Risk · Greeks, scenarios and P&L explain
Second-order Greeks of the stored Heston surface, where a vol move's P&L is mostly convexity, and how well the Greeks explain a hedged position's daily P&L.
Surface 2026-10-28·80 of 90 grid nodes·6 maturities
Convexity-dominated vega
9.0%
vega-weighted share of the 35 of 80 nodes with vomma P&L ratio ½·vomma·|Δσ|/vega > 0.25; 31 of them at |ln(K/F)| ≥ 0.09, where node vega averages 663 against 1,351 nearer the money
$Vega · ref. straddle
+$1,766
per vol pt, one SPX contract · fit of 2026-10-28
$Gamma · ref. straddle
+$810
P&L of a 1% spot move, one SPX contract · fit of 2026-10-28
$Vanna · ref. straddle
+$8.83
per 1% spot, per vol pt, one SPX contract · fit of 2026-10-28
$Volga · ref. straddle
−$0.05
per vol pt²; P&L ≈ ½·$volga·Δσ², one SPX contract · fit of 2026-10-28
Cash Greeks of the scenario grid's reference book: one 30-day SPX straddle struck at the forward (7,745.1; S 7,744.0), Black-76 at the fit's ATM-forward vol 13.26%, × 100 for one SPX contract. $gamma is ½·Γ·(1% of S)²·100. Unit conversions of the same Greeks, not a position: the site holds no book.
Greeks by maturity and ln(K/F)
M6 Greeks source · OK| T | −0.300 | −0.261 | −0.221 | −0.182 | −0.143 | −0.104 | −0.064 | −0.025 | +0.014 | +0.054 | +0.093 | +0.132 | +0.171 | +0.211 | +0.250 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14d | no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F |
⚠ 1.37
84
K 6,198, IV 34.8%
|
⚠ 1.17
224
K 6,447, IV 32.3%
|
⚠ 0.94
546
K 6,705, IV 29.5%
|
⚠ 0.70
1,165
K 6,974, IV 26.3%
|
⚠ 0.43
1,906
K 7,253, IV 22.5%
|
0.14
1,368
K 7,544, IV 17.6%
|
0.16
1,743
K 7,846, IV 11.5%
|
⚠ 1.87
2,073
K 8,160, IV 12.2%
|
no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F |
| 30d |
⚠ 0.80
335
K 5,738, IV 37.8%
|
⚠ 0.72
547
K 5,968, IV 35.7%
|
⚠ 0.64
868
K 6,207, IV 33.3%
|
⚠ 0.55
1,326
K 6,455, IV 30.8%
|
⚠ 0.45
1,906
K 6,714, IV 28.0%
|
⚠ 0.34
2,476
K 6,983, IV 24.8%
|
0.21
2,590
K 7,263, IV 21.1%
|
0.07
1,259
K 7,554, IV 16.6%
|
0.06
1,277
K 7,857, IV 11.6%
|
⚠ 0.86
5,517
K 8,171, IV 11.7%
|
⚠ 1.66
2,257
K 8,499, IV 13.6%
|
⚠ 2.33
609
K 8,839, IV 15.3%
|
no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F | no data: OTM value below 5e-06·F |
| 60d |
⚠ 0.39
1,480
K 5,754, IV 35.3%
|
⚠ 0.36
1,891
K 5,984, IV 33.2%
|
⚠ 0.32
2,362
K 6,224, IV 31.0%
|
⚠ 0.27
2,855
K 6,474, IV 28.6%
|
0.22
3,274
K 6,733, IV 26.0%
|
0.17
3,404
K 7,003, IV 23.1%
|
0.10
2,826
K 7,283, IV 19.8%
|
0.03
1,026
K 7,575, IV 16.2%
|
0.02
772
K 7,879, IV 12.4%
|
⚠ 0.36
7,584
K 8,194, IV 11.5%
|
⚠ 0.79
6,591
K 8,523, IV 12.8%
|
⚠ 1.15
3,610
K 8,864, IV 14.3%
|
⚠ 1.44
1,701
K 9,219, IV 15.8%
|
⚠ 1.70
745
K 9,589, IV 17.1%
|
⚠ 1.93
312
K 9,973, IV 18.4%
|
| 91d |
⚠ 0.25
2,527
K 5,777, IV 33.3%
|
0.23
2,967
K 6,008, IV 31.4%
|
0.20
3,406
K 6,249, IV 29.3%
|
0.17
3,778
K 6,499, IV 27.1%
|
0.14
3,956
K 6,759, IV 24.7%
|
0.10
3,718
K 7,030, IV 22.1%
|
0.06
2,723
K 7,312, IV 19.3%
|
0.01
827
K 7,605, IV 16.3%
|
0.01
518
K 7,910, IV 13.3%
|
0.18
7,238
K 8,227, IV 11.9%
|
⚠ 0.46
9,441
K 8,556, IV 12.5%
|
⚠ 0.71
6,897
K 8,899, IV 13.6%
|
⚠ 0.92
4,189
K 9,256, IV 14.9%
|
⚠ 1.10
2,352
K 9,626, IV 16.1%
|
⚠ 1.26
1,266
K 10,012, IV 17.3%
|
| 180d |
0.11
4,504
K 5,830, IV 30.0%
|
0.10
4,797
K 6,064, IV 28.4%
|
0.08
4,962
K 6,307, IV 26.7%
|
0.07
4,908
K 6,560, IV 25.0%
|
0.05
4,510
K 6,823, IV 23.1%
|
0.04
3,622
K 7,096, IV 21.2%
|
0.02
2,171
K 7,380, IV 19.2%
|
0.00
487
K 7,676, IV 17.1%
|
0.00
223
K 7,984, IV 15.0%
|
0.04
4,476
K 8,303, IV 13.5%
|
0.13
10,891
K 8,636, IV 12.9%
|
⚠ 0.25
12,886
K 8,982, IV 13.1%
|
⚠ 0.37
11,131
K 9,342, IV 13.8%
|
⚠ 0.48
8,334
K 9,716, IV 14.5%
|
⚠ 0.57
5,807
K 10,106, IV 15.3%
|
| 365d |
0.04
6,324
K 5,957, IV 27.1%
|
0.03
6,179
K 6,195, IV 25.9%
|
0.03
5,803
K 6,443, IV 24.7%
|
0.02
5,140
K 6,702, IV 23.5%
|
0.02
4,150
K 6,970, IV 22.3%
|
0.01
2,852
K 7,249, IV 21.0%
|
0.00
1,389
K 7,540, IV 19.7%
|
0.00
166
K 7,842, IV 18.3%
|
0.00
−4
K 8,156, IV 17.0%
|
0.01
2,017
K 8,483, IV 15.9%
|
0.02
6,778
K 8,823, IV 14.9%
|
0.05
12,688
K 9,176, IV 14.3%
|
0.09
16,761
K 9,544, IV 14.0%
|
0.13
17,631
K 9,927, IV 14.1%
|
0.18
16,054
K 10,324, IV 14.3%
|
Hover or focus a cell (arrow keys move) for its strike, IV and z-score.
Each cell: the vomma P&L ratio on top, the second-order share of a vol move's P&L with Δσ the surface's per-maturity shock; shading (cividis) runs from 0 to the 0.25 threshold; under it, Black–Scholes vomma (∂²V/∂σ², per unit index, per (1.00 vol)²). Outlined cells marked ⚠ exceed the threshold (the surface's own rule). Unstable nodes by maturity: 14d 6, 30d 9, 60d 10, 91d 6, 180d 4, 365d 0.
