HUBS - Detail Report

Quick Overview

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)	Binomial IV (Period)	Yahoo IV (Period)	1σ Lower (68.27%)	1σ Upper	2σ Lower (95.45%)	2σ Upper
Daily	3.12%	2.48%	2.72%	4.52%	4.05%	4.13%	224.24	243.14	215.35	253.18
Weekly	6.92%	6.21%	7.12%	10.51%	8.91%	9.09%	213.60	255.26	195.39	279.04
Monthly	12.93%	12.78%	13.16%	21.02%	18.54%	18.92%	193.98	281.08	161.14	338.35
Quarterly	22.27%	21.85%	23.47%	37.69%	32.12%	32.76%	169.35	321.95	122.83	443.90
Annual	—	—	—	—	64.24%	65.53%	122.83	443.90	64.61	843.87
Option Time Horizon	—	—	—	—	24.71%	25.20%	182.38	298.95	142.45	382.74

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $233.50 | Strike (K): $240.00 (first OTM call ≥ spot) | Observed Mid-Price: $20.8500 (Bid $19.4000 / Ask $22.3000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 64.24% (CRR binomial tree, American, n=20 steps) | BS IV: 64.62% (European Black-Scholes) | Yahoo IV (Annual): 65.53% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.13. Further, an Excess Kurtosis of 4.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.24%	17	0.60%	0.60%
-9.24% to -6.90%	35	1.23%	1.82%
-6.90% to -4.56%	119	4.17%	5.99%
-4.56% to -2.22%	330	11.55%	17.54%
-2.22% to 0.12%	888	31.08%	48.62%
0.12% to 2.46%	1004	35.14%	83.76%
2.46% to 4.80%	322	11.27%	95.03%
4.80% to 7.14%	86	3.01%	98.04%
7.14% to 9.48%	28	0.98%	99.02%
Greater than 9.48%	28	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.00%	3.24%	77.11%	68.27%
±2σ	-6.12%	6.36%	94.71%	95.45%
±3σ	-9.24%	9.48%	98.42%	99.73%

Descriptive Statistics

Mean	0.120%
Standard Error	0.058%
Median	0.188%
Mode	0.000%
Standard Deviation	3.121%
Sample Variance	9.738%
Kurtosis	4.64
Skewness	0.13
Range	39.611%
Minimum	-19.855%
Maximum	19.756%
Count	2857

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.162%	1529	53.52%	1.157%
Negative	-2.248%	1318	46.13%	-1.037%
Zero	0.000%	10	0.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.85%
20	1 Month	7.84%
60	1 Quarter	5.15%
250	1 Year	4.42%
750	3 Years	3.72%
1,250	5 Years	4.52%
2,500	10 Years	4.23%
5,000	20 Years	4.25%
12,500	50 Years	4.25%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.61. Further, an Excess Kurtosis of 11.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.32%	0	0.00%	0.00%
-3.32% to -1.47%	0	0.00%	0.00%
-1.47% to 0.39%	0	0.00%	0.00%
0.39% to 2.25%	482	16.86%	16.86%
2.25% to 4.10%	1336	46.75%	63.61%
4.10% to 5.96%	595	20.82%	84.43%
5.96% to 7.82%	245	8.57%	93.00%
7.82% to 9.67%	102	3.57%	96.57%
9.67% to 11.53%	42	1.47%	98.04%
Greater than 11.53%	56	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.63%	6.58%	84.57%	68.27%
±2σ	-0.85%	9.05%	95.66%	95.45%
±3σ	-3.32%	11.53%	98.04%	99.73%

Descriptive Statistics

Mean	4.104%
Standard Error	0.046%
Median	3.437%
Mode	3.476%
Standard Deviation	2.475%
Sample Variance	6.124%
Kurtosis	11.83
Skewness	2.61
Range	28.407%
Minimum	1.014%
Maximum	29.421%
Count	2858

