GPRO - 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	4.17%	3.69%	3.72%	5.44%	7.00%	6.99%	0.75	0.86	0.70	0.93
Weekly	9.46%	10.76%	9.70%	12.81%	15.41%	15.38%	0.69	0.94	0.59	1.10
Monthly	18.83%	25.60%	18.25%	30.72%	32.07%	32.03%	0.58	1.11	0.42	1.53
Quarterly	33.98%	56.08%	41.69%	59.34%	55.54%	55.47%	0.46	1.40	0.27	2.44
Annual	—	—	—	—	111.09%	110.94%	0.27	2.44	0.09	7.43
Option Time Horizon	—	—	—	—	42.73%	42.67%	0.53	1.23	0.34	1.89

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $0.81 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0750 (Bid $0.0500 / Ask $0.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 111.09% (CRR binomial tree, American, n=20 steps) | BS IV: 110.78% (European Black-Scholes) | Yahoo IV (Annual): 110.94% → 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 0.81. Further, an Excess Kurtosis of 9.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.56%	22	0.75%	0.75%
-12.56% to -9.43%	26	0.89%	1.64%
-9.43% to -6.30%	93	3.17%	4.81%
-6.30% to -3.17%	322	10.99%	15.80%
-3.17% to -0.04%	998	34.06%	49.86%
-0.04% to 3.09%	1020	34.81%	84.68%
3.09% to 6.22%	307	10.48%	95.15%
6.22% to 9.35%	81	2.76%	97.92%
9.35% to 12.48%	29	0.99%	98.91%
Greater than 12.48%	32	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.21%	4.14%	80.03%	68.27%
±2σ	-8.39%	8.31%	95.09%	95.45%
±3σ	-12.56%	12.48%	98.16%	99.73%

Descriptive Statistics

Mean	-0.039%
Standard Error	0.077%
Median	0.000%
Mode	0.000%
Standard Deviation	4.174%
Sample Variance	17.424%
Kurtosis	9.75
Skewness	0.81
Range	67.195%
Minimum	-26.103%
Maximum	41.092%
Count	2930

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.954%	1384	47.23%	1.395%
Negative	-2.875%	1462	49.90%	-1.435%
Zero	0.000%	84	2.87%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	9.89%
20	1 Month	8.49%
60	1 Quarter	6.66%
250	1 Year	9.01%
750	3 Years	6.09%
1,250	5 Years	5.44%
2,500	10 Years	5.34%
5,000	20 Years	5.50%
12,500	50 Years	5.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.22. Further, an Excess Kurtosis of 36.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.68%	0	0.00%	0.00%
-5.68% to -2.92%	0	0.00%	0.00%
-2.92% to -0.15%	0	0.00%	0.00%
-0.15% to 2.61%	382	13.03%	13.03%
2.61% to 5.38%	1503	51.28%	64.31%
5.38% to 8.14%	635	21.66%	85.98%
8.14% to 10.90%	229	7.81%	93.79%
10.90% to 13.67%	96	3.28%	97.07%
13.67% to 16.43%	47	1.60%	98.67%
Greater than 16.43%	39	1.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.69%	9.06%	88.23%	68.27%
±2σ	-2.00%	12.75%	96.28%	95.45%
±3σ	-5.68%	16.43%	98.67%	99.73%

Descriptive Statistics

Mean	5.375%
Standard Error	0.068%
Median	4.440%
Mode	3.448%
Standard Deviation	3.685%
Sample Variance	13.582%
Kurtosis	36.75
Skewness	4.22
Range	61.328%
Minimum	1.001%
Maximum	62.329%
Count	2931

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.375%	2931	100.00%	5.375%
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 0.69. Further, an Excess Kurtosis of 15.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.91%	18	0.61%	0.61%
-10.91% to -8.12%	31	1.06%	1.67%
-8.12% to -5.33%	80	2.73%	4.40%
-5.33% to -2.54%	346	11.80%	16.21%
-2.54% to 0.26%	1033	35.24%	51.45%
0.26% to 3.05%	947	32.31%	83.76%
3.05% to 5.84%	330	11.26%	95.02%
5.84% to 8.63%	87	2.97%	97.99%
8.63% to 11.43%	39	1.33%	99.32%
Greater than 11.43%	20	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.47%	3.98%	78.61%	68.27%
±2σ	-7.19%	7.70%	94.98%	95.45%
±3σ	-10.91%	11.43%	98.70%	99.73%