| T | −0.30 | −0.26 | −0.22 | −0.18 | −0.14 | −0.10 | −0.06 | −0.03 | +0.01 | +0.05 | +0.09 | +0.13 | +0.17 | +0.21 | +0.25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14d | T 14d · ln(K/F) −0.300: no stored Greeks | T 14d · ln(K/F) −0.261: no stored Greeks | 34.8; T 14d · ln(K/F) −0.221 · K 6,198 · IV 34.8% · IV 34.8 | 32.3; T 14d · ln(K/F) −0.182 · K 6,447 · IV 32.3% · IV 32.3 | 29.5; T 14d · ln(K/F) −0.143 · K 6,705 · IV 29.5% · IV 29.5 | 26.3; T 14d · ln(K/F) −0.104 · K 6,974 · IV 26.3% · IV 26.3 | 22.5; T 14d · ln(K/F) −0.064 · K 7,253 · IV 22.5% · IV 22.5 | 17.6; T 14d · ln(K/F) −0.025 · K 7,544 · IV 17.6% · IV 17.6 | 11.5; T 14d · ln(K/F) +0.014 · K 7,846 · IV 11.5% · IV 11.5 | 12.2; T 14d · ln(K/F) +0.054 · K 8,160 · IV 12.2% · IV 12.2 | T 14d · ln(K/F) +0.093: no stored Greeks | T 14d · ln(K/F) +0.132: no stored Greeks | T 14d · ln(K/F) +0.171: no stored Greeks | T 14d · ln(K/F) +0.211: no stored Greeks | T 14d · ln(K/F) +0.250: no stored Greeks |
| 30d | 37.8; T 30d · ln(K/F) −0.300 · K 5,738 · IV 37.8% · IV 37.8 | 35.7; T 30d · ln(K/F) −0.261 · K 5,968 · IV 35.7% · IV 35.7 | 33.3; T 30d · ln(K/F) −0.221 · K 6,207 · IV 33.3% · IV 33.3 | 30.8; T 30d · ln(K/F) −0.182 · K 6,455 · IV 30.8% · IV 30.8 | 28.0; T 30d · ln(K/F) −0.143 · K 6,714 · IV 28.0% · IV 28.0 | 24.8; T 30d · ln(K/F) −0.104 · K 6,983 · IV 24.8% · IV 24.8 | 21.1; T 30d · ln(K/F) −0.064 · K 7,263 · IV 21.1% · IV 21.1 | 16.6; T 30d · ln(K/F) −0.025 · K 7,554 · IV 16.6% · IV 16.6 | 11.6; T 30d · ln(K/F) +0.014 · K 7,857 · IV 11.6% · IV 11.6 | 11.7; T 30d · ln(K/F) +0.054 · K 8,171 · IV 11.7% · IV 11.7 | 13.6; T 30d · ln(K/F) +0.093 · K 8,499 · IV 13.6% · IV 13.6 | 15.3; T 30d · ln(K/F) +0.132 · K 8,839 · IV 15.3% · IV 15.3 | T 30d · ln(K/F) +0.171: no stored Greeks | T 30d · ln(K/F) +0.211: no stored Greeks | T 30d · ln(K/F) +0.250: no stored Greeks |
| 60d | 35.3; T 60d · ln(K/F) −0.300 · K 5,754 · IV 35.3% · IV 35.3 | 33.2; T 60d · ln(K/F) −0.261 · K 5,984 · IV 33.2% · IV 33.2 | 31.0; T 60d · ln(K/F) −0.221 · K 6,224 · IV 31.0% · IV 31.0 | 28.6; T 60d · ln(K/F) −0.182 · K 6,474 · IV 28.6% · IV 28.6 | 26.0; T 60d · ln(K/F) −0.143 · K 6,733 · IV 26.0% · IV 26.0 | 23.1; T 60d · ln(K/F) −0.104 · K 7,003 · IV 23.1% · IV 23.1 | 19.8; T 60d · ln(K/F) −0.064 · K 7,283 · IV 19.8% · IV 19.8 | 16.2; T 60d · ln(K/F) −0.025 · K 7,575 · IV 16.2% · IV 16.2 | 12.4; T 60d · ln(K/F) +0.014 · K 7,879 · IV 12.4% · IV 12.4 | 11.5; T 60d · ln(K/F) +0.054 · K 8,194 · IV 11.5% · IV 11.5 | 12.8; T 60d · ln(K/F) +0.093 · K 8,523 · IV 12.8% · IV 12.8 | 14.3; T 60d · ln(K/F) +0.132 · K 8,864 · IV 14.3% · IV 14.3 | 15.8; T 60d · ln(K/F) +0.171 · K 9,219 · IV 15.8% · IV 15.8 | 17.1; T 60d · ln(K/F) +0.211 · K 9,589 · IV 17.1% · IV 17.1 | 18.4; T 60d · ln(K/F) +0.250 · K 9,973 · IV 18.4% · IV 18.4 |
| 91d | 33.3; T 91d · ln(K/F) −0.300 · K 5,777 · IV 33.3% · IV 33.3 | 31.4; T 91d · ln(K/F) −0.261 · K 6,008 · IV 31.4% · IV 31.4 | 29.3; T 91d · ln(K/F) −0.221 · K 6,249 · IV 29.3% · IV 29.3 | 27.1; T 91d · ln(K/F) −0.182 · K 6,499 · IV 27.1% · IV 27.1 | 24.7; T 91d · ln(K/F) −0.143 · K 6,759 · IV 24.7% · IV 24.7 | 22.1; T 91d · ln(K/F) −0.104 · K 7,030 · IV 22.1% · IV 22.1 | 19.3; T 91d · ln(K/F) −0.064 · K 7,312 · IV 19.3% · IV 19.3 | 16.3; T 91d · ln(K/F) −0.025 · K 7,605 · IV 16.3% · IV 16.3 | 13.3; T 91d · ln(K/F) +0.014 · K 7,910 · IV 13.3% · IV 13.3 | 11.9; T 91d · ln(K/F) +0.054 · K 8,227 · IV 11.9% · IV 11.9 | 12.5; T 91d · ln(K/F) +0.093 · K 8,556 · IV 12.5% · IV 12.5 | 13.6; T 91d · ln(K/F) +0.132 · K 8,899 · IV 13.6% · IV 13.6 | 14.9; T 91d · ln(K/F) +0.171 · K 9,256 · IV 14.9% · IV 14.9 | 16.1; T 91d · ln(K/F) +0.211 · K 9,626 · IV 16.1% · IV 16.1 | 17.3; T 91d · ln(K/F) +0.250 · K 10,012 · IV 17.3% · IV 17.3 |
| 180d | 30.0; T 180d · ln(K/F) −0.300 · K 5,830 · IV 30.0% · IV 30.0 | 28.4; T 180d · ln(K/F) −0.261 · K 6,064 · IV 28.4% · IV 28.4 | 26.7; T 180d · ln(K/F) −0.221 · K 6,307 · IV 26.7% · IV 26.7 | 25.0; T 180d · ln(K/F) −0.182 · K 6,560 · IV 25.0% · IV 25.0 | 23.1; T 180d · ln(K/F) −0.143 · K 6,823 · IV 23.1% · IV 23.1 | 21.2; T 180d · ln(K/F) −0.104 · K 7,096 · IV 21.2% · IV 21.2 | 19.2; T 180d · ln(K/F) −0.064 · K 7,380 · IV 19.2% · IV 19.2 | 17.1; T 180d · ln(K/F) −0.025 · K 7,676 · IV 17.1% · IV 17.1 | 15.0; T 180d · ln(K/F) +0.014 · K 7,984 · IV 15.0% · IV 15.0 | 13.5; T 180d · ln(K/F) +0.054 · K 8,303 · IV 13.5% · IV 13.5 | 12.9; T 180d · ln(K/F) +0.093 · K 8,636 · IV 12.9% · IV 12.9 | 13.1; T 180d · ln(K/F) +0.132 · K 8,982 · IV 13.1% · IV 13.1 | 13.8; T 180d · ln(K/F) +0.171 · K 9,342 · IV 13.8% · IV 13.8 | 14.5; T 180d · ln(K/F) +0.211 · K 9,716 · IV 14.5% · IV 14.5 | 15.3; T 180d · ln(K/F) +0.250 · K 10,106 · IV 15.3% · IV 15.3 |
| 365d | 27.1; T 365d · ln(K/F) −0.300 · K 5,957 · IV 27.1% · IV 27.1 | 25.9; T 365d · ln(K/F) −0.261 · K 6,195 · IV 25.9% · IV 25.9 | 24.7; T 365d · ln(K/F) −0.221 · K 6,443 · IV 24.7% · IV 24.7 | 23.5; T 365d · ln(K/F) −0.182 · K 6,702 · IV 23.5% · IV 23.5 | 22.3; T 365d · ln(K/F) −0.143 · K 6,970 · IV 22.3% · IV 22.3 | 21.0; T 365d · ln(K/F) −0.104 · K 7,249 · IV 21.0% · IV 21.0 | 19.7; T 365d · ln(K/F) −0.064 · K 7,540 · IV 19.7% · IV 19.7 | 18.3; T 365d · ln(K/F) −0.025 · K 7,842 · IV 18.3% · IV 18.3 | 17.0; T 365d · ln(K/F) +0.014 · K 8,156 · IV 17.0% · IV 17.0 | 15.9; T 365d · ln(K/F) +0.054 · K 8,483 · IV 15.9% · IV 15.9 | 14.9; T 365d · ln(K/F) +0.093 · K 8,823 · IV 14.9% · IV 14.9 | 14.3; T 365d · ln(K/F) +0.132 · K 9,176 · IV 14.3% · IV 14.3 | 14.0; T 365d · ln(K/F) +0.171 · K 9,544 · IV 14.0% · IV 14.0 | 14.1; T 365d · ln(K/F) +0.211 · K 9,927 · IV 14.1% · IV 14.1 | 14.3; T 365d · ln(K/F) +0.250 · K 10,324 · IV 14.3% · IV 14.3 |
Hover or focus a cell (arrow keys move) for its details.
