BLND - 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	5.31%	4.58%	4.80%	7.92%	5.85%	5.81%	1.58	1.77	1.49	1.88
Weekly	11.66%	11.66%	12.03%	18.03%	12.87%	12.78%	1.47	1.90	1.29	2.16
Monthly	26.03%	25.59%	26.76%	38.72%	26.79%	26.61%	1.28	2.18	0.98	2.85
Quarterly	50.18%	62.60%	52.79%	66.67%	46.40%	46.09%	1.05	2.66	0.66	4.22
Annual	—	—	—	—	92.79%	92.19%	0.66	4.22	0.26	10.68
Option Time Horizon	—	—	—	—	35.02%	34.80%	1.18	2.37	0.83	3.36

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $1.67 | Strike (K): $2.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1250 (Bid $0.0000 / Ask $0.2500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 92.79% (CRR binomial tree, American, n=20 steps) | BS IV: 92.65% (European Black-Scholes) | Yahoo IV (Annual): 92.19% → 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 0.32. Further, an Excess Kurtosis of 4.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.00%	3	0.26%	0.26%
-16.00% to -12.02%	12	1.02%	1.28%
-12.02% to -8.04%	46	3.91%	5.19%
-8.04% to -4.05%	146	12.43%	17.62%
-4.05% to -0.07%	395	33.62%	51.23%
-0.07% to 3.91%	365	31.06%	82.30%
3.91% to 7.89%	138	11.74%	94.04%
7.89% to 11.87%	43	3.66%	97.70%
11.87% to 15.85%	13	1.11%	98.81%
Greater than 15.85%	14	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.38%	5.23%	76.43%	68.27%
±2σ	-10.69%	10.54%	94.30%	95.45%
±3σ	-16.00%	15.85%	98.55%	99.73%

Descriptive Statistics

Mean	-0.074%
Standard Error	0.155%
Median	-0.292%
Mode	0.000%
Standard Deviation	5.308%
Sample Variance	28.171%
Kurtosis	4.18
Skewness	0.32
Range	63.997%
Minimum	-35.374%
Maximum	28.623%
Count	1175

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.186%	518	44.09%	1.845%
Negative	-3.728%	605	51.49%	-1.920%
Zero	0.000%	52	4.43%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.21%
20	1 Month	8.56%
60	1 Quarter	7.06%
250	1 Year	5.86%
750	3 Years	7.63%
1,250	5 Years	7.92%
2,500	10 Years	7.92%
5,000	20 Years	7.92%
12,500	50 Years	7.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.59. Further, an Excess Kurtosis of 15.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.75%	0	0.00%	0.00%
-5.75% to -2.32%	0	0.00%	0.00%
-2.32% to 1.11%	0	0.00%	0.00%
1.11% to 4.55%	231	19.64%	19.64%
4.55% to 7.98%	508	43.20%	62.84%
7.98% to 11.42%	231	19.64%	82.48%
11.42% to 14.85%	126	10.71%	93.20%
14.85% to 18.28%	42	3.57%	96.77%
18.28% to 21.72%	21	1.79%	98.55%
Greater than 21.72%	17	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.40%	12.56%	80.02%	68.27%
±2σ	-1.17%	17.14%	95.66%	95.45%
±3σ	-5.75%	21.72%	98.55%	99.73%

Descriptive Statistics

Mean	7.982%
Standard Error	0.133%
Median	6.887%
Mode	4.762%
Standard Deviation	4.578%
Sample Variance	20.954%
Kurtosis	15.33
Skewness	2.59
Range	56.085%
Minimum	1.602%
Maximum	57.687%
Count	1176

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.982%	1176	100.00%	7.982%
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 0.14. Further, an Excess Kurtosis of 1.15 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.23%	4	0.34%	0.34%
-14.23% to -10.62%	16	1.36%	1.70%
-10.62% to -7.02%	55	4.68%	6.38%
-7.02% to -3.42%	157	13.35%	19.73%
-3.42% to 0.19%	375	31.89%	51.62%
0.19% to 3.79%	355	30.19%	81.80%
3.79% to 7.39%	138	11.73%	93.54%
7.39% to 11.00%	44	3.74%	97.28%
11.00% to 14.60%	27	2.30%	99.57%
Greater than 14.60%	5	0.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.62%	4.99%	72.79%	68.27%
±2σ	-9.42%	9.80%	93.71%	95.45%
±3σ	-14.23%	14.60%	99.23%	99.73%