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.104%	2858	100.00%	4.104%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.54. Further, an Excess Kurtosis of 4.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.13%	12	0.42%	0.42%
-8.13% to -6.09%	24	0.84%	1.26%
-6.09% to -4.05%	100	3.50%	4.76%
-4.05% to -2.01%	388	13.58%	18.33%
-2.01% to 0.03%	964	33.73%	52.06%
0.03% to 2.07%	870	30.44%	82.51%
2.07% to 4.11%	333	11.65%	94.16%
4.11% to 6.15%	101	3.53%	97.69%
6.15% to 8.19%	42	1.47%	99.16%
Greater than 8.19%	24	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.69%	2.75%	75.79%	68.27%
±2σ	-5.41%	5.47%	94.58%	95.45%
±3σ	-8.13%	8.19%	98.74%	99.73%

Descriptive Statistics

Mean	0.031%
Standard Error	0.051%
Median	-0.076%
Mode	0.000%
Standard Deviation	2.719%
Sample Variance	7.392%
Kurtosis	4.80
Skewness	0.54
Range	37.742%
Minimum	-13.906%
Maximum	23.836%
Count	2858

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.049%	1383	48.39%	0.992%
Negative	-1.870%	1467	51.33%	-0.960%
Zero	0.000%	8	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.11. Further, an Excess Kurtosis of 1.96 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.16%	5	0.84%	0.84%
-20.16% to -14.97%	9	1.52%	2.36%
-14.97% to -9.78%	26	4.38%	6.75%
-9.78% to -4.59%	68	11.47%	18.21%
-4.59% to 0.60%	190	32.04%	50.25%
0.60% to 5.79%	184	31.03%	81.28%
5.79% to 10.98%	78	13.15%	94.44%
10.98% to 16.17%	23	3.88%	98.31%
16.17% to 21.36%	7	1.18%	99.49%
Greater than 21.36%	3	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.32%	7.52%	73.86%	68.27%
±2σ	-13.24%	14.44%	94.77%	95.45%
±3σ	-20.16%	21.36%	98.65%	99.73%

Descriptive Statistics

Mean	0.604%
Standard Error	0.284%
Median	0.493%
Mode	-2.639%
Standard Deviation	6.920%
Sample Variance	47.882%
Kurtosis	1.96
Skewness	-0.11
Range	57.861%
Minimum	-28.922%
Maximum	28.939%
Count	593

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.225%	321	54.13%	2.828%
Negative	-4.849%	272	45.87%	-2.224%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.99%
12	1 Quarter	12.70%
52	1 Year	10.55%
156	3 Years	8.73%
260	5 Years	10.51%
520	10 Years	9.99%
1,040	20 Years	10.03%
2,600	50 Years	10.03%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.85. Further, an Excess Kurtosis of 4.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.96%	0	0.00%	0.00%
-7.96% to -3.31%	0	0.00%	0.00%
-3.31% to 1.34%	0	0.00%	0.00%
1.34% to 6.00%	124	20.88%	20.88%
6.00% to 10.65%	253	42.59%	63.47%
10.65% to 15.31%	120	20.20%	83.67%
15.31% to 19.96%	50	8.42%	92.09%
19.96% to 24.62%	20	3.37%	95.45%
24.62% to 29.27%	18	3.03%	98.48%
Greater than 29.27%	9	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.45%	16.86%	80.47%	68.27%
±2σ	-1.76%	23.07%	94.78%	95.45%
±3σ	-7.97%	29.27%	98.48%	99.73%

Descriptive Statistics

Mean	10.653%
Standard Error	0.255%
Median	8.940%
Mode	6.626%
Standard Deviation	6.206%
Sample Variance	38.514%
Kurtosis	4.65
Skewness	1.85
Range	44.450%
Minimum	2.846%
Maximum	47.296%
Count	594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.653%	594	100.00%	10.653%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 1.00. Further, an Excess Kurtosis of 3.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.40%	0	0.00%	0.00%
-21.40% to -16.07%	6	1.01%	1.01%
-16.07% to -10.73%	18	3.03%	4.04%
-10.73% to -5.39%	90	15.15%	19.19%
-5.39% to -0.06%	202	34.01%	53.20%
-0.06% to 5.28%	184	30.98%	84.18%
5.28% to 10.62%	54	9.09%	93.27%
10.62% to 15.96%	24	4.04%	97.31%
15.96% to 21.29%	7	1.18%	98.48%
Greater than 21.29%	9	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.17%	7.06%	75.42%	68.27%
±2σ	-14.29%	14.18%	95.45%	95.45%
±3σ	-21.40%	21.29%	98.48%	99.73%

