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Regarding the Greeks ...
A question came in a week or so ago regarding "gamma" and that "short dated options are prone to gamma effect and therefore are not a good idea". "What am I missing?"
First of all, let me make clear that I do not watch "gamma", "theta", or any of the greeks that are associated with options. The only greek that I really care about is delta, and I care about it only because:
- it's a rough proxy for the probability of the option hitting expiration and being out of the money (OTM), and
- I have set a minimum threshold of delta that I will sell premium (-0.25 or smaller for puts, 0.25 or smaller for calls).
Since I sell options and collect the premium from the sale, I want my options to expire OTM, which means they are worthless. The take away is that if the option is OTM then I pocket all of the money I received when I sold it, and that's that. Smaller deltas --> greater chance of option being OTM.
What follows is a bit technical, and in the big picture of cash-secured puts and covered calls, is really not needed. It shows a bit of mental gymnastics, and the end shows that there MAY be a reason to trade short duration options (e.g. sell them), but the conclusions I make are a reach and note, I don't really pay attention to this. It *could* be one of the factors of why selling premium is successful -- I simply don't know.
That being said, I'm willing to look at this a bit more ... I always like option analysis.
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The stock price, the option price, option delta, and option gamma are all related. While option pricing is beyond the scope of where I want to take this blog entry, let's simply assume that an option price is established by and is fairly valued by the market. An example is a good way to think about this; let's start with the stock price, option price, option Delta, then move into Gamma.
This past Friday INTC fired an alert in the GreekGodTrading Twitter account ( https://twitter.com/GreekGodTrading ) and here is an echo of what went out to the folks who follow me:
INTC:!P_CSPv1.6. INTC 191025P48, MinBid=$0.68, MinPrem=$56.88, Last=$50.88, AROO=21%, Prob=70%, Spread=$0.01, ROO=1.3%, Days2Exp=22, CashReqd=$5020, IVRank=16.1, StrikeInc=$0.50, Delta=-0.2418, ImplVol=0.38, Fisher=2. 10/4/2019 3:28:40 PM
Lots of info there, but there are a couple of things that are important for this discussion:
- Last=$50.88: INTC was trading at $50.88 when this alert fired
- MinBid=$0.68: The half-way point between the ask and the bid, for the option INTC 191025P48, was $0.68, meaning, one contract would net you $68, less commissions, if you sold the contract when the alert sounded.
- Delta=-0.2418: the option INTC 191025P48 had a delta of -0.2418; what does this mean?
The units on Delta are "$ change in option price per $ change in underlying".
When an alert fires, various prices (underlying, option) are fairly stable. Here's a table of INTC and consecutive entries where if the previous line would not have triggered an alert, the following one would have. You can see that INTC fired more/less solidly for about 30 minutes this past Friday:
Price of INTC is in the 2nd column from the left; Delta is in the right column. Bid/Ask, in the middle of the able, show the relative tightness of the spread (typically $0.01). The time span is about 32 minutes.
What should be evident is that everything remains in a tight range, so even if you are late to an alert, the overall conditions are fairly stationary. This is important for you if you desire to echo my trades (not recommended by the way -- this is only for informational purposes).
Here's a chart that shows the same data:
The x-axis is the underlying price of INTC. The option price of INTC 191025P48 is shown on the left axis, and the Delta of the option is shown on the right axis.
What is evident here is that as price goes up, option price decreases (left axis, blue dots), as we expect, AND, option Delta changes (decreases in magnitude - becomes less negative) as price goes up of the stock.
So what? Well, all this simply shows is that there is some behavior out there that relates stock price (x-axis), put option price (left axis, blue), and option delta (right axis, orange). It isn't overly useful except to say that it is understood.
This next graph shows a general relationship between the delta of an option (0 to -0.3), the days to expiration for the option (8 to 29), and the number of strike intervals from the price (1-4). Options are listed in these intervals ($0.50, $1.00, $2.50, $5.00, etc.) so it is important to know where various option deltas lay vs. days to expiration (DTE) as well as the option chain strike intervals:
The colored part of the graph shows Delta as a function of Days to Expiration as well as the number of intervals we are from a strike price. Anywhere in the orange represents a delta of -0.25 to -0.20, and for the data set shown, this could be 2-3 option chain strike intervals below the current price, especially if we are out 29 days or more, OR, if we are within 8-15 days, it most certainly points to being within 1 strike of the current price of the stock.
In the picture above, Gamma is the slope of the change in delta, and now, you can see that it is a function of Days to Expiration as well as as how far we are away from the stock price.
There are other things that influence Gamma, but think of a marble on the surface of the Delta curve .... as it rolls, does it pick up speed? If so, then Gamma is not constant, e.g., it has some influence on the option price and option delta.
A view-from-the-top of the same graph is shown below, and makes this "where is Delta in the -0.2 to -0.25 range (?) a bit easier to see:
Now, with all of that Delta stuff behind us ...
The original question was about trading Gamma, and a statement that short-duration options have poor Gamma so they should not be traded.
If I take the option prices as shown above in the two graphics, and then take the difference between the Deltas and do some simple manipulations, I can get a picture of the Gamma:
The relationship is kind of "concave" or somewhat parabolic -- for the shortest days to expiration (8), we have virtually no gamma (no change in delta as a function of time duration to expiration), and out beyond 15 days, the influence becomes less and less, to where at 29 days, it is virtually nil.
The arrow I drew points to the 15-day evaluation point, and shows a maximum negative gamma occurs when we are 2-3 strikes away from the underlying price, AND, we are at 15-days to expiration. Note that the X-Y chart above, with the underlying price of INTC, the option price, and the option Delta are all for an option expiring on 10/25, or 18 days from the time this is written. That puts us on the "back wall" of the surface shown above, so Gamma is clearly not zero.
A couple of things are evident to me:
- Trades that are within two weeks of expiration show a lessening of gamma -- the change in delta, as a function of distance to the underlying stock price AND the number of days to expiration, gets less and less as we march closer to options expiration. If we choose to care about Gamma as we get closer to option expiration we can care less about it.
- Trades that are longer than two weeks from expiration, say 4 weeks, see very little influence of gamma too (evaluated with n = 100 optionable stocks or so). Hence, selling premium out at 4 weeks before OE should see the change in delta remain fairly constant.
- I'm not seeing a real problem with a changing Gamma in the bigger picture. Even if I choose a 15-day period to expiration, and I am 3 strikes away from the current stock strike price (the minimum in the surface graph so the maximum influence of Gamma for the data shown), it really doesn't matter to me. At this point I'm seeing a $0.07 change per $1.00 change in Delta, or 7% of an already small number, so the influence on option pricing is pretty insignificant.
In the end I think it boils down to this: if you are selling premium, delta matters more than gamma. Gamma may matter around the 15-day to OE mark, but in general, it isn't driving a major decision.
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I welcome input from those who have studied this more than I.
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As with all my ramblings, you are responsible for your own actions and I am not. Nothing I've written here is advice to buy or sell any security, so don't do it unless you absolutely take ownership for your actions.
Regards,
Paul
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