Descriptive Statistics

Mean	0.187%
Standard Error	0.140%
Median	0.000%
Mode	0.000%
Standard Deviation	4.805%
Sample Variance	23.088%
Kurtosis	1.15
Skewness	0.14
Range	38.750%
Minimum	-18.750%
Maximum	20.000%
Count	1176

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.879%	571	48.55%	1.883%
Negative	-3.588%	556	47.28%	-1.696%
Zero	0.000%	49	4.17%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.65. Further, an Excess Kurtosis of 2.72 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.30%	0	0.00%	0.00%
-35.30% to -26.55%	2	0.82%	0.82%
-26.55% to -17.80%	11	4.51%	5.33%
-17.80% to -9.05%	34	13.93%	19.26%
-9.05% to -0.30%	80	32.79%	52.05%
-0.30% to 8.45%	74	30.33%	82.38%
8.45% to 17.19%	29	11.89%	94.26%
17.19% to 25.94%	8	3.28%	97.54%
25.94% to 34.69%	4	1.64%	99.18%
Greater than 34.69%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.97%	11.36%	74.18%	68.27%
±2σ	-23.63%	23.02%	94.67%	95.45%
±3σ	-35.29%	34.69%	99.18%	99.73%

Descriptive Statistics

Mean	-0.303%
Standard Error	0.747%
Median	-0.925%
Mode	0.000%
Standard Deviation	11.664%
Sample Variance	136.055%
Kurtosis	2.72
Skewness	0.65
Range	92.745%
Minimum	-35.075%
Maximum	57.670%
Count	244

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.279%	110	45.08%	4.183%
Negative	-8.485%	129	52.87%	-4.486%
Zero	0.000%	5	2.05%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	19.51%
12	1 Quarter	16.84%
52	1 Year	12.92%
156	3 Years	17.19%
260	5 Years	18.03%
520	10 Years	18.03%
1,040	20 Years	18.03%
2,600	50 Years	18.03%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.17. Further, an Excess Kurtosis of 9.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.78%	0	0.00%	0.00%
-14.78% to -6.04%	0	0.00%	0.00%
-6.04% to 2.71%	0	0.00%	0.00%
2.71% to 11.45%	54	22.04%	22.04%
11.45% to 20.19%	94	38.37%	60.41%
20.19% to 28.93%	50	20.41%	80.82%
28.93% to 37.68%	30	12.24%	93.06%
37.68% to 46.42%	12	4.90%	97.96%
46.42% to 55.16%	2	0.82%	98.78%
Greater than 55.16%	3	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.53%	31.85%	76.73%	68.27%
±2σ	-3.12%	43.50%	96.33%	95.45%
±3σ	-14.78%	55.16%	98.78%	99.73%

Descriptive Statistics

Mean	20.191%
Standard Error	0.745%
Median	17.833%
Mode	16.667%
Standard Deviation	11.657%
Sample Variance	135.878%
Kurtosis	9.65
Skewness	2.17
Range	96.400%
Minimum	4.651%
Maximum	101.051%
Count	245

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.191%	245	100.00%	20.191%
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 0.78. Further, an Excess Kurtosis of 3.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.48%	1	0.41%	0.41%
-34.48% to -25.46%	2	0.82%	1.22%
-25.46% to -16.44%	7	2.86%	4.08%
-16.44% to -7.41%	39	15.92%	20.00%
-7.41% to 1.61%	81	33.06%	53.06%
1.61% to 10.63%	74	30.20%	83.27%
10.63% to 19.66%	23	9.39%	92.65%
19.66% to 28.68%	12	4.90%	97.55%
28.68% to 37.70%	4	1.63%	99.18%
Greater than 37.70%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.42%	13.64%	75.51%	68.27%
±2σ	-22.45%	25.67%	94.29%	95.45%
±3σ	-34.48%	37.70%	98.78%	99.73%

