OCTOBER
PROFILE

The straddle carries 200 ATM-equivalents of vega and the call spread takes 222 of them back. Each 7725 option is a full at-the-money option on this tenor, so 200 of them is 200 units of vega, $207k per vol point. The 8000 call is a 19 delta with 69 percent of the ATM vega and the 8050 call a 14 delta with 57 percent, so each spread sold is short 0.11 of an option and 2,000 of them is short 222. The position nets to -21.9 ATM-equivalents, -$23k per vol point.

Gamma nets close to flat for the same reason: the two short 8000 calls per spread carry more gamma than the two long 8050 calls, and 2,000 spreads of that difference is about the gamma of the 200 straddle options. Vanna does not net. The straddle sits on the vanna zero and the call spread sits on the call-side vanna peak, so the position is long +68 deltas per vol point with almost nothing on the other side. Delta is short 8,584 SPX-equivalent, most of it from the spread.

The straddle is long gamma at every level and largest at 7725; the call spread sold is short gamma below about 8025 and long above it. At the mark the two nearly cancel at -4.3 deltas per point. Between 7515 and 7811 the spread's short gamma wins and the position is short, at its shortest near 7680 with -4.6 deltas per point. Above 7811 both structures are long and the total climbs to 33 near 8215.

In practice the position has almost no gamma to hedge inside a 300 point band around the mark, and a rally through 8000 turns it into a long-gamma book quickly: at 8100 the total is 29 deltas per point, at 8200 it is 33. The same rally moves the delta from -8,584 at the mark to -4,583 at 8100.

Time concentrates gamma onto the strikes, and the two structures do not concentrate at the same rate. At the mark the straddle's gamma goes from 25 deltas per point now to 29 at 30 days, 43 at two weeks, 61 at one week and 160 on the last day. The call spread's short gamma at the mark deepens first, from -29 now to -56 at two weeks, then fades to -31 at one week and 0 on the last day, because with a week or less to run the 8000 and 8050 calls are too far from a 7717 index to carry gamma there at all.

So at the mark the position is short gamma through the middle of its life (-11 at 30 days, -13 at two weeks) and long gamma at the end (29 at one week, 160 on the last day), when it is 100 straddles at the money and nothing else. The short-gamma band moves toward the spread as time passes: 7515 to 7811 now, 7684 to 7990 at two weeks, and on the last day a narrow trough between 7849 and 8024 where the short 8000 calls sit, with the long 8050 calls giving back +1057 just above. A rally into the spread in the final week is where the numbers get large in both directions.

The position is short vega only inside a narrow band around the mark, from 7567 to 7806. That is where the straddles are at the money and the call spread is on the steep part of the vega curve. Below 7567 the spread loses its vega faster than the straddles lose theirs and the total turns positive; above 7806 the 8050 leg moves toward the money while the 8000 leg moves through it, and the spread itself becomes long vega.

The size of that swing is the point. From -$23k per point at 7700 to +$266k per point at 8235: a 500 point rally changes the vega by about $289k per vol point, and a rally is usually where vol falls. The weighted vega of -21.9 at the mark describes one level of the ladder, not the position.

Almost all of the vanna is the call spread. A straddle at the money has no vanna to speak of, and this one contributes -20 deltas per vol point at the mark. The 8000 and 8050 calls sit at 19 and 14 delta, the call-side vanna peak on this tenor, and short the lower strike against long the higher one leaves +88 deltas per vol point: when vol rises the long 8050 call, the one nearer the vanna peak, gains more delta than the short 8000 call loses, so the position gets longer as vol rises and shorter as vol falls.

The profile flips three times: at 7323, at 7699 just below the mark, and at 8233 above the spread. Between the mark and 7975 vanna climbs to +889 deltas per vol point, which is where a vol move rearranges the delta the most. That is the skew bucket of this book, and it is where the risk lives on a fast move with vol.

Vega itself moves $21k per vol point per vol point. Three points of vol lower and the position is short $86k a point; three higher and it is long $42k. That is the volga of the wings: the 8000 and 8050 calls are the part of the surface where vega changes fastest with vol, and the spread sold carries it. A vol-down grind therefore makes the position shorter vega as it goes, which compounds against it; a vol spike takes the short vega away.

Delta is the more stable number in the table, moving about 46 SPX-equivalent per vol point. Gamma goes from -20 to +4 deltas per point across the six-point range: lower vol pulls the strikes closer in vol terms and the short spread gamma dominates, higher vol spreads the distribution and the straddle gamma comes through.