| T | −0.30 | −0.26 | −0.22 | −0.18 | −0.14 | −0.10 | −0.06 | −0.03 | +0.01 | +0.05 | +0.09 | +0.13 | +0.17 | +0.21 | +0.25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14d | T 14d · ln(K/F) −0.300: no stored Greeks | T 14d · ln(K/F) −0.261: no stored Greeks | 2.8; T 14d · ln(K/F) −0.221 · K 6,198 · IV 34.8% · Vega 2.8 | 8.7; T 14d · ln(K/F) −0.182 · K 6,447 · IV 32.3% · Vega 8.7 | 26.3; T 14d · ln(K/F) −0.143 · K 6,705 · IV 29.5% · Vega 26.3 | 75.7; T 14d · ln(K/F) −0.104 · K 6,974 · IV 26.3% · Vega 75.7 | 201.5; T 14d · ln(K/F) −0.064 · K 7,253 · IV 22.5% · Vega 201.5 | 458.1; T 14d · ln(K/F) −0.025 · K 7,544 · IV 17.6% · Vega 458.1 | 496.7; T 14d · ln(K/F) +0.014 · K 7,846 · IV 11.5% · Vega 496.7 | 50.5; T 14d · ln(K/F) +0.054 · K 8,160 · IV 12.2% · Vega 50.5 | T 14d · ln(K/F) +0.093: no stored Greeks | T 14d · ln(K/F) +0.132: no stored Greeks | T 14d · ln(K/F) +0.171: no stored Greeks | T 14d · ln(K/F) +0.211: no stored Greeks | T 14d · ln(K/F) +0.250: no stored Greeks |
| 30d | 16.6; T 30d · ln(K/F) −0.300 · K 5,738 · IV 37.8% · Vega 16.6 | 30.0; T 30d · ln(K/F) −0.261 · K 5,968 · IV 35.7% · Vega 30.0 | 54.0; T 30d · ln(K/F) −0.221 · K 6,207 · IV 33.3% · Vega 54.0 | 96.1; T 30d · ln(K/F) −0.182 · K 6,455 · IV 30.8% · Vega 96.1 | 168.9; T 30d · ln(K/F) −0.143 · K 6,714 · IV 28.0% · Vega 168.9 | 291.1; T 30d · ln(K/F) −0.104 · K 6,983 · IV 24.8% · Vega 291.1 | 486.8; T 30d · ln(K/F) −0.064 · K 7,263 · IV 21.1% · Vega 486.8 | 759.4; T 30d · ln(K/F) −0.025 · K 7,554 · IV 16.6% · Vega 759.4 | 811.3; T 30d · ln(K/F) +0.014 · K 7,857 · IV 11.6% · Vega 811.3 | 254.4; T 30d · ln(K/F) +0.054 · K 8,171 · IV 11.7% · Vega 254.4 | 54.0; T 30d · ln(K/F) +0.093 · K 8,499 · IV 13.6% · Vega 54.0 | 10.4; T 30d · ln(K/F) +0.132 · K 8,839 · IV 15.3% · Vega 10.4 | T 30d · ln(K/F) +0.171: no stored Greeks | T 30d · ln(K/F) +0.211: no stored Greeks | T 30d · ln(K/F) +0.250: no stored Greeks |
| 60d | 119.0; T 60d · ln(K/F) −0.300 · K 5,754 · IV 35.3% · Vega 119.0 | 167.7; T 60d · ln(K/F) −0.261 · K 5,984 · IV 33.2% · Vega 167.7 | 235.7; T 60d · ln(K/F) −0.221 · K 6,224 · IV 31.0% · Vega 235.7 | 330.5; T 60d · ln(K/F) −0.182 · K 6,474 · IV 28.6% · Vega 330.5 | 461.7; T 60d · ln(K/F) −0.143 · K 6,733 · IV 26.0% · Vega 461.7 | 640.8; T 60d · ln(K/F) −0.104 · K 7,003 · IV 23.1% · Vega 640.8 | 876.7; T 60d · ln(K/F) −0.064 · K 7,283 · IV 19.8% · Vega 876.7 | 1,145.2; T 60d · ln(K/F) −0.025 · K 7,575 · IV 16.2% · Vega 1,145.2 | 1,207.1; T 60d · ln(K/F) +0.014 · K 7,879 · IV 12.4% · Vega 1,207.1 | 663.3; T 60d · ln(K/F) +0.054 · K 8,194 · IV 11.5% · Vega 663.3 | 262.8; T 60d · ln(K/F) +0.093 · K 8,523 · IV 12.8% · Vega 262.8 | 99.6; T 60d · ln(K/F) +0.132 · K 8,864 · IV 14.3% · Vega 99.6 | 37.3; T 60d · ln(K/F) +0.171 · K 9,219 · IV 15.8% · Vega 37.3 | 13.8; T 60d · ln(K/F) +0.211 · K 9,589 · IV 17.1% · Vega 13.8 | 5.1; T 60d · ln(K/F) +0.250 · K 9,973 · IV 18.4% · Vega 5.1 |
| 91d | 259.7; T 91d · ln(K/F) −0.300 · K 5,777 · IV 33.3% · Vega 259.7 | 336.8; T 91d · ln(K/F) −0.261 · K 6,008 · IV 31.4% · Vega 336.8 | 436.5; T 91d · ln(K/F) −0.221 · K 6,249 · IV 29.3% · Vega 436.5 | 565.3; T 91d · ln(K/F) −0.182 · K 6,499 · IV 27.1% · Vega 565.3 | 730.6; T 91d · ln(K/F) −0.143 · K 6,759 · IV 24.7% · Vega 730.6 | 939.4; T 91d · ln(K/F) −0.104 · K 7,030 · IV 22.1% · Vega 939.4 | 1,191.0; T 91d · ln(K/F) −0.064 · K 7,312 · IV 19.3% · Vega 1,191.0 | 1,447.0; T 91d · ln(K/F) −0.025 · K 7,605 · IV 16.3% · Vega 1,447.0 | 1,512.1; T 91d · ln(K/F) +0.014 · K 7,910 · IV 13.3% · Vega 1,512.1 | 1,047.8; T 91d · ln(K/F) +0.054 · K 8,227 · IV 11.9% · Vega 1,047.8 | 529.1; T 91d · ln(K/F) +0.093 · K 8,556 · IV 12.5% · Vega 529.1 | 250.2; T 91d · ln(K/F) +0.132 · K 8,899 · IV 13.6% · Vega 250.2 | 117.5; T 91d · ln(K/F) +0.171 · K 9,256 · IV 14.9% · Vega 117.5 | 55.2; T 91d · ln(K/F) +0.211 · K 9,626 · IV 16.1% · Vega 55.2 | 26.0; T 91d · ln(K/F) +0.250 · K 10,012 · IV 17.3% · Vega 26.0 |
| 180d | 671.3; T 180d · ln(K/F) −0.300 · K 5,830 · IV 30.0% · Vega 671.3 | 803.0; T 180d · ln(K/F) −0.261 · K 6,064 · IV 28.4% · Vega 803.0 | 959.8; T 180d · ln(K/F) −0.221 · K 6,307 · IV 26.7% · Vega 959.8 | 1,145.2; T 180d · ln(K/F) −0.182 · K 6,560 · IV 25.0% · Vega 1,145.2 | 1,361.1; T 180d · ln(K/F) −0.143 · K 6,823 · IV 23.1% · Vega 1,361.1 | 1,604.8; T 180d · ln(K/F) −0.104 · K 7,096 · IV 21.2% · Vega 1,604.8 | 1,861.0; T 180d · ln(K/F) −0.064 · K 7,380 · IV 19.2% · Vega 1,861.0 | 2,082.4; T 180d · ln(K/F) −0.025 · K 7,676 · IV 17.1% · Vega 2,082.4 | 2,151.5; T 180d · ln(K/F) +0.014 · K 7,984 · IV 15.0% · Vega 2,151.5 | 1,886.1; T 180d · ln(K/F) +0.054 · K 8,303 · IV 13.5% · Vega 1,886.1 | 1,333.9; T 180d · ln(K/F) +0.093 · K 8,636 · IV 12.9% · Vega 1,333.9 | 825.9; T 180d · ln(K/F) +0.132 · K 8,982 · IV 13.1% · Vega 825.9 | 487.6; T 180d · ln(K/F) +0.171 · K 9,342 · IV 13.8% · Vega 487.6 | 284.3; T 180d · ln(K/F) +0.211 · K 9,716 · IV 14.5% · Vega 284.3 | 165.7; T 180d · ln(K/F) +0.250 · K 10,106 · IV 15.3% · Vega 165.7 |
| 365d | 1,417.2; T 365d · ln(K/F) −0.300 · K 5,957 · IV 27.1% · Vega 1,417.2 | 1,611.1; T 365d · ln(K/F) −0.261 · K 6,195 · IV 25.9% · Vega 1,611.1 | 1,826.3; T 365d · ln(K/F) −0.221 · K 6,443 · IV 24.7% · Vega 1,826.3 | 2,061.1; T 365d · ln(K/F) −0.182 · K 6,702 · IV 23.5% · Vega 2,061.1 | 2,310.9; T 365d · ln(K/F) −0.143 · K 6,970 · IV 22.3% · Vega 2,310.9 | 2,565.1; T 365d · ln(K/F) −0.104 · K 7,249 · IV 21.0% · Vega 2,565.1 | 2,803.4; T 365d · ln(K/F) −0.064 · K 7,540 · IV 19.7% · Vega 2,803.4 | 2,990.1; T 365d · ln(K/F) −0.025 · K 7,842 · IV 18.3% · Vega 2,990.1 | 3,068.8; T 365d · ln(K/F) +0.014 · K 8,156 · IV 17.0% · Vega 3,068.8 | 2,968.0; T 365d · ln(K/F) +0.054 · K 8,483 · IV 15.9% · Vega 2,968.0 | 2,640.2; T 365d · ln(K/F) +0.093 · K 8,823 · IV 14.9% · Vega 2,640.2 | 2,132.2; T 365d · ln(K/F) +0.132 · K 9,176 · IV 14.3% · Vega 2,132.2 | 1,581.7; T 365d · ln(K/F) +0.171 · K 9,544 · IV 14.0% · Vega 1,581.7 | 1,107.4; T 365d · ln(K/F) +0.211 · K 9,927 · IV 14.1% · Vega 1,107.4 | 749.6; T 365d · ln(K/F) +0.250 · K 10,324 · IV 14.3% · Vega 749.6 |
Hover or focus a cell (arrow keys move) for its details.
