GH - 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	4.31%	3.17%	3.77%	5.79%	3.44%	3.51%	99.62	106.70	96.25	110.44
Weekly	9.74%	9.47%	10.59%	13.76%	7.57%	7.73%	95.59	111.20	88.62	119.94
Monthly	20.79%	20.35%	20.54%	29.91%	15.75%	16.10%	88.08	120.68	75.24	141.27
Quarterly	45.02%	36.53%	34.98%	55.00%	27.28%	27.88%	78.49	135.43	59.75	177.90
Annual	—	—	—	—	54.55%	55.76%	59.75	177.90	34.63	306.98
Option Time Horizon	—	—	—	—	20.98%	21.45%	83.59	127.17	67.76	156.86

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $103.10 | Strike (K): $105.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.0500 (Bid $7.0000 / Ask $9.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 54.55% (CRR binomial tree, American, n=20 steps) | BS IV: 54.72% (European Black-Scholes) | Yahoo IV (Annual): 55.76% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.61. Further, an Excess Kurtosis of 6.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.78%	6	0.32%	0.32%
-12.78% to -9.54%	19	1.03%	1.35%
-9.54% to -6.31%	69	3.73%	5.08%
-6.31% to -3.08%	230	12.42%	17.49%
-3.08% to 0.15%	653	35.26%	52.75%
0.15% to 3.39%	568	30.67%	83.42%
3.39% to 6.62%	209	11.29%	94.71%
6.62% to 9.86%	61	3.29%	98.00%
9.86% to 13.09%	20	1.08%	99.08%
Greater than 13.09%	17	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.16%	4.47%	76.78%	68.27%
±2σ	-8.47%	8.78%	95.73%	95.45%
±3σ	-12.78%	13.09%	98.76%	99.73%

Descriptive Statistics

Mean	0.155%
Standard Error	0.100%
Median	-0.011%
Mode	0.000%
Standard Deviation	4.311%
Sample Variance	18.581%
Kurtosis	6.03
Skewness	0.61
Range	55.720%
Minimum	-27.145%
Maximum	28.575%
Count	1852

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.222%	915	49.41%	1.592%
Negative	-2.866%	929	50.16%	-1.438%
Zero	0.000%	8	0.43%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.28%
20	1 Month	5.83%
60	1 Quarter	4.73%
250	1 Year	5.45%
750	3 Years	5.44%
1,250	5 Years	5.79%
2,500	10 Years	5.84%
5,000	20 Years	5.84%
12,500	50 Years	5.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.50. Further, an Excess Kurtosis of 11.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.76%	0	0.00%	0.00%
-3.76% to -1.38%	0	0.00%	0.00%
-1.38% to 0.99%	0	0.00%	0.00%
0.99% to 3.37%	330	17.81%	17.81%
3.37% to 5.75%	830	44.79%	62.60%
5.75% to 8.13%	400	21.59%	84.19%
8.13% to 10.51%	165	8.90%	93.09%
10.51% to 12.88%	70	3.78%	96.87%
12.88% to 15.26%	25	1.35%	98.22%
Greater than 15.26%	33	1.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.58%	8.92%	81.44%	68.27%
±2σ	-0.59%	12.09%	96.17%	95.45%
±3σ	-3.76%	15.26%	98.22%	99.73%

Descriptive Statistics

Mean	5.750%
Standard Error	0.074%
Median	4.939%
Mode	2.522%
Standard Deviation	3.170%
Sample Variance	10.047%
Kurtosis	11.31
Skewness	2.50
Range	29.797%
Minimum	1.490%
Maximum	31.287%
Count	1853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.750%	1853	100.00%	5.750%
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 Fairly Symmetrical with a Skewness factor of 0.09. Further, an Excess Kurtosis of 3.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.23%	11	0.59%	0.59%
-11.23% to -8.41%	21	1.13%	1.73%
-8.41% to -5.58%	73	3.94%	5.67%
-5.58% to -2.75%	224	12.09%	17.75%
-2.75% to 0.07%	599	32.33%	50.08%
0.07% to 2.90%	595	32.11%	82.19%
2.90% to 5.73%	207	11.17%	93.36%
5.73% to 8.56%	90	4.86%	98.22%
8.56% to 11.38%	22	1.19%	99.41%
Greater than 11.38%	11	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.69%	3.85%	74.69%	68.27%
±2σ	-7.46%	7.62%	94.82%	95.45%
±3σ	-11.24%	11.38%	98.81%	99.73%