Descriptive Statistics

Mean	0.257%
Standard Error	0.069%
Median	0.177%
Mode	0.000%
Standard Deviation	3.723%
Sample Variance	13.858%
Kurtosis	15.72
Skewness	0.69
Range	77.332%
Minimum	-27.007%
Maximum	50.325%
Count	2931

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.746%	1507	51.42%	1.412%
Negative	-2.498%	1355	46.23%	-1.155%
Zero	0.000%	69	2.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.82. Further, an Excess Kurtosis of 4.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.60%	2	0.33%	0.33%
-28.60% to -21.50%	6	0.99%	1.32%
-21.50% to -14.40%	24	3.95%	5.26%
-14.40% to -7.30%	72	11.84%	17.11%
-7.30% to -0.20%	217	35.69%	52.80%
-0.20% to 6.89%	193	31.74%	84.54%
6.89% to 13.99%	58	9.54%	94.08%
13.99% to 21.09%	22	3.62%	97.70%
21.09% to 28.19%	7	1.15%	98.85%
Greater than 28.19%	7	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.67%	9.26%	77.80%	68.27%
±2σ	-19.13%	18.73%	95.56%	95.45%
±3σ	-28.60%	28.19%	98.52%	99.73%

Descriptive Statistics

Mean	-0.205%
Standard Error	0.384%
Median	-0.862%
Mode	0.000%
Standard Deviation	9.465%
Sample Variance	89.594%
Kurtosis	4.70
Skewness	0.82
Range	93.534%
Minimum	-39.640%
Maximum	53.894%
Count	608

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.189%	271	44.57%	3.204%
Negative	-6.320%	328	53.95%	-3.409%
Zero	0.000%	9	1.48%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	18.68%
12	1 Quarter	13.67%
52	1 Year	22.54%
156	3 Years	14.39%
260	5 Years	12.81%
520	10 Years	12.59%
1,040	20 Years	12.96%
2,600	50 Years	12.96%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.13. Further, an Excess Kurtosis of 32.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.19%	0	0.00%	0.00%
-18.19% to -10.12%	0	0.00%	0.00%
-10.12% to -2.05%	0	0.00%	0.00%
-2.05% to 6.03%	72	11.82%	11.82%
6.03% to 14.10%	321	52.71%	64.53%
14.10% to 22.17%	131	21.51%	86.04%
22.17% to 30.25%	48	7.88%	93.92%
30.25% to 38.32%	14	2.30%	96.22%
38.32% to 46.39%	13	2.13%	98.36%
Greater than 46.39%	10	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.34%	24.86%	90.31%	68.27%
±2σ	-7.43%	35.63%	95.89%	95.45%
±3σ	-18.19%	46.39%	98.36%	99.73%

Descriptive Statistics

Mean	14.099%
Standard Error	0.436%
Median	10.891%
Mode	5.133%
Standard Deviation	10.764%
Sample Variance	115.873%
Kurtosis	32.66
Skewness	4.13
Range	133.447%
Minimum	3.553%
Maximum	137.000%
Count	609

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.099%	609	100.00%	14.099%
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 1.03. Further, an Excess Kurtosis of 7.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.91%	6	0.99%	0.99%
-27.91% to -20.63%	2	0.33%	1.31%
-20.63% to -13.36%	21	3.45%	4.76%
-13.36% to -6.08%	70	11.49%	16.26%
-6.08% to 1.20%	231	37.93%	54.19%
1.20% to 8.47%	183	30.05%	84.24%
8.47% to 15.74%	59	9.69%	93.92%
15.74% to 23.02%	25	4.11%	98.03%
23.02% to 30.30%	4	0.66%	98.69%
Greater than 30.30%	8	1.31%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.50%	10.89%	78.49%	68.27%
±2σ	-18.20%	20.59%	95.89%	95.45%
±3σ	-27.90%	30.29%	97.70%	99.73%

