-of-the-money options have deltas near zero and barely react to stock movement.

Delta is also roughly the probability that an option expires in-the-money. A 0.20 delta call has approximately a 20% chance of expiring with value. This is useful for selecting strike prices based on how aggressive or conservative you want the position to be.

Theta: The Option Buyer's Enemy

Theta measures how much an option's premium decays each day from time passing alone. If an option has a theta of -0.05, it loses $0.05 per share (or $5 per contract) every day with all else equal.

Time decay is not linear: it accelerates as expiration approaches. An option loses a smaller fraction of its value when there are 60 days left than when there are 10 days left.

• Option buyers: Fight negative theta every day. You need the stock to move enough, fast enough, to overcome time decay.
• Option sellers: Collect positive theta. Time working for you is the structural edge of selling premium.

This is why experienced options traders often skew toward selling premium rather than buying it. Time always runs out. The only question is who it runs out on.

Vega: Volatility Risk

Vega measures how much an option's premium changes when implied volatility moves 1 percentage point. An option with vega of 0.10 gains $0.10 if implied volatility rises 1%.

This matters because you can correctly predict stock direction and still lose money if implied volatility drops. This happens constantly around earnings: implied volatility spikes into the announcement, then collapses after (the "IV crush"), even if the stock moves in your direction. Option buyers who aren't watching vega get caught by this regularly.

• Long options have positive vega. Rising volatility helps you.
• Short options have negative vega. Rising volatility hurts you.

Gamma: How Delta Changes

Gamma measures how much delta changes when the stock moves $1. High gamma means your exposure can shift rapidly. At-the-money options near expiration have high gamma: a small stock move can push delta from 0.40 to 0.60 almost instantly.

For option sellers, high gamma near expiration is a risk. A stock that moves hard against a short position in the final days can cause delta to spike and losses to accelerate. This is why short options positions are typically managed or closed before the last few days of expiration.

Previous and next

• Previous: Options trading: the real mechanics (part 1 of 3)
• Next: What VIX tells you (and what it doesn't) (part 3 of 3)

The Greeks don't tell you what a trade will do. They tell you how it will respond to what the market does. Know your exposures before the market moves, not after.