Descriptive Statistics

Mean	0.075%
Standard Error	0.088%
Median	0.066%
Mode	0.000%
Standard Deviation	3.770%
Sample Variance	14.210%
Kurtosis	3.12
Skewness	0.09
Range	45.611%
Minimum	-20.113%
Maximum	25.498%
Count	1853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.782%	941	50.78%	1.413%
Negative	-2.734%	907	48.95%	-1.338%
Zero	0.000%	5	0.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.18. Further, an Excess Kurtosis of 3.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.42%	2	0.52%	0.52%
-28.42% to -21.11%	0	0.00%	0.52%
-21.11% to -13.81%	14	3.64%	4.16%
-13.81% to -6.50%	60	15.58%	19.74%
-6.50% to 0.80%	133	34.55%	54.29%
0.80% to 8.11%	104	27.01%	81.30%
8.11% to 15.41%	47	12.21%	93.51%
15.41% to 22.72%	15	3.90%	97.40%
22.72% to 30.02%	8	2.08%	99.48%
Greater than 30.02%	2	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.94%	10.54%	75.58%	68.27%
±2σ	-18.68%	20.28%	95.84%	95.45%
±3σ	-28.42%	30.02%	98.96%	99.73%

Descriptive Statistics

Mean	0.804%
Standard Error	0.496%
Median	-0.012%
Mode	0.464%
Standard Deviation	9.740%
Sample Variance	94.875%
Kurtosis	3.09
Skewness	0.18
Range	90.692%
Minimum	-50.764%
Maximum	39.928%
Count	385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.043%	191	49.61%	3.990%
Negative	-6.324%	194	50.39%	-3.187%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.33%
12	1 Quarter	9.49%
52	1 Year	12.54%
156	3 Years	12.82%
260	5 Years	13.76%
520	10 Years	13.70%
1,040	20 Years	13.70%
2,600	50 Years	13.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.45. Further, an Excess Kurtosis of 36.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.50%	0	0.00%	0.00%
-13.50% to -6.39%	0	0.00%	0.00%
-6.39% to 0.71%	0	0.00%	0.00%
0.71% to 7.81%	51	13.21%	13.21%
7.81% to 14.92%	183	47.41%	60.62%
14.92% to 22.02%	93	24.09%	84.72%
22.02% to 29.12%	39	10.10%	94.82%
29.12% to 36.23%	14	3.63%	98.45%
36.23% to 43.33%	1	0.26%	98.70%
Greater than 43.33%	5	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.45%	24.39%	87.82%	68.27%
±2σ	-4.03%	33.86%	98.19%	95.45%
±3σ	-13.50%	43.33%	98.70%	99.73%

Descriptive Statistics

Mean	14.916%
Standard Error	0.482%
Median	12.497%
Mode	9.165%
Standard Deviation	9.471%
Sample Variance	89.694%
Kurtosis	36.44
Skewness	4.45
Range	109.274%
Minimum	4.296%
Maximum	113.570%
Count	386

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.916%	386	100.00%	14.916%
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 2.75. Further, an Excess Kurtosis of 23.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.50%	0	0.00%	0.00%
-31.50% to -23.55%	2	0.52%	0.52%
-23.55% to -15.61%	11	2.85%	3.37%
-15.61% to -7.66%	57	14.77%	18.13%
-7.66% to 0.28%	128	33.16%	51.30%
0.28% to 8.23%	122	31.61%	82.90%
8.23% to 16.17%	48	12.44%	95.34%
16.17% to 24.12%	16	4.15%	99.48%
24.12% to 32.06%	0	0.00%	99.48%
Greater than 32.06%	2	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.31%	10.88%	79.53%	68.27%
±2σ	-20.90%	21.47%	97.41%	95.45%
±3σ	-31.50%	32.06%	99.48%	99.73%