| T | −0.30 | −0.26 | −0.22 | −0.18 | −0.14 | −0.10 | −0.06 | −0.03 | +0.01 | +0.05 | +0.09 | +0.13 | +0.17 | +0.21 | +0.25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14d | T 14d · ln(K/F) −0.300: no stored Greeks | T 14d · ln(K/F) −0.261: no stored Greeks | −0.017; T 14d · ln(K/F) −0.221 · K 6,198 · IV 34.8% · Vanna −0.017 | −0.051; T 14d · ln(K/F) −0.182 · K 6,447 · IV 32.3% · Vanna −0.051 | −0.144; T 14d · ln(K/F) −0.143 · K 6,705 · IV 29.5% · Vanna −0.144 | −0.377; T 14d · ln(K/F) −0.104 · K 6,974 · IV 26.3% · Vanna −0.377 | −0.849; T 14d · ln(K/F) −0.064 · K 7,253 · IV 22.5% · Vanna −0.849 | −1.215; T 14d · ln(K/F) −0.025 · K 7,544 · IV 17.6% · Vanna −1.215 | +1.843; T 14d · ln(K/F) +0.014 · K 7,846 · IV 11.5% · Vanna +1.843 | +0.613; T 14d · ln(K/F) +0.054 · K 8,160 · IV 12.2% · Vanna +0.613 | T 14d · ln(K/F) +0.093: no stored Greeks | T 14d · ln(K/F) +0.132: no stored Greeks | T 14d · ln(K/F) +0.171: no stored Greeks | T 14d · ln(K/F) +0.211: no stored Greeks | T 14d · ln(K/F) +0.250: no stored Greeks |
| 30d | −0.053; T 30d · ln(K/F) −0.300 · K 5,738 · IV 37.8% · Vanna −0.053 | −0.095; T 30d · ln(K/F) −0.261 · K 5,968 · IV 35.7% · Vanna −0.095 | −0.165; T 30d · ln(K/F) −0.221 · K 6,207 · IV 33.3% · Vanna −0.165 | −0.284; T 30d · ln(K/F) −0.182 · K 6,455 · IV 30.8% · Vanna −0.284 | −0.472; T 30d · ln(K/F) −0.143 · K 6,714 · IV 28.0% · Vanna −0.472 | −0.749; T 30d · ln(K/F) −0.104 · K 6,983 · IV 24.8% · Vanna −0.749 | −1.069; T 30d · ln(K/F) −0.064 · K 7,263 · IV 21.1% · Vanna −1.069 | −1.033; T 30d · ln(K/F) −0.025 · K 7,554 · IV 16.6% · Vanna −1.033 | +1.397; T 30d · ln(K/F) +0.014 · K 7,857 · IV 11.6% · Vanna +1.397 | +1.575; T 30d · ln(K/F) +0.054 · K 8,171 · IV 11.7% · Vanna +1.575 | +0.430; T 30d · ln(K/F) +0.093 · K 8,499 · IV 13.6% · Vanna +0.430 | +0.092; T 30d · ln(K/F) +0.132 · K 8,839 · IV 15.3% · Vanna +0.092 | T 30d · ln(K/F) +0.171: no stored Greeks | T 30d · ln(K/F) +0.211: no stored Greeks | T 30d · ln(K/F) +0.250: no stored Greeks |
| 60d | −0.217; T 60d · ln(K/F) −0.300 · K 5,754 · IV 35.3% · Vanna −0.217 | −0.301; T 60d · ln(K/F) −0.261 · K 5,984 · IV 33.2% · Vanna −0.301 | −0.412; T 60d · ln(K/F) −0.221 · K 6,224 · IV 31.0% · Vanna −0.412 | −0.558; T 60d · ln(K/F) −0.182 · K 6,474 · IV 28.6% · Vanna −0.558 | −0.739; T 60d · ln(K/F) −0.143 · K 6,733 · IV 26.0% · Vanna −0.739 | −0.939; T 60d · ln(K/F) −0.104 · K 7,003 · IV 23.1% · Vanna −0.939 | −1.071; T 60d · ln(K/F) −0.064 · K 7,283 · IV 19.8% · Vanna −1.071 | −0.788; T 60d · ln(K/F) −0.025 · K 7,575 · IV 16.2% · Vanna −0.788 | +0.953; T 60d · ln(K/F) +0.014 · K 7,879 · IV 12.4% · Vanna +0.953 | +2.149; T 60d · ln(K/F) +0.054 · K 8,194 · IV 11.5% · Vanna +2.149 | +1.189; T 60d · ln(K/F) +0.093 · K 8,523 · IV 12.8% · Vanna +1.189 | +0.511; T 60d · ln(K/F) +0.132 · K 8,864 · IV 14.3% · Vanna +0.511 | +0.204; T 60d · ln(K/F) +0.171 · K 9,219 · IV 15.8% · Vanna +0.204 | +0.079; T 60d · ln(K/F) +0.211 · K 9,589 · IV 17.1% · Vanna +0.079 | +0.030; T 60d · ln(K/F) +0.250 · K 9,973 · IV 18.4% · Vanna +0.030 |
| 91d | −0.347; T 91d · ln(K/F) −0.300 · K 5,777 · IV 33.3% · Vanna −0.347 | −0.440; T 91d · ln(K/F) −0.261 · K 6,008 · IV 31.4% · Vanna −0.440 | −0.555; T 91d · ln(K/F) −0.221 · K 6,249 · IV 29.3% · Vanna −0.555 | −0.691; T 91d · ln(K/F) −0.182 · K 6,499 · IV 27.1% · Vanna −0.691 | −0.839; T 91d · ln(K/F) −0.143 · K 6,759 · IV 24.7% · Vanna −0.839 | −0.969; T 91d · ln(K/F) −0.104 · K 7,030 · IV 22.1% · Vanna −0.969 | −0.986; T 91d · ln(K/F) −0.064 · K 7,312 · IV 19.3% · Vanna −0.986 | −0.614; T 91d · ln(K/F) −0.025 · K 7,605 · IV 16.3% · Vanna −0.614 | +0.733; T 91d · ln(K/F) +0.014 · K 7,910 · IV 13.3% · Vanna +0.733 | +2.138; T 91d · ln(K/F) +0.054 · K 8,227 · IV 11.9% · Vanna +2.138 | +1.672; T 91d · ln(K/F) +0.093 · K 8,556 · IV 12.5% · Vanna +1.672 | +0.936; T 91d · ln(K/F) +0.132 · K 8,899 · IV 13.6% · Vanna +0.936 | +0.478; T 91d · ln(K/F) +0.171 · K 9,256 · IV 14.9% · Vanna +0.478 | +0.236; T 91d · ln(K/F) +0.211 · K 9,626 · IV 16.1% · Vanna +0.236 | +0.115; T 91d · ln(K/F) +0.250 · K 10,012 · IV 17.3% · Vanna +0.115 |
| 180d | −0.542; T 180d · ln(K/F) −0.300 · K 5,830 · IV 30.0% · Vanna −0.542 | −0.627; T 180d · ln(K/F) −0.261 · K 6,064 · IV 28.4% · Vanna −0.627 | −0.717; T 180d · ln(K/F) −0.221 · K 6,307 · IV 26.7% · Vanna −0.717 | −0.801; T 180d · ln(K/F) −0.182 · K 6,560 · IV 25.0% · Vanna −0.801 | −0.863; T 180d · ln(K/F) −0.143 · K 6,823 · IV 23.1% · Vanna −0.863 | −0.865; T 180d · ln(K/F) −0.104 · K 7,096 · IV 21.2% · Vanna −0.865 | −0.733; T 180d · ln(K/F) −0.064 · K 7,380 · IV 19.2% · Vanna −0.733 | −0.334; T 180d · ln(K/F) −0.025 · K 7,676 · IV 17.1% · Vanna −0.334 | +0.495; T 180d · ln(K/F) +0.014 · K 7,984 · IV 15.0% · Vanna +0.495 | +1.583; T 180d · ln(K/F) +0.054 · K 8,303 · IV 13.5% · Vanna +1.583 | +2.041; T 180d · ln(K/F) +0.093 · K 8,636 · IV 12.9% · Vanna +2.041 | +1.709; T 180d · ln(K/F) +0.132 · K 8,982 · IV 13.1% · Vanna +1.709 | +1.187; T 180d · ln(K/F) +0.171 · K 9,342 · IV 13.8% · Vanna +1.187 | +0.761; T 180d · ln(K/F) +0.211 · K 9,716 · IV 14.5% · Vanna +0.761 | +0.471; T 180d · ln(K/F) +0.250 · K 10,106 · IV 15.3% · Vanna +0.471 |
| 365d | −0.657; T 365d · ln(K/F) −0.300 · K 5,957 · IV 27.1% · Vanna −0.657 | −0.703; T 365d · ln(K/F) −0.261 · K 6,195 · IV 25.9% · Vanna −0.703 | −0.736; T 365d · ln(K/F) −0.221 · K 6,443 · IV 24.7% · Vanna −0.736 | −0.744; T 365d · ln(K/F) −0.182 · K 6,702 · IV 23.5% · Vanna −0.744 | −0.712; T 365d · ln(K/F) −0.143 · K 6,970 · IV 22.3% · Vanna −0.712 | −0.615; T 365d · ln(K/F) −0.104 · K 7,249 · IV 21.0% · Vanna −0.615 | −0.422; T 365d · ln(K/F) −0.064 · K 7,540 · IV 19.7% · Vanna −0.422 | −0.094; T 365d · ln(K/F) −0.025 · K 7,842 · IV 18.3% · Vanna −0.094 | +0.393; T 365d · ln(K/F) +0.014 · K 8,156 · IV 17.0% · Vanna +0.393 | +1.008; T 365d · ln(K/F) +0.054 · K 8,483 · IV 15.9% · Vanna +1.008 | +1.596; T 365d · ln(K/F) +0.093 · K 8,823 · IV 14.9% · Vanna +1.596 | +1.920; T 365d · ln(K/F) +0.132 · K 9,176 · IV 14.3% · Vanna +1.920 | +1.880; T 365d · ln(K/F) +0.171 · K 9,544 · IV 14.0% · Vanna +1.880 | +1.595; T 365d · ln(K/F) +0.211 · K 9,927 · IV 14.1% · Vanna +1.595 | +1.235; T 365d · ln(K/F) +0.250 · K 10,324 · IV 14.3% · Vanna +1.235 |
Hover or focus a cell (arrow keys move) for its details.