Descriptive Statistics

Mean	-0.055%
Standard Error	0.292%
Median	-0.494%
Mode	-4.941%
Standard Deviation	7.116%
Sample Variance	50.638%
Kurtosis	3.49
Skewness	1.00
Range	60.191%
Minimum	-20.536%
Maximum	39.655%
Count	594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.423%	277	46.63%	2.529%
Negative	-4.857%	316	53.20%	-2.584%
Zero	0.000%	1	0.17%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.06. Further, an Excess Kurtosis of 0.45 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.56%	0	0.00%	0.00%
-36.56% to -26.87%	2	1.47%	1.47%
-26.87% to -17.17%	8	5.88%	7.35%
-17.17% to -7.48%	15	11.03%	18.38%
-7.48% to 2.22%	44	32.35%	50.74%
2.22% to 11.91%	42	30.88%	81.62%
11.91% to 21.61%	15	11.03%	92.65%
21.61% to 31.31%	8	5.88%	98.53%
31.31% to 41.00%	2	1.47%	100.00%
Greater than 41.00%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.71%	15.15%	72.79%	68.27%
±2σ	-23.64%	28.08%	92.65%	95.45%
±3σ	-36.57%	41.00%	100.00%	99.73%

Descriptive Statistics

Mean	2.219%
Standard Error	1.109%
Median	2.144%
Mode	-30.227%
Standard Deviation	12.928%
Sample Variance	167.130%
Kurtosis	0.45
Skewness	0.06
Range	68.593%
Minimum	-30.227%
Maximum	38.366%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.594%	78	57.35%	6.076%
Negative	-9.045%	58	42.65%	-3.857%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.15%
12	1 Year	20.79%
36	3 Years	18.28%
60	5 Years	21.02%
120	10 Years	20.57%
240	20 Years	20.62%
600	50 Years	20.62%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.29. Further, an Excess Kurtosis of 9.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.55%	0	0.00%	0.00%
-14.55% to -4.96%	0	0.00%	0.00%
-4.96% to 4.62%	0	0.00%	0.00%
4.62% to 14.20%	28	20.44%	20.44%
14.20% to 23.79%	56	40.88%	61.31%
23.79% to 33.37%	26	18.98%	80.29%
33.37% to 42.95%	17	12.41%	92.70%
42.95% to 52.53%	6	4.38%	97.08%
52.53% to 62.12%	2	1.46%	98.54%
Greater than 62.12%	2	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.01%	36.56%	82.48%	68.27%
±2σ	-1.77%	49.34%	97.08%	95.45%
±3σ	-14.55%	62.12%	98.54%	99.73%

Descriptive Statistics

Mean	23.785%
Standard Error	1.092%
Median	19.847%
Mode	7.121%
Standard Deviation	12.777%
Sample Variance	163.243%
Kurtosis	9.43
Skewness	2.29
Range	93.936%
Minimum	7.121%
Maximum	101.057%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.785%	137	100.00%	23.785%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 1.20 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.99%	0	0.00%	0.00%
-39.99% to -30.11%	0	0.00%	0.00%
-30.11% to -20.24%	8	5.84%	5.84%
-20.24% to -10.37%	19	13.87%	19.71%
-10.37% to -0.50%	48	35.04%	54.74%
-0.50% to 9.37%	38	27.74%	82.48%
9.37% to 19.25%	13	9.49%	91.97%
19.25% to 29.12%	5	3.65%	95.62%
29.12% to 38.99%	5	3.65%	99.27%
Greater than 38.99%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.66%	12.67%	75.91%	68.27%
±2σ	-26.82%	25.83%	94.89%	95.45%
±3σ	-39.99%	38.99%	99.27%	99.73%