Descriptive Statistics

Mean	1.195%
Standard Error	0.393%
Median	0.725%
Mode	0.000%
Standard Deviation	9.700%
Sample Variance	94.099%
Kurtosis	7.01
Skewness	1.03
Range	106.848%
Minimum	-33.714%
Maximum	73.134%
Count	609

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.467%	322	52.87%	3.948%
Negative	-6.008%	279	45.81%	-2.752%
Zero	0.000%	8	1.31%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.29. Further, an Excess Kurtosis of 3.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -57.65%	0	0.00%	0.00%
-57.65% to -43.52%	0	0.00%	0.00%
-43.52% to -29.40%	4	2.86%	2.86%
-29.40% to -15.27%	28	20.00%	22.86%
-15.27% to -1.15%	48	34.29%	57.14%
-1.15% to 12.98%	32	22.86%	80.00%
12.98% to 27.11%	19	13.57%	93.57%
27.11% to 41.23%	5	3.57%	97.14%
41.23% to 55.36%	2	1.43%	98.57%
Greater than 55.36%	2	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.98%	17.69%	76.43%	68.27%
±2σ	-38.81%	36.52%	97.14%	95.45%
±3σ	-57.65%	55.36%	98.57%	99.73%

Descriptive Statistics

Mean	-1.145%
Standard Error	1.592%
Median	-3.318%
Mode	-36.424%
Standard Deviation	18.834%
Sample Variance	354.711%
Kurtosis	3.18
Skewness	1.29
Range	117.312%
Minimum	-36.424%
Maximum	80.888%
Count	140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.775%	55	39.29%	6.590%
Negative	-12.739%	85	60.71%	-7.734%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	32.49%
12	1 Year	59.77%
36	3 Years	35.39%
60	5 Years	30.72%
120	10 Years	29.21%
240	20 Years	29.86%
600	50 Years	29.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.16. Further, an Excess Kurtosis of 27.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.40%	0	0.00%	0.00%
-41.40% to -22.20%	0	0.00%	0.00%
-22.20% to -3.00%	0	0.00%	0.00%
-3.00% to 16.20%	16	11.35%	11.35%
16.20% to 35.40%	74	52.48%	63.83%
35.40% to 54.60%	35	24.82%	88.65%
54.60% to 73.80%	9	6.38%	95.04%
73.80% to 92.99%	3	2.13%	97.16%
92.99% to 112.19%	2	1.42%	98.58%
Greater than 112.19%	2	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.80%	61.00%	90.07%	68.27%
±2σ	-15.80%	86.59%	96.45%	95.45%
±3σ	-41.40%	112.19%	98.58%	99.73%

Descriptive Statistics

Mean	35.398%
Standard Error	2.156%
Median	29.428%
Mode	31.250%
Standard Deviation	25.598%
Sample Variance	655.277%
Kurtosis	27.31
Skewness	4.16
Range	228.429%
Minimum	7.741%
Maximum	236.170%
Count	141

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.398%	141	100.00%	35.398%
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 -0.03. Further, an Excess Kurtosis of -0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.48%	0	0.00%	0.00%
-50.48% to -36.79%	2	1.42%	1.42%
-36.79% to -23.11%	8	5.67%	7.09%
-23.11% to -9.42%	23	16.31%	23.40%
-9.42% to 4.27%	40	28.37%	51.77%
4.27% to 17.96%	36	25.53%	77.30%
17.96% to 31.65%	24	17.02%	94.33%
31.65% to 45.34%	7	4.96%	99.29%
45.34% to 59.02%	1	0.71%	100.00%
Greater than 59.02%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.98%	22.52%	68.79%	68.27%
±2σ	-32.23%	40.77%	95.74%	95.45%
±3σ	-50.48%	59.02%	100.00%	99.73%

Descriptive Statistics

Mean	4.271%
Standard Error	1.537%
Median	3.739%
Mode	-14.130%
Standard Deviation	18.251%
Sample Variance	333.113%
Kurtosis	-0.08
Skewness	-0.03
Range	96.886%
Minimum	-43.436%
Maximum	53.450%
Count	141