| T | −0.30 | −0.26 | −0.22 | −0.18 | −0.14 | −0.10 | −0.06 | −0.03 | +0.01 | +0.05 | +0.09 | +0.13 | +0.17 | +0.21 | +0.25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14d | T 14d · ln(K/F) −0.300: no stored Greeks | T 14d · ln(K/F) −0.261: no stored Greeks | 0.00; T 14d · ln(K/F) −0.221 · K 6,198 · IV 34.8% · OTM delta 0.00 (put) | 0.00; T 14d · ln(K/F) −0.182 · K 6,447 · IV 32.3% · OTM delta 0.00 (put) | −0.01; T 14d · ln(K/F) −0.143 · K 6,705 · IV 29.5% · OTM delta −0.01 (put) | −0.02; T 14d · ln(K/F) −0.104 · K 6,974 · IV 26.3% · OTM delta −0.02 (put) | −0.07; T 14d · ln(K/F) −0.064 · K 7,253 · IV 22.5% · OTM delta −0.07 (put) | −0.23; T 14d · ln(K/F) −0.025 · K 7,544 · IV 17.6% · OTM delta −0.23 (put) | +0.27; T 14d · ln(K/F) +0.014 · K 7,846 · IV 11.5% · OTM delta +0.27 (call) | +0.01; T 14d · ln(K/F) +0.054 · K 8,160 · IV 12.2% · OTM delta +0.01 (call) | T 14d · ln(K/F) +0.093: no stored Greeks | T 14d · ln(K/F) +0.132: no stored Greeks | T 14d · ln(K/F) +0.171: no stored Greeks | T 14d · ln(K/F) +0.211: no stored Greeks | T 14d · ln(K/F) +0.250: no stored Greeks |
| 30d | 0.00; T 30d · ln(K/F) −0.300 · K 5,738 · IV 37.8% · OTM delta 0.00 (put) | 0.00; T 30d · ln(K/F) −0.261 · K 5,968 · IV 35.7% · OTM delta 0.00 (put) | −0.01; T 30d · ln(K/F) −0.221 · K 6,207 · IV 33.3% · OTM delta −0.01 (put) | −0.02; T 30d · ln(K/F) −0.182 · K 6,455 · IV 30.8% · OTM delta −0.02 (put) | −0.03; T 30d · ln(K/F) −0.143 · K 6,714 · IV 28.0% · OTM delta −0.03 (put) | −0.07; T 30d · ln(K/F) −0.104 · K 6,983 · IV 24.8% · OTM delta −0.07 (put) | −0.14; T 30d · ln(K/F) −0.064 · K 7,263 · IV 21.1% · OTM delta −0.14 (put) | −0.29; T 30d · ln(K/F) −0.025 · K 7,554 · IV 16.6% · OTM delta −0.29 (put) | +0.34; T 30d · ln(K/F) +0.014 · K 7,857 · IV 11.6% · OTM delta +0.34 (call) | +0.06; T 30d · ln(K/F) +0.054 · K 8,171 · IV 11.7% · OTM delta +0.06 (call) | +0.01; T 30d · ln(K/F) +0.093 · K 8,499 · IV 13.6% · OTM delta +0.01 (call) | 0.00; T 30d · ln(K/F) +0.132 · K 8,839 · IV 15.3% · OTM delta 0.00 (call) | T 30d · ln(K/F) +0.171: no stored Greeks | T 30d · ln(K/F) +0.211: no stored Greeks | T 30d · ln(K/F) +0.250: no stored Greeks |
| 60d | −0.02; T 60d · ln(K/F) −0.300 · K 5,754 · IV 35.3% · OTM delta −0.02 (put) | −0.02; T 60d · ln(K/F) −0.261 · K 5,984 · IV 33.2% · OTM delta −0.02 (put) | −0.03; T 60d · ln(K/F) −0.221 · K 6,224 · IV 31.0% · OTM delta −0.03 (put) | −0.05; T 60d · ln(K/F) −0.182 · K 6,474 · IV 28.6% · OTM delta −0.05 (put) | −0.08; T 60d · ln(K/F) −0.143 · K 6,733 · IV 26.0% · OTM delta −0.08 (put) | −0.12; T 60d · ln(K/F) −0.104 · K 7,003 · IV 23.1% · OTM delta −0.12 (put) | −0.20; T 60d · ln(K/F) −0.064 · K 7,283 · IV 19.8% · OTM delta −0.20 (put) | −0.34; T 60d · ln(K/F) −0.025 · K 7,575 · IV 16.2% · OTM delta −0.34 (put) | +0.40; T 60d · ln(K/F) +0.014 · K 7,879 · IV 12.4% · OTM delta +0.40 (call) | +0.13; T 60d · ln(K/F) +0.054 · K 8,194 · IV 11.5% · OTM delta +0.13 (call) | +0.04; T 60d · ln(K/F) +0.093 · K 8,523 · IV 12.8% · OTM delta +0.04 (call) | +0.01; T 60d · ln(K/F) +0.132 · K 8,864 · IV 14.3% · OTM delta +0.01 (call) | 0.00; T 60d · ln(K/F) +0.171 · K 9,219 · IV 15.8% · OTM delta 0.00 (call) | 0.00; T 60d · ln(K/F) +0.211 · K 9,589 · IV 17.1% · OTM delta 0.00 (call) | 0.00; T 60d · ln(K/F) +0.250 · K 9,973 · IV 18.4% · OTM delta 0.00 (call) |
| 91d | −0.03; T 91d · ln(K/F) −0.300 · K 5,777 · IV 33.3% · OTM delta −0.03 (put) | −0.04; T 91d · ln(K/F) −0.261 · K 6,008 · IV 31.4% · OTM delta −0.04 (put) | −0.06; T 91d · ln(K/F) −0.221 · K 6,249 · IV 29.3% · OTM delta −0.06 (put) | −0.08; T 91d · ln(K/F) −0.182 · K 6,499 · IV 27.1% · OTM delta −0.08 (put) | −0.11; T 91d · ln(K/F) −0.143 · K 6,759 · IV 24.7% · OTM delta −0.11 (put) | −0.16; T 91d · ln(K/F) −0.104 · K 7,030 · IV 22.1% · OTM delta −0.16 (put) | −0.24; T 91d · ln(K/F) −0.064 · K 7,312 · IV 19.3% · OTM delta −0.24 (put) | −0.36; T 91d · ln(K/F) −0.025 · K 7,605 · IV 16.3% · OTM delta −0.36 (put) | +0.43; T 91d · ln(K/F) +0.014 · K 7,910 · IV 13.3% · OTM delta +0.43 (call) | +0.19; T 91d · ln(K/F) +0.054 · K 8,227 · IV 11.9% · OTM delta +0.19 (call) | +0.07; T 91d · ln(K/F) +0.093 · K 8,556 · IV 12.5% · OTM delta +0.07 (call) | +0.03; T 91d · ln(K/F) +0.132 · K 8,899 · IV 13.6% · OTM delta +0.03 (call) | +0.01; T 91d · ln(K/F) +0.171 · K 9,256 · IV 14.9% · OTM delta +0.01 (call) | 0.00; T 91d · ln(K/F) +0.211 · K 9,626 · IV 16.1% · OTM delta 0.00 (call) | 0.00; T 91d · ln(K/F) +0.250 · K 10,012 · IV 17.3% · OTM delta 0.00 (call) |
| 180d | −0.06; T 180d · ln(K/F) −0.300 · K 5,830 · IV 30.0% · OTM delta −0.06 (put) | −0.08; T 180d · ln(K/F) −0.261 · K 6,064 · IV 28.4% · OTM delta −0.08 (put) | −0.10; T 180d · ln(K/F) −0.221 · K 6,307 · IV 26.7% · OTM delta −0.10 (put) | −0.13; T 180d · ln(K/F) −0.182 · K 6,560 · IV 25.0% · OTM delta −0.13 (put) | −0.17; T 180d · ln(K/F) −0.143 · K 6,823 · IV 23.1% · OTM delta −0.17 (put) | −0.22; T 180d · ln(K/F) −0.104 · K 7,096 · IV 21.2% · OTM delta −0.22 (put) | −0.29; T 180d · ln(K/F) −0.064 · K 7,380 · IV 19.2% · OTM delta −0.29 (put) | −0.39; T 180d · ln(K/F) −0.025 · K 7,676 · IV 17.1% · OTM delta −0.39 (put) | +0.47; T 180d · ln(K/F) +0.014 · K 7,984 · IV 15.0% · OTM delta +0.47 (call) | +0.30; T 180d · ln(K/F) +0.054 · K 8,303 · IV 13.5% · OTM delta +0.30 (call) | +0.16; T 180d · ln(K/F) +0.093 · K 8,636 · IV 12.9% · OTM delta +0.16 (call) | +0.08; T 180d · ln(K/F) +0.132 · K 8,982 · IV 13.1% · OTM delta +0.08 (call) | +0.04; T 180d · ln(K/F) +0.171 · K 9,342 · IV 13.8% · OTM delta +0.04 (call) | +0.02; T 180d · ln(K/F) +0.211 · K 9,716 · IV 14.5% · OTM delta +0.02 (call) | +0.01; T 180d · ln(K/F) +0.250 · K 10,106 · IV 15.3% · OTM delta +0.01 (call) |
| 365d | −0.11; T 365d · ln(K/F) −0.300 · K 5,957 · IV 27.1% · OTM delta −0.11 (put) | −0.13; T 365d · ln(K/F) −0.261 · K 6,195 · IV 25.9% · OTM delta −0.13 (put) | −0.15; T 365d · ln(K/F) −0.221 · K 6,443 · IV 24.7% · OTM delta −0.15 (put) | −0.19; T 365d · ln(K/F) −0.182 · K 6,702 · IV 23.5% · OTM delta −0.19 (put) | −0.23; T 365d · ln(K/F) −0.143 · K 6,970 · IV 22.3% · OTM delta −0.23 (put) | −0.27; T 365d · ln(K/F) −0.104 · K 7,249 · IV 21.0% · OTM delta −0.27 (put) | −0.34; T 365d · ln(K/F) −0.064 · K 7,540 · IV 19.7% · OTM delta −0.34 (put) | −0.41; T 365d · ln(K/F) −0.025 · K 7,842 · IV 18.3% · OTM delta −0.41 (put) | +0.50; T 365d · ln(K/F) +0.014 · K 8,156 · IV 17.0% · OTM delta +0.50 (call) | +0.40; T 365d · ln(K/F) +0.054 · K 8,483 · IV 15.9% · OTM delta +0.40 (call) | +0.29; T 365d · ln(K/F) +0.093 · K 8,823 · IV 14.9% · OTM delta +0.29 (call) | +0.20; T 365d · ln(K/F) +0.132 · K 9,176 · IV 14.3% · OTM delta +0.20 (call) | +0.12; T 365d · ln(K/F) +0.171 · K 9,544 · IV 14.0% · OTM delta +0.12 (call) | +0.08; T 365d · ln(K/F) +0.211 · K 9,927 · IV 14.1% · OTM delta +0.08 (call) | +0.05; T 365d · ln(K/F) +0.250 · K 10,324 · IV 14.3% · OTM delta +0.05 (call) |
Hover or focus a cell (arrow keys move) for its details.