Descriptive Statistics

Mean	1.609%
Standard Error	0.769%
Median	0.334%
Mode	0.000%
Standard Deviation	12.031%
Sample Variance	144.742%
Kurtosis	3.02
Skewness	0.78
Range	98.353%
Minimum	-35.135%
Maximum	63.218%
Count	245

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.069%	127	51.84%	5.219%
Negative	-7.898%	112	45.71%	-3.610%
Zero	0.000%	6	2.45%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.28. Further, an Excess Kurtosis of 3.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.19%	0	0.00%	0.00%
-79.19% to -59.67%	0	0.00%	0.00%
-59.67% to -40.15%	2	3.57%	3.57%
-40.15% to -20.62%	11	19.64%	23.21%
-20.62% to -1.10%	16	28.57%	51.79%
-1.10% to 18.42%	20	35.71%	87.50%
18.42% to 37.94%	3	5.36%	92.86%
37.94% to 57.46%	2	3.57%	96.43%
57.46% to 76.98%	1	1.79%	98.21%
Greater than 76.98%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.13%	24.93%	75.00%	68.27%
±2σ	-53.16%	50.95%	96.43%	95.45%
±3σ	-79.19%	76.98%	98.21%	99.73%

Descriptive Statistics

Mean	-1.103%
Standard Error	3.478%
Median	-3.498%
Mode	-47.410%
Standard Deviation	26.029%
Sample Variance	677.500%
Kurtosis	3.60
Skewness	1.28
Range	148.197%
Minimum	-47.410%
Maximum	100.787%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.900%	25	44.64%	8.884%
Negative	-18.643%	30	53.57%	-9.987%
Zero	0.000%	1	1.79%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	35.44%
12	1 Year	25.63%
36	3 Years	38.43%
60	5 Years	38.72%
120	10 Years	38.72%
240	20 Years	38.72%
600	50 Years	38.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.40. Further, an Excess Kurtosis of 1.98 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.30%	0	0.00%	0.00%
-28.30% to -9.11%	0	0.00%	0.00%
-9.11% to 10.08%	0	0.00%	0.00%
10.08% to 29.27%	10	17.54%	17.54%
29.27% to 48.47%	22	38.60%	56.14%
48.47% to 67.66%	16	28.07%	84.21%
67.66% to 86.85%	5	8.77%	92.98%
86.85% to 106.04%	0	0.00%	92.98%
106.04% to 125.23%	3	5.26%	98.25%
Greater than 125.23%	1	1.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.88%	74.06%	78.95%	68.27%
±2σ	-2.71%	99.64%	92.98%	95.45%
±3σ	-28.30%	125.23%	98.25%	99.73%

Descriptive Statistics

Mean	48.466%
Standard Error	3.389%
Median	41.357%
Mode	13.815%
Standard Deviation	25.589%
Sample Variance	654.772%
Kurtosis	1.98
Skewness	1.40
Range	113.458%
Minimum	13.815%
Maximum	127.273%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.466%	57	100.00%	48.466%
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 0.88. Further, an Excess Kurtosis of 1.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -73.31%	0	0.00%	0.00%
-73.31% to -53.24%	0	0.00%	0.00%
-53.24% to -33.17%	2	3.51%	3.51%
-33.17% to -13.10%	7	12.28%	15.79%
-13.10% to 6.97%	24	42.11%	57.89%
6.97% to 27.04%	14	24.56%	82.46%
27.04% to 47.11%	5	8.77%	91.23%
47.11% to 67.18%	3	5.26%	96.49%
67.18% to 87.25%	1	1.75%	98.25%
Greater than 87.25%	1	1.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.79%	33.73%	75.44%	68.27%
±2σ	-46.55%	60.49%	92.98%	95.45%
±3σ	-73.31%	87.25%	98.25%	99.73%