Descriptive Statistics

Mean	0.283%
Standard Error	0.539%
Median	-0.004%
Mode	-0.321%
Standard Deviation	10.593%
Sample Variance	112.211%
Kurtosis	23.73
Skewness	2.75
Range	130.204%
Minimum	-28.376%
Maximum	101.828%
Count	386

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.336%	193	50.00%	3.668%
Negative	-6.771%	193	50.00%	-3.386%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.87. Further, an Excess Kurtosis of 1.76 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.10%	0	0.00%	0.00%
-59.10% to -43.51%	1	1.14%	1.14%
-43.51% to -27.92%	2	2.27%	3.41%
-27.92% to -12.33%	14	15.91%	19.32%
-12.33% to 3.26%	29	32.95%	52.27%
3.26% to 18.86%	30	34.09%	86.36%
18.86% to 34.45%	6	6.82%	93.18%
34.45% to 50.04%	1	1.14%	94.32%
50.04% to 65.63%	5	5.68%	100.00%
Greater than 65.63%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.52%	24.05%	77.27%	68.27%
±2σ	-38.31%	44.84%	92.05%	95.45%
±3σ	-59.10%	65.63%	100.00%	99.73%

Descriptive Statistics

Mean	3.264%
Standard Error	2.216%
Median	0.136%
Mode	-48.032%
Standard Deviation	20.788%
Sample Variance	432.157%
Kurtosis	1.76
Skewness	0.87
Range	113.228%
Minimum	-48.032%
Maximum	65.196%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.538%	46	52.27%	9.168%
Negative	-12.370%	42	47.73%	-5.904%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	17.75%
12	1 Year	31.03%
36	3 Years	30.33%
60	5 Years	29.91%
120	10 Years	29.60%
240	20 Years	29.60%
600	50 Years	29.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.32. Further, an Excess Kurtosis of 7.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.28%	0	0.00%	0.00%
-25.28% to -10.02%	0	0.00%	0.00%
-10.02% to 5.25%	0	0.00%	0.00%
5.25% to 20.51%	16	17.98%	17.98%
20.51% to 35.77%	42	47.19%	65.17%
35.77% to 51.04%	17	19.10%	84.27%
51.04% to 66.30%	8	8.99%	93.26%
66.30% to 81.57%	3	3.37%	96.63%
81.57% to 96.83%	1	1.12%	97.75%
Greater than 96.83%	2	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.42%	56.13%	82.02%	68.27%
±2σ	-4.93%	76.48%	96.63%	95.45%
±3σ	-25.28%	96.83%	97.75%	99.73%

Descriptive Statistics

Mean	35.775%
Standard Error	2.157%
Median	29.989%
Mode	13.324%
Standard Deviation	20.353%
Sample Variance	414.245%
Kurtosis	7.44
Skewness	2.32
Range	118.068%
Minimum	13.324%
Maximum	131.392%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.775%	89	100.00%	35.775%
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 1.18. Further, an Excess Kurtosis of 4.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.05%	0	0.00%	0.00%
-61.05% to -45.65%	0	0.00%	0.00%
-45.65% to -30.24%	6	6.74%	6.74%
-30.24% to -14.84%	9	10.11%	16.85%
-14.84% to 0.56%	34	38.20%	55.06%
0.56% to 15.96%	26	29.21%	84.27%
15.96% to 31.37%	8	8.99%	93.26%
31.37% to 46.77%	4	4.49%	97.75%
46.77% to 62.17%	1	1.12%	98.88%
Greater than 62.17%	1	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.98%	21.10%	78.65%	68.27%
±2σ	-40.51%	41.63%	96.63%	95.45%
±3σ	-61.05%	62.17%	98.88%	99.73%

