# Option Charm

Option Charm indicates how much the delta will change as one trading day passes. Charm is more commonly referred to as "Delta Decay". sdsad

The above diagram illustrates the effect of option charm on the delta of an option. The diagram shows option delta across a series of strike prices calculated at 3 different points in time. Notice how the delta of an ITM call option approaches 1 as the option approaches expiration? And that the OTM call options approach 0 as the option nears its expiration date?

Because Option Delta is a probability estimate of the options intrinsic value, Charm is especially useful right near the options expiration date. As expiration closes in, the probability of an option that is out of the money expiring in the money decreases rapidly as each trading day passes and the option charm will estimate how much the decay will be.

The type of trader most likely to benefit from the use of option charm are those traders who use options as a hedging tool. A trader that is hedging his/her delta at the close of business may want to consider the delta decay that the portfolio will experience overnight and hence look at the charm of his/her option position.

The change in the delta will be especially evident the day before a stock goes ex-dividend.

All other things being equal, upon market open the next day the delta of the portfolio will differ by this decay. This may actually prevent the trader from over or under hedging.

The Charm value is the same for call and put options and will range in value from -1 to 1.

ITM call options and OTM put options will have positive charm values. Conversely, OTM call options and ITM put options will have negative charm. So, basically, option charm decreases as the strike price increases.

The above is a sample of what you can expect to see from Option Charm values. Notice that for ITM call options and OTM put options show positive charm, while it reverses for OTM calls and ITM puts?

PeterSeptember 13th, 2013 at 8:28am

Hi Eric,

Once an option expires all ITM options will have a delta of 1 and OTM deltas of 0 - so as each day passes ITM options will continue to approach 1 unless the underlying prices moves to make the option OTM.

The Y axis in the graph displays the actual delta calculated against stock price movements on the X axis. I included 3 graphs to show how delta will change with differing time-frames - i.e. approaching 1 for ITM options.

Hope this helps - let me know if anything is unclear.

EricSeptember 12th, 2013 at 3:45pm

Hi Peter,

Can you clarify why the charm approaches 1 for ITM option nearing expiration. I would think that once an ITM option is near expiration the delta is already 1, so any day that passes the delta wont change by much - i.e. it would stay at close to 1.

Is the Y axis a multiple of the previous delta? As in the Charm being 1 means the delta after 1 day is (Delta from the day before) * 1?

Really appreciate your help!

PeterDecember 27th, 2012 at 5:14am

Hi optiongeek,

Yep - I'm curious ;-) if you're ok with it I can add it to the spreadsheet.

optiongeekDecember 24th, 2012 at 8:46am

Thanks, Peter, appreciate the feedback.

By dusting off my old Calculus text (chain rule) I was able to come up with the analytic formula by differentiating the formula for delta w.r.t dt. I'd be happy to send it to you if you were curious. I haven't been able to find it anywhere else but I was able to confirm my result using Wolfram Alpha.

PeterDecember 9th, 2012 at 4:09pm

Hi optiongeek,

I didn't use a separate formula for Charm: I calculated the delta for today and then delta for tomorrow. The difference between the two is the Charm.

So if you wanted to, you could have a column for delta and then a second column for tomorrow's delta just adding one day to the date for today() should do it.

optiongeekDecember 7th, 2012 at 8:55am

Hi there, I'm looking for the analytic formula for option charm for some work I'm doing. There's something publish on the wikipedia page (Greeks (finance)) but I'm not sure I trust it. From the diagram above, you do seem to have coded up charm in excel. I looked at the spreadsheet you publish but it doesn't seem to have charm. Is there any chance you could send me the spreadsheet you used to produce the above? Thanks.

PeterAugust 29th, 2012 at 7:29pm

No, I think it makes sense that ATM charm has the lowest values as the time effect has a greater impact on OTM and ITM options.

Re: AnonymousAugust 26th, 2012 at 5:26am

If charm is delta decay, wouldn't the ATM options have the highest charm?

ATM charm is zero as delta is kept at 50.

PeterOctober 12th, 2011 at 7:16pm

If the decay was based on gamma then it would peak for the ATM options as the gamma curve also peaks ATM. However, the behavior for delta is different to gamma and doesn't have the peak in the middle at time to expiration approaches.

For ITM options the delta will increase closer to 1 (-1 for puts) as each day passes and for OTM options they approach 0. Therefore there is no peak in the curve.

AnonymousOctober 12th, 2011 at 7:35am

If charm is delta decay, wouldn't the ATM options have the highest charm?

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