Unstable nodes · ratio > 0.25
| Maturity | ln(K/F) | Vomma P&L ratio | Strike K | IV | Vomma | z |
|---|---|---|---|---|---|---|
| 30d | +0.132 | 2.329 | 8,839 | 15.3% | 609 | −0.85 |
| 60d | +0.250 | 1.935 | 9,973 | 18.4% | 312 | −0.93 |
| 14d | +0.054 | 1.866 | 8,160 | 12.2% | 2,073 | −0.48 |
| 60d | +0.211 | 1.701 | 9,589 | 17.1% | 745 | −0.82 |
| 30d | +0.093 | 1.656 | 8,499 | 13.6% | 2,257 | −0.43 |
| 60d | +0.171 | 1.442 | 9,219 | 15.8% | 1,701 | −0.57 |
| 14d | −0.221 | 1.374 | 6,198 | 34.8% | 84 | −0.99 |
| 91d | +0.250 | 1.258 | 10,012 | 17.3% | 1,266 | −0.68 |
| 14d | −0.182 | 1.167 | 6,447 | 32.3% | 224 | −0.95 |
| 60d | +0.132 | 1.146 | 8,864 | 14.3% | 3,610 | −0.08 |
| 91d | +0.211 | 1.100 | 9,626 | 16.1% | 2,352 | −0.41 |
| 14d | −0.143 | 0.944 | 6,705 | 29.5% | 546 | −0.87 |
| 91d | +0.171 | 0.922 | 9,256 | 14.9% | 4,189 | +0.07 |
| 30d | +0.054 | 0.859 | 8,171 | 11.7% | 5,517 | +0.41 |
| 30d | −0.300 | 0.801 | 5,738 | 37.8% | 335 | −0.92 |
| 60d | +0.093 | 0.793 | 8,523 | 12.8% | 6,591 | +0.69 |
| 30d | −0.261 | 0.722 | 5,968 | 35.7% | 547 | −0.87 |
| 91d | +0.132 | 0.712 | 8,899 | 13.6% | 6,897 | +0.77 |
| 14d | −0.104 | 0.700 | 6,974 | 26.3% | 1,165 | −0.71 |
| 30d | −0.221 | 0.637 | 6,207 | 33.3% | 868 | −0.79 |
| 180d | +0.250 | 0.568 | 10,106 | 15.3% | 5,807 | +0.48 |
| 30d | −0.182 | 0.546 | 6,455 | 30.8% | 1,326 | −0.67 |
| 180d | +0.211 | 0.475 | 9,716 | 14.5% | 8,334 | +1.14 |
| 91d | +0.093 | 0.461 | 8,556 | 12.5% | 9,441 | +1.42 |
| 30d | −0.143 | 0.447 | 6,714 | 28.0% | 1,906 | −0.52 |
| 14d | −0.064 | 0.430 | 7,253 | 22.5% | 1,906 | −0.52 |
| 60d | −0.300 | 0.393 | 5,754 | 35.3% | 1,480 | −0.63 |
| 180d | +0.171 | 0.370 | 9,342 | 13.8% | 11,131 | +1.86 |
| 60d | +0.054 | 0.362 | 8,194 | 11.5% | 7,584 | +0.94 |
| 60d | −0.261 | 0.357 | 5,984 | 33.2% | 1,891 | −0.52 |
| 30d | −0.104 | 0.337 | 6,983 | 24.8% | 2,476 | −0.37 |
| 60d | −0.221 | 0.317 | 6,224 | 31.0% | 2,362 | −0.40 |
| 60d | −0.182 | 0.273 | 6,474 | 28.6% | 2,855 | −0.28 |
| 180d | +0.132 | 0.253 | 8,982 | 13.1% | 12,886 | +2.31 |
| 91d | −0.300 | 0.251 | 5,777 | 33.3% | 2,527 | −0.36 |
Vomma P&L ratio against ln(K/F)
80 nodes; 35 above the flag threshold 0.25.
| Maturity | ln(K/F) | Vomma P&L ratio |
|---|---|---|
| 30d | +0.132 | 2.329 |
| 60d | +0.250 | 1.935 |
| 14d | +0.054 | 1.866 |
| 60d | +0.211 | 1.701 |
| 30d | +0.093 | 1.656 |
| 60d | +0.171 | 1.442 |
| 14d | −0.221 | 1.374 |
| 91d | +0.250 | 1.258 |
| 14d | −0.182 | 1.167 |
| 60d | +0.132 | 1.146 |
Largest at short maturities away from the money, where a vol move's P&L is mostly convexity rather than vega.
Scenario grid · spot × vol, full revaluation
| Vol | −10% | −5% | −3% | −1% | 0% | +1% | +3% | +5% | +10% |
|---|---|---|---|---|---|---|---|---|---|
| −5 vol pts | +549+$54,948; spot −10%, vol −5 vol pts: P&L +549 idx pts; spot −10%, vol −5 vol pts: P&L +$54,948 per SPX contract | +160+$15,956; spot −5%, vol −5 vol pts: P&L +160 idx pts; spot −5%, vol −5 vol pts: P&L +$15,956 per SPX contract | +18+$1,780; spot −3%, vol −5 vol pts: P&L +18 idx pts; spot −3%, vol −5 vol pts: P&L +$1,780 per SPX contract | −75−$7,497; spot −1%, vol −5 vol pts: P&L −75 idx pts; spot −1%, vol −5 vol pts: P&L −$7,497 per SPX contract | −88−$8,828; spot 0%, vol −5 vol pts: P&L −88 idx pts; spot 0%, vol −5 vol pts: P&L −$8,828 per SPX contract | −76−$7,598; spot +1%, vol −5 vol pts: P&L −76 idx pts; spot +1%, vol −5 vol pts: P&L −$7,598 per SPX contract | +13+$1,274; spot +3%, vol −5 vol pts: P&L +13 idx pts; spot +3%, vol −5 vol pts: P&L +$1,274 per SPX contract | +149+$14,863; spot +5%, vol −5 vol pts: P&L +149 idx pts; spot +5%, vol −5 vol pts: P&L +$14,863 per SPX contract | +526+$52,606; spot +10%, vol −5 vol pts: P&L +526 idx pts; spot +10%, vol −5 vol pts: P&L +$52,606 per SPX contract |
| −2 vol pts | +550+$54,955; spot −10%, vol −2 vol pts: P&L +550 idx pts; spot −10%, vol −2 vol pts: P&L +$54,955 per SPX contract | +169+$16,924; spot −5%, vol −2 vol pts: P&L +169 idx pts; spot −5%, vol −2 vol pts: P&L +$16,924 per SPX contract | +46+$4,642; spot −3%, vol −2 vol pts: P&L +46 idx pts; spot −3%, vol −2 vol pts: P&L +$4,642 per SPX contract | −26−$2,563; spot −1%, vol −2 vol pts: P&L −26 idx pts; spot −1%, vol −2 vol pts: P&L −$2,563 per SPX contract | −35−$3,531; spot 0%, vol −2 vol pts: P&L −35 idx pts; spot 0%, vol −2 vol pts: P&L −$3,531 per SPX contract | −26−$2,607; spot +1%, vol −2 vol pts: P&L −26 idx pts; spot +1%, vol −2 vol pts: P&L −$2,607 per SPX contract | +43+$4,327; spot +3%, vol −2 vol pts: P&L +43 idx pts; spot +3%, vol −2 vol pts: P&L +$4,327 per SPX contract | +161+$16,053; spot +5%, vol −2 vol pts: P&L +161 idx pts; spot +5%, vol −2 vol pts: P&L +$16,053 per SPX contract | +526+$52,630; spot +10%, vol −2 vol pts: P&L +526 idx pts; spot +10%, vol −2 vol pts: P&L +$52,630 per SPX contract |
| 0 vol pts | +550+$54,995; spot −10%, vol 0 vol pts: P&L +550 idx pts; spot −10%, vol 0 vol pts: P&L +$54,995 per SPX contract | +181+$18,109; spot −5%, vol 0 vol pts: P&L +181 idx pts; spot −5%, vol 0 vol pts: P&L +$18,109 per SPX contract | +70+$7,028; spot −3%, vol 0 vol pts: P&L +70 idx pts; spot −3%, vol 0 vol pts: P&L +$7,028 per SPX contract | +8+$809; spot −1%, vol 0 vol pts: P&L +8 idx pts; spot −1%, vol 0 vol pts: P&L +$809 per SPX contract | 0$0; spot 0%, vol 0 vol pts: P&L 0 idx pts; spot 0%, vol 0 vol pts: P&L $0 per SPX contract | +8+$801; spot +1%, vol 0 vol pts: P&L +8 idx pts; spot +1%, vol 0 vol pts: P&L +$801 per SPX contract | +68+$6,840; spot +3%, vol 0 vol pts: P&L +68 idx pts; spot +3%, vol 0 vol pts: P&L +$6,840 per SPX contract | +174+$17,431; spot +5%, vol 0 vol pts: P&L +174 idx pts; spot +5%, vol 0 vol pts: P&L +$17,431 per SPX contract | +527+$52,727; spot +10%, vol 0 vol pts: P&L +527 idx pts; spot +10%, vol 0 vol pts: P&L +$52,727 per SPX contract |