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.427%	88	62.41%	9.628%
Negative	-14.253%	53	37.59%	-5.358%
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 1.24. Further, an Excess Kurtosis of 3.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -104.95%	0	0.00%	0.00%
-104.95% to -79.47%	0	0.00%	0.00%
-79.47% to -53.98%	2	4.26%	4.26%
-53.98% to -28.50%	9	19.15%	23.40%
-28.50% to -3.01%	15	31.91%	55.32%
-3.01% to 22.47%	13	27.66%	82.98%
22.47% to 47.96%	3	6.38%	89.36%
47.96% to 73.44%	4	8.51%	97.87%
73.44% to 98.93%	0	0.00%	97.87%
Greater than 98.93%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.99%	30.97%	74.47%	68.27%
±2σ	-70.97%	64.95%	97.87%	95.45%
±3σ	-104.95%	98.93%	97.87%	99.73%

Descriptive Statistics

Mean	-3.014%
Standard Error	4.956%
Median	-7.495%
Mode	-59.742%
Standard Deviation	33.980%
Sample Variance	1154.626%
Kurtosis	3.08
Skewness	1.24
Range	183.700%
Minimum	-59.742%
Maximum	123.958%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.463%	19	40.43%	11.102%
Negative	-24.572%	27	57.45%	-14.116%
Zero	0.000%	1	2.13%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	135.76%
12	3 Years	75.10%
20	5 Years	59.34%
40	10 Years	52.97%
80	20 Years	54.77%
200	50 Years	54.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.66. Further, an Excess Kurtosis of 9.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -92.31%	0	0.00%	0.00%
-92.31% to -50.24%	0	0.00%	0.00%
-50.24% to -8.18%	0	0.00%	0.00%
-8.18% to 33.88%	5	10.42%	10.42%
33.88% to 75.94%	27	56.25%	66.67%
75.94% to 118.00%	9	18.75%	85.42%
118.00% to 160.06%	1	2.08%	87.50%
160.06% to 202.12%	5	10.42%	97.92%
202.12% to 244.18%	0	0.00%	97.92%
Greater than 244.18%	1	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.86%	132.02%	85.42%	68.27%
±2σ	-36.22%	188.10%	97.92%	95.45%
±3σ	-92.30%	244.18%	97.92%	99.73%

Descriptive Statistics

Mean	75.938%
Standard Error	8.095%
Median	55.402%
Mode	16.798%
Standard Deviation	56.081%
Sample Variance	3145.116%
Kurtosis	9.56
Skewness	2.66
Range	322.091%
Minimum	16.798%
Maximum	338.889%
Count	48

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.938%	48	100.00%	75.938%
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 1.13. Further, an Excess Kurtosis of 1.81 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -110.83%	0	0.00%	0.00%
-110.83% to -79.56%	0	0.00%	0.00%
-79.56% to -48.29%	1	2.08%	2.08%
-48.29% to -17.02%	8	16.67%	18.75%
-17.02% to 14.25%	20	41.67%	60.42%
14.25% to 45.52%	11	22.92%	83.33%
45.52% to 76.79%	5	10.42%	93.75%
76.79% to 108.06%	1	2.08%	95.83%
108.06% to 139.33%	1	2.08%	97.92%
Greater than 139.33%	1	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.44%	55.94%	70.83%	68.27%
±2σ	-69.13%	97.63%	95.83%	95.45%
±3σ	-110.83%	139.33%	97.92%	99.73%

Descriptive Statistics

Mean	14.250%
Standard Error	6.018%
Median	6.575%
Mode	-55.039%
Standard Deviation	41.692%
Sample Variance	1738.217%
Kurtosis	1.81
Skewness	1.13
Range	207.039%
Minimum	-55.039%
Maximum	152.000%
Count	48

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.055%	27	56.25%	22.531%
Negative	-19.874%	20	41.67%	-8.281%
Zero	0.000%	1	2.08%	0.000%

GPRO Deep Analytical Report