The simplest way to use Delta, is to view it as :
The probability of that option expiring In-The-Money
Example of SPX OTM, ATM and OTM Puts and Calls
SPX is traded at 1242 as of 5th Sept 08.
Note that Sept 1240 Put and Call, which represents Near-The-Money, but for ease of explanation, let's just say they are both ATM Put and ATM Call.
These ATM options have close to 0.50 delta (ignore the +ve and -ve signs). This means that these ATM options have ~50% chance of being ITM by the expiration date. It makes sense, since SPX last traded at 1242, can only move up or down and all things being equal, SPX has a 50-50 chance of going either way. The ATM options reflect this probability.
Now look at the deep ITM 1180 Call, it's delta is 0.92 or a simply a 92% chance, given all things being equal, that by expiration, this 1180 Call will remain In-The-Money. Remember that this Sept Options have only 10 more days to expiration. This is a meaningful interpretation because, ITM 1180 Call strike being 62 points deep ITM currently, does obviously have a much better chance of remaining ITM by expiration as compared to OTM 1300 Call strike, which has a mere 12% (delta of 0.12) of being ITM in 10 days' time.
For this OTM 1300 Call strike to be ITM, SPX must rally past 1300 in the next 10 days. Whereas, SPX just needs to stay rather unchanged or can even dive in the next 10 days, and yet the 1180 Call strike will still be ITM, as long as SPX stays above 1180. Between the 2 options, the ITM 1180 Call, has 2 out of 3 scenarios covered and hence a higher probability of staying ITM by expiration and thus a much higher Delta of 0.92
Hence, as a back-of-the-envelope review, an option's probability of becoming ITM by expiration, can be obtained by simply looking at the option Delta.
Option Delta - Absolute Put and Call Deltas Add Up to ~1
The 1240Call has 0.53 and the 1240Put has 0.47. Note, that +ve or -ve Delta is NOT a function of whether it is a Put or Call.
The example shows -0.47 for 1240Put, only because it is saying that a LONG Put, a bearish position, will generate a -ve 0.47 Delta.
Note that the absolute values of ATM 1240 Call and ATM 1240 Put, add up to 1; ie
|0.53| + |-0.47| = 1
In fact, if SPX was traded at 1240 exactly, these ATM 1240Call and ATM 1240Put would each have a delta of 0.5, and will practically add up to a full integer 1.
This is also the reason that a Straddle, which is a Long ATM Call and Long ATM Put position, will not be profitable, when only a small movement occurs. A perfect straddle, has exactly ZERO delta; the Long ATM Call option has +ve0.5 and the Long ATM Put option has -ve 0.5, and the combined position, results in an absolute 0 delta value. Thus, for Straddles to be profitable, a huge move must occur in either direction.
However, notice that both the deep OTM Call (1180) and deep ITM Put (1300) options, and conversely ITM Call and OTM Put options, their corresponding Deltas do not absolutely add up to 1.
The reason is that these OTM/ITM option Deltas are artificially affected by Implied Volatility, Gamma and +ve/-ve PutCall Volatility skew. This is a topic for another day.
But suffice to say that the Straddle's delta changes because the Gamma of the Call and Put options change when the underlying starts making large price movements. This Gamma then causes the Straddle to either net gain or lose Delta, which translates to profits.
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