Descriptive Statistics

Mean	6.967%
Standard Error	3.544%
Median	3.485%
Mode	-49.804%
Standard Deviation	26.760%
Sample Variance	716.084%
Kurtosis	1.26
Skewness	0.88
Range	142.228%
Minimum	-49.804%
Maximum	92.424%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.720%	31	54.39%	13.444%
Negative	-14.201%	26	45.61%	-6.478%
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 1.76. Further, an Excess Kurtosis of 3.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -152.89%	0	0.00%	0.00%
-152.89% to -115.25%	0	0.00%	0.00%
-115.25% to -77.62%	0	0.00%	0.00%
-77.62% to -39.98%	3	15.79%	15.79%
-39.98% to -2.34%	9	47.37%	63.16%
-2.34% to 35.30%	5	26.32%	89.47%
35.30% to 72.94%	0	0.00%	89.47%
72.94% to 110.57%	0	0.00%	89.47%
110.57% to 148.21%	2	10.53%	100.00%
Greater than 148.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-52.52%	47.84%	84.21%	68.27%
±2σ	-102.71%	98.03%	89.47%	95.45%
±3σ	-152.89%	148.21%	100.00%	99.73%

Descriptive Statistics

Mean	-2.341%
Standard Error	11.513%
Median	-10.256%
Mode	-64.337%
Standard Deviation	50.184%
Sample Variance	2518.392%
Kurtosis	3.05
Skewness	1.76
Range	189.957%
Minimum	-64.337%
Maximum	125.620%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	59.752%	5	26.32%	15.724%
Negative	-26.403%	13	68.42%	-18.065%
Zero	0.000%	1	5.26%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	38.79%
12	3 Years	65.37%
20	5 Years	66.67%
40	10 Years	66.67%
80	20 Years	66.67%
200	50 Years	66.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.31. Further, an Excess Kurtosis of 1.83 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -88.17%	0	0.00%	0.00%
-88.17% to -41.23%	0	0.00%	0.00%
-41.23% to 5.72%	0	0.00%	0.00%
5.72% to 52.67%	4	20.00%	20.00%
52.67% to 99.62%	8	40.00%	60.00%
99.62% to 146.56%	3	15.00%	75.00%
146.56% to 193.51%	4	20.00%	95.00%
193.51% to 240.46%	0	0.00%	95.00%
240.46% to 287.40%	1	5.00%	100.00%
Greater than 287.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	37.02%	162.21%	80.00%	68.27%
±2σ	-25.58%	224.81%	95.00%	95.45%
±3σ	-88.17%	287.40%	100.00%	99.73%

Descriptive Statistics

Mean	99.616%
Standard Error	13.997%
Median	70.725%
Mode	23.625%
Standard Deviation	62.596%
Sample Variance	3918.254%
Kurtosis	1.83
Skewness	1.31
Range	252.237%
Minimum	23.625%
Maximum	275.862%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	99.616%	20	100.00%	99.616%
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 1.25. Further, an Excess Kurtosis of 2.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -135.14%	0	0.00%	0.00%
-135.14% to -95.55%	0	0.00%	0.00%
-95.55% to -55.96%	1	5.00%	5.00%
-55.96% to -16.36%	2	10.00%	15.00%
-16.36% to 23.23%	9	45.00%	60.00%
23.23% to 62.82%	5	25.00%	85.00%
62.82% to 102.42%	2	10.00%	95.00%
102.42% to 142.01%	0	0.00%	95.00%
142.01% to 181.60%	1	5.00%	100.00%
Greater than 181.60%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.56%	76.02%	75.00%	68.27%
±2σ	-82.35%	128.81%	95.00%	95.45%
±3σ	-135.14%	181.60%	100.00%	99.73%

Descriptive Statistics

Mean	23.230%
Standard Error	11.804%
Median	10.743%
Mode	-56.777%
Standard Deviation	52.791%
Sample Variance	2786.872%
Kurtosis	2.94
Skewness	1.25
Range	235.493%
Minimum	-56.777%
Maximum	178.716%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	44.028%	14	70.00%	30.820%
Negative	-25.298%	6	30.00%	-7.589%
Zero	0.000%	0	0.00%	0.000%

BLND Deep Analytical Report