| +2 vol pts | +551+$55,119; spot −10%, vol +2 vol pts: P&L +551 idx pts; spot −10%, vol +2 vol pts: P&L +$55,119 per SPX contract | +197+$19,674; spot −5%, vol +2 vol pts: P&L +197 idx pts; spot −5%, vol +2 vol pts: P&L +$19,674 per SPX contract | +97+$9,660; spot −3%, vol +2 vol pts: P&L +97 idx pts; spot −3%, vol +2 vol pts: P&L +$9,660 per SPX contract | +42+$4,217; spot −1%, vol +2 vol pts: P&L +42 idx pts; spot −1%, vol +2 vol pts: P&L +$4,217 per SPX contract | +35+$3,531; spot 0%, vol +2 vol pts: P&L +35 idx pts; spot 0%, vol +2 vol pts: P&L +$3,531 per SPX contract | +42+$4,246; spot +1%, vol +2 vol pts: P&L +42 idx pts; spot +1%, vol +2 vol pts: P&L +$4,246 per SPX contract | +96+$9,596; spot +3%, vol +2 vol pts: P&L +96 idx pts; spot +3%, vol +2 vol pts: P&L +$9,596 per SPX contract | +192+$19,204; spot +5%, vol +2 vol pts: P&L +192 idx pts; spot +5%, vol +2 vol pts: P&L +$19,204 per SPX contract | +530+$52,975; spot +10%, vol +2 vol pts: P&L +530 idx pts; spot +10%, vol +2 vol pts: P&L +$52,975 per SPX contract |
| +5 vol pts | +556+$55,578; spot −10%, vol +5 vol pts: P&L +556 idx pts; spot −10%, vol +5 vol pts: P&L +$55,578 per SPX contract | +226+$22,586; spot −5%, vol +5 vol pts: P&L +226 idx pts; spot −5%, vol +5 vol pts: P&L +$22,586 per SPX contract | +139+$13,921; spot −3%, vol +5 vol pts: P&L +139 idx pts; spot −3%, vol +5 vol pts: P&L +$13,921 per SPX contract | +94+$9,372; spot −1%, vol +5 vol pts: P&L +94 idx pts; spot −1%, vol +5 vol pts: P&L +$9,372 per SPX contract | +88+$8,827; spot 0%, vol +5 vol pts: P&L +88 idx pts; spot 0%, vol +5 vol pts: P&L +$8,827 per SPX contract | +95+$9,455; spot +1%, vol +5 vol pts: P&L +95 idx pts; spot +1%, vol +5 vol pts: P&L +$9,455 per SPX contract | +140+$14,039; spot +3%, vol +5 vol pts: P&L +140 idx pts; spot +3%, vol +5 vol pts: P&L +$14,039 per SPX contract | +224+$22,437; spot +5%, vol +5 vol pts: P&L +224 idx pts; spot +5%, vol +5 vol pts: P&L +$22,437 per SPX contract | +538+$53,756; spot +10%, vol +5 vol pts: P&L +538 idx pts; spot +10%, vol +5 vol pts: P&L +$53,756 per SPX contract |
| +10 vol pts | +573+$57,329; spot −10%, vol +10 vol pts: P&L +573 idx pts; spot −10%, vol +10 vol pts: P&L +$57,329 per SPX contract | +285+$28,496; spot −5%, vol +10 vol pts: P&L +285 idx pts; spot −5%, vol +10 vol pts: P&L +$28,496 per SPX contract | +215+$21,533; spot −3%, vol +10 vol pts: P&L +215 idx pts; spot −3%, vol +10 vol pts: P&L +$21,533 per SPX contract | +180+$18,027; spot −1%, vol +10 vol pts: P&L +180 idx pts; spot −1%, vol +10 vol pts: P&L +$18,027 per SPX contract | +177+$17,653; spot 0%, vol +10 vol pts: P&L +177 idx pts; spot 0%, vol +10 vol pts: P&L +$17,653 per SPX contract | +182+$18,199; spot +1%, vol +10 vol pts: P&L +182 idx pts; spot +1%, vol +10 vol pts: P&L +$18,199 per SPX contract | +219+$21,944; spot +3%, vol +10 vol pts: P&L +219 idx pts; spot +3%, vol +10 vol pts: P&L +$21,944 per SPX contract | +289+$28,876; spot +5%, vol +10 vol pts: P&L +289 idx pts; spot +5%, vol +10 vol pts: P&L +$28,876 per SPX contract | +563+$56,318; spot +10%, vol +10 vol pts: P&L +563 idx pts; spot +10%, vol +10 vol pts: P&L +$56,318 per SPX contract |
Hover or focus a cell (arrow keys move) for its details.
Long one 30-day SPX straddle struck at the 30-day forward, on one unit of the index, delta-hedged at inception in the index at its Black-Scholes (sticky-strike) delta; instantaneous shocks, full Black-76 revaluation on the headline Heston fit's smile; as of 2026-10-28; sticky-strike dynamics shown (the file also holds sticky-moneyness). P&L in index points per straddle on one unit of the index (×100 for one SPX contract).
Sticky-moneyness dynamics: the same book and shocks
| Vol | −10% | −5% | −3% | −1% | 0% | +1% | +3% | +5% | +10% |
|---|---|---|---|---|---|---|---|---|---|
| −5 vol pts | +549+$54,949; spot −10%, vol −5 vol pts: P&L +549 idx pts; spot −10%, vol −5 vol pts: P&L +$54,949 per SPX contract | +158+$15,794; spot −5%, vol −5 vol pts: P&L +158 idx pts; spot −5%, vol −5 vol pts: P&L +$15,794 per SPX contract | +5+$499; spot −3%, vol −5 vol pts: P&L +5 idx pts; spot −3%, vol −5 vol pts: P&L +$499 per SPX contract | −94−$9,428; spot −1%, vol −5 vol pts: P&L −94 idx pts; spot −1%, vol −5 vol pts: P&L −$9,428 per SPX contract | −88−$8,828; spot 0%, vol −5 vol pts: P&L −88 idx pts; spot 0%, vol −5 vol pts: P&L −$8,828 per SPX contract | −54−$5,389; spot +1%, vol −5 vol pts: P&L −54 idx pts; spot +1%, vol −5 vol pts: P&L −$5,389 per SPX contract | +54+$5,443; spot +3%, vol −5 vol pts: P&L +54 idx pts; spot +3%, vol −5 vol pts: P&L +$5,443 per SPX contract | +185+$18,453; spot +5%, vol −5 vol pts: P&L +185 idx pts; spot +5%, vol −5 vol pts: P&L +$18,453 per SPX contract | +541+$54,081; spot +10%, vol −5 vol pts: P&L +541 idx pts; spot +10%, vol −5 vol pts: P&L +$54,081 per SPX contract |
| −2 vol pts | +550+$54,966; spot −10%, vol −2 vol pts: P&L +550 idx pts; spot −10%, vol −2 vol pts: P&L +$54,966 per SPX contract | +163+$16,273; spot −5%, vol −2 vol pts: P&L +163 idx pts; spot −5%, vol −2 vol pts: P&L +$16,273 per SPX contract | +24+$2,399; spot −3%, vol −2 vol pts: P&L +24 idx pts; spot −3%, vol −2 vol pts: P&L +$2,399 per SPX contract | −46−$4,595; spot −1%, vol −2 vol pts: P&L −46 idx pts; spot −1%, vol −2 vol pts: P&L −$4,595 per SPX contract | −35−$3,531; spot 0%, vol −2 vol pts: P&L −35 idx pts; spot 0%, vol −2 vol pts: P&L −$3,531 per SPX contract | −3−$324; spot +1%, vol −2 vol pts: P&L −3 idx pts; spot +1%, vol −2 vol pts: P&L −$324 per SPX contract | +95+$9,478; spot +3%, vol −2 vol pts: P&L +95 idx pts; spot +3%, vol −2 vol pts: P&L +$9,478 per SPX contract | +215+$21,518; spot +5%, vol −2 vol pts: P&L +215 idx pts; spot +5%, vol −2 vol pts: P&L +$21,518 per SPX contract | +556+$55,593; spot +10%, vol −2 vol pts: P&L +556 idx pts; spot +10%, vol −2 vol pts: P&L +$55,593 per SPX contract |
| 0 vol pts | +550+$55,037; spot −10%, vol 0 vol pts: P&L +550 idx pts; spot −10%, vol 0 vol pts: P&L +$55,037 per SPX contract | +171+$17,105; spot −5%, vol 0 vol pts: P&L +171 idx pts; spot −5%, vol 0 vol pts: P&L +$17,105 per SPX contract | +44+$4,375; spot −3%, vol 0 vol pts: P&L +44 idx pts; spot −3%, vol 0 vol pts: P&L +$4,375 per SPX contract | −13−$1,255; spot −1%, vol 0 vol pts: P&L −13 idx pts; spot −1%, vol 0 vol pts: P&L −$1,255 per SPX contract | 0$0; spot 0%, vol 0 vol pts: P&L 0 idx pts; spot 0%, vol 0 vol pts: P&L $0 per SPX contract | +31+$3,110; spot +1%, vol 0 vol pts: P&L +31 idx pts; spot +1%, vol 0 vol pts: P&L +$3,110 per SPX contract | +124+$12,402; spot +3%, vol 0 vol pts: P&L +124 idx pts; spot +3%, vol 0 vol pts: P&L +$12,402 per SPX contract | +239+$23,882; spot +5%, vol 0 vol pts: P&L +239 idx pts; spot +5%, vol 0 vol pts: P&L +$23,882 per SPX contract | +569+$56,909; spot +10%, vol 0 vol pts: P&L +569 idx pts; spot +10%, vol 0 vol pts: P&L +$56,909 per SPX contract |
