What is the Delta of an Option and How To Use It
February 2021
The "delta" of an option is how much the value of an option will move in relation to the futures contract it is attached to. Most quote screens do not provide the delta, but here is one that does:
Go to that web page and you will see futures quotes. To the right side of the futures quotes, you will see the word "options" by each futures contract month.
Click on the July corn option link and you will see a page that starts with the $1.80 strike price options for July corn. Scroll all the way down and the bottom and you will see the highest strike price for July corn is $9.50.
Now scroll back to the top of that page and you will see the label of each column. To the left of the strike price column is information regarding call options, namely the "close", aka the last trade during trading hours, "delta" and "premium". The premium on this quote screen is the number of dollars that each 5,000 bushel option contract is valued, i.e.: what it will cost to buy or what one could sell it for.
Most people refer to the premium in terms of cents per bushel, which this page refers to as the "close". If you take the number in the "close" column times 5,000 bushels per option, you will get the number listed as the premium on this page.
Go to the July $5.20 strike price. Look left and see the delta for the $5.20 call option. At this moment, the delta for the July $5.20 call is 0.55. That means for every ten cents July futures moves, the value of that call option will move 5.5 cents or 55% of the futures move.
Go to the right side of the strike price column and note the delta for $5.20 put is 0.45.
Scroll up and down the strike prices and see how the delta changes as the strike price of the option is further away from the current futures price.
Futures prices have a limit as to how many cents the futures price can change. For corn, it is 25 cents.
Options have no daily trading limit. Therefore, the price change of an option will reflect the real value of the futures contract when the futures price is limited by the daily limit.
Let’s say July corn goes limit up. The delta of the July $5.20 call is 0.55. For every ten cents July futures moves, the value of July $5.20 call will move 5.5 cents. If July futures goes 25 cents higher tomorrow, the July call will move 13.75 cents (55% of 25 cents).
But suppose the July call price, aka the premium, settles at a price 17.75 cents higher than the today? That is 4 cents more than the delta indicates its price should have moved. Thus, one divides the delta of 0.55 into 4 cents = 7.27 cents. That means the futures prices would have been up 32+ cents if there had not been the 25 cent daily trading limit.
Another way to get the same answer is take the change for the day in premium (price of the option). If the July $5.20 call option closes up 17.75 cents, one divides the delta into the 17.75 cents = 32.27 cents. That also means if there was no daily trading limit of the futures price change, July futures would have settled 32¼ cents higher that day.
A third way to determine how far the futures price would move had there been no limits on the futures price ti select an option with a delta of 1 (one) which means the value of the delta changes penny for penny with the futures. If the futures closed limit-up 25 cents and a call option with a delta of one closed 29 cents higher, then one can see the that futures would have closed up 29 cents if there were no daily trading limits.
In reality, on limit move days of futures price, the option premium change is an exaggeration of the futures price move.
Why?
People who are short (sold position) in July futures when it locked limit-up just lost 25 cents a bushel. The market looks like it will open higher the next day because it is locked limit up, so the trader who is short futures will buy a July call option to offset the expected higher opening of futures the next day. That extra buying inflates the price of call options on the days of limit moves of future prices.
The vast majority of times, it is a mistake to buy a call when the futures are locked limit up or buy a put when the market is locked limit down.