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July 10, 2014

Option Delta and Option Gamma

The option “greeks” help explain how and why option prices move. Option delta and option gamma are especially important because they can determine how movements in the stock can affect an option’s price. Let’s take a brief look at how they can affect each other.

Delta and Gamma

Option delta measures how much the theoretical value of an option will change if the stock moves up or down by $1. For example, if a call option is priced at 3.50 and has an option delta of 0.60 and the stock moves higher by $1, the call option should increase in price to 4.10 (3.50 + 0.60). Long calls have positive deltas meaning that if the stock gains value so does the option value all constants being equal. Long puts have negative deltas meaning that if the stock gains value the options value will decrease all constants being equal.

Option gamma is the rate of change of an option’s delta relative to a change in the stock. In other words, option gamma can determine the degree of delta move. For example, if a call option has an option delta of 0.40 and an option gamma of 0.10 and the stock moves higher by $1, the new delta would be 0.50 (0.40 + 0.10).

Think of it this way. If your option position has a large option gamma, its delta can approach 1.00 quicker than with a smaller gamma. This means it will take a shorter amount of time for the position to move in line with the stock. Stock has a delta of 1.00. Of course there are drawbacks to this as well. Large option gammas can cause the position to lose value quickly as expiration nears because the option delta can approach zero rapidly which in turn can lower the option premium. Generally options with greater deltas are more expensive compared to options with lower deltas.


Option gamma is usually highest for near-term and at-the-money (ATM) strike prices and it usually declines if the strike price moves more in-the-money (ITM) or out-of-the-money (OTM). As the stock moves up or down, option gamma drops in value because option delta may be either approaching 1.00 or zero. Because option gamma is based on how option delta moves, it decreases as option delta approaches its limits of either 1.00 or zero.

An Example

Here is a theoretical example. Assume an option trader owns a 30 strike call when the stock is at $30 and the option has one day left until expiration. In this case the option delta should be close to if not at 0.50. If the stock rises the option will be ITM and if it falls it will be OTM. It really has a 50/50 chance of being ITM or OTM with one day left until expiration.

If the stock moves up to $31 with one day left until expiration and is now ITM, then the option delta might be closer to 0.95 because the option has a very good chance of expiring ITM with only one day left until expiration. This would have made the option gamma for the 30 strike call 0.45.

Option delta not only moves as the stock moves but also for different expirations. Instead of only one day left until expiration let’s pretend there are now 30 days until expiration. This will change the option gamma because there is more uncertainty with more time until expiration on whether the option will expire ITM versus the expiration with only one day left. If the stock rose to $31 with 30 days left until expiration, the option delta might rise to 0.60 meaning the option gamma was 0.10. As discussed before in this blog, sometimes market makers will look at the option delta as the odds of the option expiring in the money. In this case, the option with 30 days left until expiration has a little less of a chance of expiring ITM versus the option with only one day left until expiration because of more time and uncertainty; thus a lower option delta.

Closing Thoughts

Option delta and option gamma are critical for option traders to understand particularly how they can affect each other and the position. A couple of the key components to analyze are if the strike prices are ATM, ITM or OTM and how much time there is left until expiration. An option trader can think of option delta as the rate of speed for the position and option gamma as how quickly it gets there.

John Kmiecik

Senior Options Instructor

Market Taker Mentoring

June 18, 2014

AAPL Butterfly After the Split

There has been more talk than usual about Apple Inc. (AAPL) before and now just after the split. Several traders have asked me about what type of AAPL option trade they can use if they think AAPL will rise to around $100 in a few short weeks. Truth be told, there is more than one option strategy that can profit. But an option trader should consider a directional butterfly spread particularly if he or she has a particular time frame in mind as well. Depending on how the butterfly spread is structured, the option trader can structure a high risk/reward ratio for the spread. Let’s take a look at this option strategy.

The long butterfly spread involves selling two options at one strike and then purchasing options above and below equidistant from the sold strikes. This is usually implemented with all calls or all puts. The long options are considered to be the wings and the short options are the body of the butterfly. The option strategy objective is for the stock to be trading at the sold strikes at expiration. The option strategy benefits from time decay as the stock moves closer to the short options strike price at expiration. The short options expire worthless or have lost significant value and the lower strike call on a long call butterfly spread or higher strike put for a long put butterfly spread have intrinsic value.