Descriptive Statistics

Mean	0.561%
Standard Error	2.177%
Median	-0.793%
Mode	-39.841%
Standard Deviation	20.537%
Sample Variance	421.772%
Kurtosis	4.04
Skewness	1.18
Range	132.966%
Minimum	-39.841%
Maximum	93.125%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.751%	43	48.31%	7.610%
Negative	-13.638%	46	51.69%	-7.049%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.19. Further, an Excess Kurtosis of 0.79 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -123.75%	0	0.00%	0.00%
-123.75% to -89.98%	0	0.00%	0.00%
-89.98% to -56.22%	0	0.00%	0.00%
-56.22% to -22.45%	7	23.33%	23.33%
-22.45% to 11.31%	13	43.33%	66.67%
11.31% to 45.08%	4	13.33%	80.00%
45.08% to 78.84%	3	10.00%	90.00%
78.84% to 112.61%	1	3.33%	93.33%
112.61% to 146.38%	2	6.67%	100.00%
Greater than 146.38%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.71%	56.33%	73.33%	68.27%
±2σ	-78.73%	101.35%	93.33%	95.45%
±3σ	-123.75%	146.38%	100.00%	99.73%

Descriptive Statistics

Mean	11.312%
Standard Error	8.220%
Median	0.871%
Mode	-40.449%
Standard Deviation	45.021%
Sample Variance	2026.927%
Kurtosis	0.79
Skewness	1.19
Range	167.438%
Minimum	-40.449%
Maximum	126.989%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.265%	16	53.33%	22.008%
Negative	-22.920%	14	46.67%	-10.696%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	55.14%
12	3 Years	60.89%
20	5 Years	55.00%
40	10 Years	56.63%
80	20 Years	56.63%
200	50 Years	56.63%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.14. Further, an Excess Kurtosis of 0.70 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.68%	0	0.00%	0.00%
-37.68% to -10.29%	0	0.00%	0.00%
-10.29% to 17.11%	0	0.00%	0.00%
17.11% to 44.51%	7	22.58%	22.58%
44.51% to 71.90%	14	45.16%	67.74%
71.90% to 99.30%	3	9.68%	77.42%
99.30% to 126.70%	3	9.68%	87.10%
126.70% to 154.09%	3	9.68%	96.77%
154.09% to 181.49%	1	3.23%	100.00%
Greater than 181.49%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	35.37%	108.43%	80.65%	68.27%
±2σ	-1.16%	144.96%	96.77%	95.45%
±3σ	-37.68%	181.49%	100.00%	99.73%

Descriptive Statistics

Mean	71.903%
Standard Error	6.561%
Median	60.537%
Mode	21.001%
Standard Deviation	36.529%
Sample Variance	1334.392%
Kurtosis	0.70
Skewness	1.14
Range	153.125%
Minimum	21.001%
Maximum	174.126%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	71.903%	31	100.00%	71.903%
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 Fairly Symmetrical with a Skewness factor of 0.20. Further, an Excess Kurtosis of -0.81 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -102.74%	0	0.00%	0.00%
-102.74% to -76.51%	0	0.00%	0.00%
-76.51% to -50.27%	2	6.45%	6.45%
-50.27% to -24.03%	5	16.13%	22.58%
-24.03% to 2.21%	11	35.48%	58.06%
2.21% to 28.45%	5	16.13%	74.19%
28.45% to 54.68%	5	16.13%	90.32%
54.68% to 80.92%	3	9.68%	100.00%
80.92% to 107.16%	0	0.00%	100.00%
Greater than 107.16%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.78%	37.19%	64.52%	68.27%
±2σ	-67.76%	72.18%	100.00%	95.45%
±3σ	-102.74%	107.16%	100.00%	99.73%

Descriptive Statistics

Mean	2.208%
Standard Error	6.283%
Median	-2.308%
Mode	-56.192%
Standard Deviation	34.984%
Sample Variance	1223.870%
Kurtosis	-0.81
Skewness	0.20
Range	125.394%
Minimum	-56.192%
Maximum	69.202%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.552%	13	41.94%	15.328%
Negative	-22.596%	18	58.06%	-13.120%
Zero	0.000%	0	0.00%	0.000%

GH Deep Analytical Report