| +2 vol pts | +552+$55,217; spot −10%, vol +2 vol pts: P&L +552 idx pts; spot −10%, vol +2 vol pts: P&L +$55,217 per SPX contract | +184+$18,363; spot −5%, vol +2 vol pts: P&L +184 idx pts; spot −5%, vol +2 vol pts: P&L +$18,363 per SPX contract | +67+$6,724; spot −3%, vol +2 vol pts: P&L +67 idx pts; spot −3%, vol +2 vol pts: P&L +$6,724 per SPX contract | +21+$2,133; spot −1%, vol +2 vol pts: P&L +21 idx pts; spot −1%, vol +2 vol pts: P&L +$2,133 per SPX contract | +35+$3,531; spot 0%, vol +2 vol pts: P&L +35 idx pts; spot 0%, vol +2 vol pts: P&L +$3,531 per SPX contract | +66+$6,572; spot +1%, vol +2 vol pts: P&L +66 idx pts; spot +1%, vol +2 vol pts: P&L +$6,572 per SPX contract | +155+$15,451; spot +3%, vol +2 vol pts: P&L +155 idx pts; spot +3%, vol +2 vol pts: P&L +$15,451 per SPX contract | +264+$26,440; spot +5%, vol +2 vol pts: P&L +264 idx pts; spot +5%, vol +2 vol pts: P&L +$26,440 per SPX contract | +584+$58,450; spot +10%, vol +2 vol pts: P&L +584 idx pts; spot +10%, vol +2 vol pts: P&L +$58,450 per SPX contract |
| +5 vol pts | +558+$55,799; spot −10%, vol +5 vol pts: P&L +558 idx pts; spot −10%, vol +5 vol pts: P&L +$55,799 per SPX contract | +209+$20,917; spot −5%, vol +5 vol pts: P&L +209 idx pts; spot −5%, vol +5 vol pts: P&L +$20,917 per SPX contract | +107+$10,706; spot −3%, vol +5 vol pts: P&L +107 idx pts; spot −3%, vol +5 vol pts: P&L +$10,706 per SPX contract | +73+$7,269; spot −1%, vol +5 vol pts: P&L +73 idx pts; spot −1%, vol +5 vol pts: P&L +$7,269 per SPX contract | +88+$8,827; spot 0%, vol +5 vol pts: P&L +88 idx pts; spot 0%, vol +5 vol pts: P&L +$8,827 per SPX contract | +118+$11,797; spot +1%, vol +5 vol pts: P&L +118 idx pts; spot +1%, vol +5 vol pts: P&L +$11,797 per SPX contract | +202+$20,194; spot +3%, vol +5 vol pts: P&L +202 idx pts; spot +3%, vol +5 vol pts: P&L +$20,194 per SPX contract | +306+$30,559; spot +5%, vol +5 vol pts: P&L +306 idx pts; spot +5%, vol +5 vol pts: P&L +$30,559 per SPX contract | +611+$61,137; spot +10%, vol +5 vol pts: P&L +611 idx pts; spot +10%, vol +5 vol pts: P&L +$61,137 per SPX contract |
| +10 vol pts | +578+$57,785; spot −10%, vol +10 vol pts: P&L +578 idx pts; spot −10%, vol +10 vol pts: P&L +$57,785 per SPX contract | +264+$26,440; spot −5%, vol +10 vol pts: P&L +264 idx pts; spot −5%, vol +10 vol pts: P&L +$26,440 per SPX contract | +181+$18,061; spot −3%, vol +10 vol pts: P&L +181 idx pts; spot −3%, vol +10 vol pts: P&L +$18,061 per SPX contract | +159+$15,908; spot −1%, vol +10 vol pts: P&L +159 idx pts; spot −1%, vol +10 vol pts: P&L +$15,908 per SPX contract | +177+$17,653; spot 0%, vol +10 vol pts: P&L +177 idx pts; spot 0%, vol +10 vol pts: P&L +$17,653 per SPX contract | +206+$20,556; spot +1%, vol +10 vol pts: P&L +206 idx pts; spot +1%, vol +10 vol pts: P&L +$20,556 per SPX contract | +284+$28,394; spot +3%, vol +10 vol pts: P&L +284 idx pts; spot +3%, vol +10 vol pts: P&L +$28,394 per SPX contract | +380+$37,956; spot +5%, vol +10 vol pts: P&L +380 idx pts; spot +5%, vol +10 vol pts: P&L +$37,956 per SPX contract | +664+$66,448; spot +10%, vol +10 vol pts: P&L +664 idx pts; spot +10%, vol +10 vol pts: P&L +$66,448 per SPX contract |
Hover or focus a cell (arrow keys move) for its details.
Same colour scale and units as the grid above. Under sticky-moneyness the smile (the headline fit’s model smile) moves with the forward, so a fixed strike's vol falls as spot falls on the negative skew; the difference between the two grids is the smile-dynamics risk a sticky-strike book ignores.
Cited on: Calibration
QV convexity and mean vanna by maturity
One value per maturity under the surface's Heston parameters; it grows with the horizon.
| Maturity | QV convexity × 10⁴ |
|---|---|
| 14d | 0.011 |
| 30d | 0.099 |
| 60d | 0.698 |
| 91d | 2.142 |
| 180d | 11.522 |
| 365d | 48.528 |
Black–Scholes vanna averaged over the strikes stored at each maturity.
| Maturity | Mean vanna |
|---|---|
| 14d | −0.0245 |
| 30d | −0.0355 |
| 60d | +0.0060 |
| 91d | +0.0578 |
| 180d | +0.1844 |
| 365d | +0.3296 |
Methodology and caveats
QV convexity is the variance of integrated variance ∫₀ᵀ v_t dt under the surface's Heston parameters (exact closed form for the CIR variance); it does not depend on strike. Vanna ((∂²V/∂S∂σ)) = −φ(d₁)·d₂/σ is negative below the forward and positive above it, so its average mostly reflects which strikes the surface holds; it is not a measure of the spot–vol leverage effect.
P&L explain · delta-hedged 1-year ATM straddle, 2020
Total P&L
+168.3idx pts
Gamma
+439.6idx pts
Vega
+403.5idx pts
Theta
−480.2idx pts
Vanna
−219.5idx pts
Volga
+41.9idx pts
Financing
−7.3idx pts
Residual
−9.7idx pts
Second-order Taylor check
0.42idx pts residual sd
vs daily P&L sd 34.7 idx pts, 252 days
Marks and Greeks share one vol input (the VIX term structure, Run A in
delta_hedger.py), so this tests the expansion, not hedge effectiveness against market prices.252 daily rebalances from 2020-01-02 to 2020-12-31; total +168.3 index points, residual −9.67.
| Component | Cumulative P&L |
|---|---|
| Total | +168.34 |
| Gamma | +439.57 |
| Vega | +403.54 |
| Theta | −480.19 |
| Vanna | −219.54 |
| Volga | +41.88 |
| Financing | −7.25 |
| Residual | −9.67 |
Methodology and caveats
Long one ATM straddle struck at 3,257.85 on 2020-01-02 with one year to expiry, delta-hedged at each close through 2020-12-31 (252 rebalances). Each day's P&L is split into Θ, Γ, ν (realised Δσ), vanna, volga and financing from the previous close's Greeks; the residual is what the second-order expansion misses (third-order terms, and the vol path between closes).
Greeks are Black–Scholes at the VIX term structure interpolated to the remaining tenor (C7, Run A); financing accrues at the simulator's flat rate. The residual is the honesty check. Its largest days are 2020-06-11 (−3.30), 2020-10-28 (−2.36), 2020-03-16 (−2.03); 39% of its sum of squares falls in 20 February – 30 April 2020, when the ex-ante vomma flag fired on 29 days (2020-02-10 → 2020-04-03). Index points per straddle on one unit of SPX.