Options research
Strangle defense: what happens after one strike is touched
Sooner or later the price of a short strangle reaches one of its two strikes. A common defense is to roll the untested strike closer to the price and collect more premium. I tested what happens after that first touch on six ETFs (SPY, QQQ, IWM, XLP, GLD and SLV), with a strangle opened on every trading day since 1993: where the price went next, and how far away the rolled strike needed to be. Whether the roll pays for itself once option prices are included is the subject of part 2.
Key findings
- After a touch, the price kept going about as often as it does on any day. A touched call strike one standard deviation away finished in the money 57% of the time, the same as normal; a touched put 40%, against 43% normally.
- The moves got larger in both directions. After a put touch, a call rolled to the same distance (measured with a 42-day volatility) was touched again 1.37 times as often as normal at 1 standard deviation and 2.42 times at 2. The same distance in the other direction, further down, was elevated about as much.
- Placing the rolled strike with a 10-day volatility instead brought it back to normal risk (1.00 times at 1 standard deviation) and moved it only 12 to 37% further out. At 180 days a 21-day volatility fit better.
- Stock ETFs needed the fast volatility after falls, gold and silver after rallies. The result held before and after 2010, above and below the 200-day average, at every VIX level and for overnight gaps.
The test
For each ETF I opened a short strangle at every daily close, with 15, 30, 45, 60, 90 or 180 calendar days to expiration and both strikes at 0.5, 1, 1.5 or 2 standard deviations of the term (SD in the charts and tables). The standard deviation comes from an exponentially weighted realized volatility with a 42-day half-life, measured on the entry day. A strike counts as touched when the day's high or low reaches it, and I follow whichever strike is touched first.
Every result is compared with a normal level: the same ETF from any day, with the same number of trading days left, measured in the same volatility units. That removes each ETF's usual drift and its fat tails, so what remains is the effect of the touch. Unless stated otherwise, the numbers are averages over the six ETFs and over the terms from 30 to 90 days.
| Strikes at | Neither touched | Call touched first | Put touched first |
|---|
45-day strangles, average of the six ETFs, share of all strangles opened.
At 1 SD neither strike was touched in 44% of 45-day strangles. Near the money the call was touched first more often, because the ETFs drifted upward. At 1.5 and 2 SD the put was touched first more often, because large falls were more common than large rallies.
Direction after the touch
Once a call strike at 1 SD was touched, the price finished beyond it at expiration 57.2% of the time. On any day, a call at the same distance with the same time left finished beyond it 57.4% of the time, so the touch added nothing to the direction beyond the ETFs' normal drift. For puts, the touched strike finished in the money 39.9% of the time against 42.9% normally: after a fall the price came back slightly more often than usual, by 3 points at 1 SD and 5 points at 2 SD. That tilt is small next to the change in the size of the moves.
Averaged over calls and puts, a touched strike finished in the money about half the time. That half is where a well-known rule of thumb comes from: a strike is touched about twice as often as it finishes in the money. How well the rule holds on 469 stocks, and where earnings gaps and the trend break it, is the subject of the study is the probability of touch really twice the probability of finishing in the money?
The size of the moves
After a put touch, I moved the untested call to the same number of standard deviations from the new price, measured with the same 42-day volatility on the day of the touch. For a 45-day strangle at 1 SD, that rolled call was touched later in 38.6% of cases. A call at the same distance on any day was touched in 28.5%.
If prices simply tended to bounce after a fall, only the rolled side would stand out. The chart also shows the same distance in the other direction, further down after a put touch, and it was elevated almost as much: 1.25 times normal at 1 SD against 1.37 for the rolled call, and 2.84 against 2.42 at 2 SD. After a touch, prices moved more in both directions. A 42-day volatility reacts slowly, so on the day of the touch it still describes the calmer market before the move, and a strike placed with it sits closer than it looks.
After a call touch, the rolled put was reached about as often as normal at 0.5 and 1 SD (0.95 to 0.96 times). At 1.5 and 2 SD it was elevated too (1.17 and 2.24 times), but such touches are rare: the call was touched first in under 5% of 45-day strangles at 2 SD.
How far to roll
If the problem is a volatility estimate that reacts too slowly, a faster one should fix it. I placed the rolled strike with the 42-day volatility and with faster versions with half-lives of 21, 10 and 5 days, each compared with a normal level measured with the same estimate.
| Strikes at | 42-day | 21-day | 10-day | 5-day | 10-day strike further out |
|---|
Rolled call after a put touch, share touched later relative to normal, by half-life of the volatility estimate. Last column: how much further from the price the 10-day estimate placed the strike than the 42-day one (median).
