The Option Greeks – Delta Gamma Theta Vega

The option greeks, along with theoretical value and implied volatility, are the output that comes from the options pricing formula.  These are important to understand, because they give important information for option trade selection and price movement

In this video, we will go into more depth about the option ‘greeks’, and their effect on our trading strategies, specifically:

  • Delta
  • Gamma
  • Theta
  • Vega



Delta Chart Delta is the sensitivity between the option price and the underlying price, specifically the expected price change of the option, with a $1 change in the underlying price.  Delta is also the probability that an option will expire in the money.

FB 52.15 – 52 call .75

The 52 call has a delta of .55.  If the FB stock price goes up 1.00, then the call will go up to around 1.30, or the current price + delta = .75 + .55.

NOTE:  The actual price should go up more than this, if this is a 1 day move and there is no change in volatility – because delta will also be increasing as the underlying price increases.

Being able to project the option price as the underlying changes is very useful for trade selection.  For instance, what if you have a trade setup – but it is a counter trade and there is strong resistance .85 from your entry – do you have enough room for a profit if you buy a call?

There is a 55% probability that the call will expire in the money, or above 52.00.  This is not the probability that the stock will remain above 52.00 until expiration.

Delta decreases as expiration approaches, especially for OTM options.  This makes sense, since the OTM option has a lower probability of expiring ITM.

These charts show you the delta for the ATM call and OTM call, as you approach expiration and the underlying remains flat.  You can see how steep the decrease in delta is into expiration, for the OTM call.


Gamma ChartAlthough we don’t talk about gamma much in our trading strategies, it is important to recognize its impact on short option selling – especially as expiration is approached.

As gamma is the change in delta for each $1 change in the underlying, it’s an indication of the acceleration of the option price change and potential risk as an OTM option approaches its strike price.

Gamma also accelerates as expiration is approached.  This is why I wouldn’t sell cheap OTM options into expiration, thinking it’s some ‘free’ money.  And it’s also the reason to close your short OTM options that are only .05-.10 and not worry about the extra money.

You have also heard me talk about doing option expiration flyers or buying cheap OTM options – this too is the potential that increasing gamma has on the option price.

Although gamma goes up into expiration when the underlying is flat, gamma actually goes down as the underlying goes up or down.  This is because, once the underlying has moved and an OTM option becomes ATM, it trades with the underlying and delta and loses its gamma potential.


Theta ChartTheta is the option’s sensitivity to time.  It gives a measure of the amount the option price will decay each day, as it approaches expiration.

This is a great indication for why it’s not enough to get the direction right, you must also pick the right strike and understand the option’s volatility, along with having time for a long option to move to a profit.

Theta is also why so many people want to sell options.  And although we do short option trading strategies, we do so with understanding the implications of short option risk and how to protect our trades.

You can see how much theta [option price decay] increases in the last few days before expiration, if there is little to no change in the underlying.  On a bigger move up or down, theta will go down into expiration.

Gamma + Theta

The impact of a flat underlying into expiration is a greater move up in gamma than down in theta.  Again, this is that ‘coiled spring’ potential to the options on a big expiration move.

You can also see how gamma and theta go down into expiration on an up move.


Vega ChartVega is the option’s sensitivity to changes in implied volatility. A rise in implied volatility increases the option prices. Vega increases with each expiration further out in time, and decreases as expiration approaches – if the underlying and MIV remain flat.

This is the case, even if volatility goes up and the underlying remains flat, because the option must expire at intrinsic value.  But if there is a volatility increase and a bigger underlying move up or down, then vega will increase.

We will look in more depth at the relationships, between the option ‘greeks’ and different changes in the pricing formula inputs, when we go into the option trading spreadsheet.