Descriptive Statistics

Mean	-0.498%
Standard Error	1.125%
Median	-1.857%
Mode	-25.917%
Standard Deviation	13.163%
Sample Variance	173.261%
Kurtosis	1.20
Skewness	0.86
Range	68.417%
Minimum	-25.917%
Maximum	42.500%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.593%	60	43.80%	4.639%
Negative	-9.141%	77	56.20%	-5.138%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.20. Further, an Excess Kurtosis of -0.62 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.19%	0	0.00%	0.00%
-60.19% to -43.48%	0	0.00%	0.00%
-43.48% to -26.78%	3	6.52%	6.52%
-26.78% to -10.08%	8	17.39%	23.91%
-10.08% to 6.62%	9	19.57%	43.48%
6.62% to 23.32%	16	34.78%	78.26%
23.32% to 40.02%	7	15.22%	93.48%
40.02% to 56.72%	3	6.52%	100.00%
56.72% to 73.42%	0	0.00%	100.00%
Greater than 73.42%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.65%	28.89%	63.04%	68.27%
±2σ	-37.92%	51.15%	95.65%	95.45%
±3σ	-60.19%	73.42%	100.00%	99.73%

Descriptive Statistics

Mean	6.618%
Standard Error	3.283%
Median	9.213%
Mode	-43.080%
Standard Deviation	22.268%
Sample Variance	495.852%
Kurtosis	-0.62
Skewness	-0.20
Range	87.262%
Minimum	-43.080%
Maximum	44.182%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.957%	26	56.52%	12.976%
Negative	-14.622%	20	43.48%	-6.357%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	30.07%
12	3 Years	35.29%
20	5 Years	37.69%
40	10 Years	36.47%
80	20 Years	36.49%
200	50 Years	36.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.81. Further, an Excess Kurtosis of 3.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.17%	0	0.00%	0.00%
-20.17% to -3.79%	0	0.00%	0.00%
-3.79% to 12.60%	0	0.00%	0.00%
12.60% to 28.98%	8	17.02%	17.02%
28.98% to 45.36%	23	48.94%	65.96%
45.36% to 61.75%	9	19.15%	85.11%
61.75% to 78.13%	3	6.38%	91.49%
78.13% to 94.52%	2	4.26%	95.74%
94.52% to 110.90%	0	0.00%	95.74%
Greater than 110.90%	2	4.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.52%	67.21%	78.72%	68.27%
±2σ	1.67%	89.06%	95.74%	95.45%
±3σ	-20.17%	110.90%	95.74%	99.73%

Descriptive Statistics

Mean	45.364%
Standard Error	3.187%
Median	42.210%
Mode	19.942%
Standard Deviation	21.846%
Sample Variance	477.237%
Kurtosis	3.95
Skewness	1.81
Range	101.878%
Minimum	19.942%
Maximum	121.820%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	45.364%	47	100.00%	45.364%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.35. Further, an Excess Kurtosis of 2.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.82%	0	0.00%	0.00%
-71.82% to -54.23%	0	0.00%	0.00%
-54.23% to -36.62%	0	0.00%	0.00%
-36.62% to -19.02%	9	19.15%	19.15%
-19.02% to -1.43%	18	38.30%	57.45%
-1.43% to 16.17%	10	21.28%	78.72%
16.17% to 33.77%	7	14.89%	93.62%
33.77% to 51.37%	1	2.13%	95.74%
51.37% to 68.97%	1	2.13%	97.87%
Greater than 68.97%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.89%	22.04%	70.21%	68.27%
±2σ	-48.36%	45.51%	95.74%	95.45%
±3σ	-71.82%	68.97%	97.87%	99.73%

Descriptive Statistics

Mean	-1.426%
Standard Error	3.423%
Median	-8.971%
Mode	-30.923%
Standard Deviation	23.466%
Sample Variance	550.673%
Kurtosis	2.24
Skewness	1.35
Range	106.780%
Minimum	-30.923%
Maximum	75.857%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.740%	20	42.55%	8.400%
Negative	-17.105%	27	57.45%	-9.826%
Zero	0.000%	0	0.00%	0.000%

HUBS Deep Analytical Report