As mentioned above, if an option trader thinks that AAPL will be trading around $100 in about three weeks, he can implement a long call butterfly spread with the sold strikes (body) right at $100. Put options could also be used but since the spread is being structured out-of-the-money (OTM), the bid/ask spreads of the options tend to be tighter versus in-the-money (ITM) options which would be the case with put options. The narrower the option trader makes the wings (long calls) the less the trade will cost but there will be less room to profit due to the breakevens. If the butterfly spread is designed with larger wings, the more it will cost but there will be a wider area between the breakevens.

At the time of this writing, AAPL is trading around $92. An option trader decides to buy a Jul-03 97/100/103 call butterfly for 0.15. The most the trader can lose is $0.15 if AAPL closes at or below $97 and at or above $103 at expiration. The breakevens on the trade are between $97.15 (97 + 0.15) and $102.85 (103 – 0.15). The maximum profit on the trade in the unlikely event AAPL closes exactly at $100 on expiration would be $2.85 (3 – 0.15). This gives this option strategy a 1 to 19 risk/reward ratio. Granted AAPL needs to move higher and be around $100 in three weeks but one could hardly argue about the risk/reward of the option strategy or the generous breakeven points of the spread.

This AAPL option trade may be a bit overwhelming for a new option trader to understand and there is more than one way to take a bite out of AAPL with a bullish bias. A directional call butterfly spread in this instance is just one way. A big advantage that the directional butterfly strategy may have over another option strategy is the high risk/reward ratio. The biggest disadvantage is the trader needs to be right about the time frame in which the stock will trading between the wings since maximum profit is earned as close to expiration as possible.

John Kmiecik

Senior Options Instructor

Market Taker Mentoring

August 2, 2012

Option Delta and Apple (AAPL)

Filed under: Uncategorized — Tags: , , , , , — Dan Passarelli @ 11:56 am

Option Delta and Apple ( AAPL )
Apple (NASDAQ: AAPL) sure is making a lot of news lately. The company recently reported earnings and subsequently fell in price. Since the fall, the stock has once again moved higher. One may expect the AAPL stock to push higher (after this dip), but some may believe the rebound will be still short-lived. Perhaps a smart move is to purchase a short-term, out-of-the-money option on the equity – let’s look for an option with a delta greater than 20 on Apple and see how the option could play out.

Option Delta and the Trade
First, let’s define option delta before we go into the option play. Option delta is a ratio that compares a stock’s change in price to the corresponding price change in said stock’s option. For this example, we are going to use the Apple September 650 call that has about an option delta of 23 percent.

What does the 23 percent mean? Let’s convert the option delta into dollars to see. This percentage means that this particular Apple option will gain or lose value just like 23 percent of 100 shares of Apple as the price changes. Look at the definition this way if it is easier, for every $1 Apple advances; the call option will increase 23 cents attributable to delta. So, Apple is currently trading at around $605

(rounded for simplicity) and we have purchased the 650 call. We need the call to advance past $650 in order (which is not out of the question) for the option to be in-the-money, but can we benefit from a rally that falls short of $650?

The Benefit of Option Delta
Apple is a major momentum stock, just look at what happens after good news – more often than not the stock rallies. In fact, I don’t think it is a stretch to say that the stock often moves quite a bit. Look at 2009 when Apple dropped as low as the $78 region in late January then rallied to finish the year above $210. That is a major gain.

Playing the September 650 call affords a trader the chance to make money in the case that the stock rallies. If the stock hits $650, that means it has moved 45 points. Take the 45 points and multiply that by 23 cents (option delta of .23) and you have a move of $10.35 in the call (45 X 0.23).

By looking at the option delta, we were able to have clear expectations for option profit based on stock movement. Does this mean that playing the delta is a fool-proof to analyze an option? No. There are other important pricing factors that affect the value of an option, too. Time (theta), volatility (vega) and more also play an important role. Delta is just one of the greeks that can be taken into account when looking for the right option to purchase. Make sure to do your homework so you can enter the option game prepared to succeed.

John Kmiecik

Senior Options Instructor

Market Taker Mentoring