In the options trading universe, delta is one of the terms that has a wide variety of meanings.
Most often, traders use the term “delta” to refer to the degree that an option is in-the-money (ITM), out-of-the-money (OTM), or at-the-money (ATM). For example, a 10-delta put is OTM, a 50-delta call is ATM, and an 80-delta call is ITM.
On the other hand, when speaking about delta as a member of the Greeks, the term “delta” gives us an idea of how much the value of a given option will change in value for a dollar move in the underlying. So if the delta of a call option that we hypothetically own is $0.25, and the underling increases by a dollar, then the value of our call option should theoretically increase by $0.25 - all else being equal.
Another common use of the term “delta” in the world of options is to equate (approximately) the delta of a given option with the probability that it finishes in-the-money. Logically, this makes sense when one uses a 50-delta (ATM) option as an example. That's because for a 50-delta option the underlying is trading right at the strike, which suggests there's around a 50-50 chance that the option finishes in-the-money or out-of-the-money.
The graphic below helps illustrate the third application of delta:
Traders that want to learn more about this application of delta, or that already use it, will definitely find a recent episode of Market Measures worth a few moments of their time.
On this installment of the show, the Market Measures team takes a closer look at delta, and specifically how accurate delta has been at predicting (historically speaking) whether ITM, OTM, and ATM options expire as expected.
The findings from the research presented on the show should be of particular interest to traders because the data may help them more efficiently select the delta of the options in their portfolios, or at least help them better understand the potential risks and rewards of their current approach.
In order to produce the necessary data for the analysis, the Market Measures team examined historical data in SPY (2005 to present), which included over 10,000 unique occurrences. The goal was to backtest the data and ascertain whether the likelihood of a given option expiring as expected was overstated, understated, or pretty close to accurate.
For example, if an option was 30-delta at the time of trade initiation (suggesting a lower chance of finishing ITM), the team would check how that option actually expired (ITM, ATM, or OTM), and so on.
As you can see in the graphic below, the data suggested that for the Put side of the options tree, the delta of the option often overstated the percent chance that a given option would finish ITM. For example, looking at the data below, 10-delta puts expired out-of-the-money more frequently than expected, as did 20-delta puts, 30-delta puts, 40-delta puts, and even 50-delta puts:
Looking more closely at the above data, we can also see that on the call side of the options tree, the delta of the options frequently understated the probability that a given call would finish in-the-money (ITM). That means that for the 50-delta call, the 40-delta call, the 30-delta call, and the 20-delta call, historical data showed that these options had a slightly better chance of finishing ITM than indicated by the delta of the option.
It should also be noted that for 10-delta calls, an overstatement (as seen on the put side) was also observed.
Given the tendency for upward drift in the markets, and the fact that equities have experienced one of the longest bull runs in market history (since the Great Recession), it may be slightly less surprising to see how the hard data shook out in this analysis.
Importantly, the team also re-ran the backtest but this time factored in the amount of premium into the overstatement/understatement analysis. In this scenario analysis (backtesting selling each of the indicated options), all of the them showed a profit in terms of premium overstatement, except for the 50-delta and 40-delta calls.
For a comprehensive review of this hard-hitting data, we hope you'll take the time to review the complete episode of Market Measures when your schedule allows.
If you have any outstanding questions related to this interpretation of “delta,” we hope you’ll leave a message in the space below, or reach out directly on Twitter (@tastytrade) or email (firstname.lastname@example.org).
Thanks for reading, and we look forward to hearing from you!
Sage Anderson has an extensive background trading equity derivatives and managing volatility-based portfolios. He has traded hundreds of thousands of contracts across the spectrum of industries in the single-stock universe.
Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.