With a 10-day half-life the rolled call was touched as often as normal at 1 SD (1.00 times) and less often at 1.5 and 2 SD (0.84 and 0.60 times). The strike moved only 12% further out at 1 SD, 23% at 1.5 SD and 37% at 2 SD. A 5-day half-life placed it further out than needed, which costs premium, and the 21-day version removed about half of the excess.
| Term | 42-day | 21-day | 10-day |
|---|
Rolled call after a put touch at 1 SD, share touched later relative to normal.
For 15-day strangles the 10-day estimate was also about right (1.06 times). At 180 days it placed the strike too far out (0.77 times), because volatility falls back over half a year, and the 21-day version fit (1.08 times).
Stock ETFs and metals
| Rolled strike | 1 SD | 1.5 SD | 2 SD | |||
|---|---|---|---|---|---|---|
| 42-day | 10-day | 42-day | 10-day | 42-day | 10-day | |
Share touched later relative to normal, 30 to 90 days. Stock ETFs: SPY, QQQ, IWM, XLP. Metals: GLD, SLV.
The six-ETF average mixes two patterns. In the four stock ETFs the excess appeared after put touches: 1.59 times normal at 1 SD and 4.23 at 2 SD with the 42-day volatility, 1.10 and 0.84 with the 10-day one. In gold and silver it appeared after call touches (1.41 and 2.71 times at 1.5 and 2 SD), while after put touches the rolled call stayed close to normal even with the slow estimate (1.01 times at 1 SD, 1.12 to 1.19 further out). In stocks volatility jumped after falls, in gold and silver after rallies, and the side that needs the faster estimate follows from that.
One cell stays high with both estimates: stock ETF call touches at 2 SD, 1.60 times normal with the 10-day volatility. These are sharp rallies inside markets that were already volatile, and they are rare.
Does it hold?
I split the put touches in the four stock ETFs (1 SD, 30 to 90 days) by period, by trend and by the VIX on the day of the touch. For each group the normal level comes only from days in the same group, so a touch with the VIX above 25 is compared with days on which the VIX was above 25.
| Touches | Number | 42-day volatility | 10-day volatility |
|---|
Rolled call after a put touch, share touched later relative to normal in the same group, with 90% intervals. Grey: fewer than 3,000 touches. Trend: the ETF's close against its own 200-day average on the day of the touch.
The excess with the slow estimate appears in every group, from 1.45 times before 2010 to 1.74 times above the 200-day average. With the 10-day estimate every group lies between 0.90 and 1.19 times normal. The quiet market with the VIX below 15 has few put touches (about 2,000), and there the slow estimate was only mildly elevated (1.17 times, interval 0.85 to 1.50).
About 14% of the put touches and 16% of the call touches in the stock ETFs happened overnight: the day opened beyond the strike. In gold and silver, which trade nearly around the clock, about 30% did.
| Touch | Overnight | 42-day volatility | 10-day volatility | ||
|---|---|---|---|---|---|
| Overnight | During the day | Overnight | During the day | ||
Rolled strike touched later relative to normal, 1 SD, 30 to 90 days, with 90% intervals. Overnight: share of touches where the day opened beyond the strike.
Touches that happened overnight and touches during the day were followed by the same pattern, and the roll needs no different rule for gaps.
What it means for strangle sellers
The touch itself said little about where the price went next. It said that the market had become more volatile and that a volatility estimate from before the move understated the distance needed. For the untested strike, a distance measured with a fast volatility (about a 10-day half-life up to three months, about 21 days for longer terms) restored a normal risk, at the cost of placing the strike 12 to 37% further out. The side that needs it is the one where volatility jumps: after falls in stock ETFs, after rallies in gold and silver.
Data and notes
- Data: daily open, high, low and close of SPY (from 1993), QQQ (1999), IWM (2000), XLP (1998), GLD (2004) and SLV (2006), split-adjusted and not dividend-adjusted, through 30 October 2026. Prices are used only to compute the statistics shown.
- Entries: every trading day, overlapping. Expiration: the first trading day on or after the entry date plus the term, settled at its close. Independent windows per ETF: about 635 at 15 days, 211 at 45 days and 52 at 180 days.
- Volatility: exponentially weighted average of squared daily log returns, half-life in calendar days. Strike distance: number of standard deviations × daily volatility × √(trading days to expiration).
- Touch: the day's high or low at or beyond the strike, first touch only; strangles with both strikes touched on the same day are left out. Roll: at the close of the touch day, same expiration, held to expiration.
- Normal level: from every trading day of the same ETF, with the same number of trading days left, standardized with that day's volatility of the same kind. In the split by group, only days of the same group.
- Intervals: 90%, from 2,000 resamples of whole calendar quarters, because touches in the same quarter overlap and the ETFs move together. The pooled stock ETF numbers in the last two tables are weighted by the number of touches and come out slightly higher than the six-ETF averages above.
- Not included here: option prices (see part 2), stops or adjustments before expiration, trading costs.
- All numbers count what happened in the past. They are not probabilities for the future, not forecasts and not financial advice.