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%	7.91%	6.34%	6.45%	1.60	1.81	1.50	1.93
Weekly	11.69%	11.71%	12.07%	17.99%	13.96%	14.19%	1.48	1.95	1.29	2.25
Monthly	26.25%	25.75%	26.94%	38.78%	29.07%	29.54%	1.27	2.27	0.95	3.04
Quarterly	50.15%	63.29%	52.75%	66.22%	50.35%	51.17%	1.03	2.81	0.62	4.65
Annual	—	—	—	—	100.70%	102.34%	0.62	4.65	0.23	12.74
Option Time Horizon	—	—	—	—	47.73%	48.51%	1.05	2.74	0.65	4.42

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $1.70 | Strike (K): $2.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.2250 (Bid $0.1500 / Ask $0.3000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 100.70% (CRR binomial tree, American, n=20 steps) | BS IV: 101.24% (European Black-Scholes) | Yahoo IV (Annual): 102.34% → 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 4.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.02%	3	0.26%	0.26%
-16.02% to -12.03%	11	0.95%	1.21%
-12.03% to -8.05%	46	3.99%	5.20%
-8.05% to -4.06%	142	12.31%	17.50%
-4.06% to -0.08%	391	33.88%	51.39%
-0.08% to 3.91%	356	30.85%	82.24%
3.91% to 7.89%	138	11.96%	94.19%
7.89% to 11.88%	40	3.47%	97.66%
11.88% to 15.87%	13	1.13%	98.79%
Greater than 15.87%	14	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.39%	5.24%	76.43%	68.27%
±2σ	-10.70%	10.55%	94.37%	95.45%
±3σ	-16.02%	15.87%	98.53%	99.73%

Descriptive Statistics

Mean	-0.076%
Standard Error	0.156%
Median	-0.295%
Mode	0.000%
Standard Deviation	5.314%
Sample Variance	28.242%
Kurtosis	4.23
Skewness	0.32
Range	63.997%
Minimum	-35.374%
Maximum	28.623%
Count	1154

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.208%	506	43.85%	1.845%
Negative	-3.720%	596	51.65%	-1.921%
Zero	0.000%	52	4.51%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.87%
20	1 Month	7.49%
60	1 Quarter	5.64%
250	1 Year	5.76%
750	3 Years	7.73%
1,250	5 Years	7.91%
2,500	10 Years	7.91%
5,000	20 Years	7.91%
12,500	50 Years	7.91%

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 15.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.78%	0	0.00%	0.00%
-5.78% to -2.34%	0	0.00%	0.00%
-2.34% to 1.10%	0	0.00%	0.00%
1.10% to 4.54%	228	19.74%	19.74%
4.54% to 7.97%	497	43.03%	62.77%
7.97% to 11.41%	227	19.65%	82.42%
11.41% to 14.85%	125	10.82%	93.25%
14.85% to 18.29%	42	3.64%	96.88%
18.29% to 21.72%	19	1.65%	98.53%
Greater than 21.72%	17	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.39%	12.56%	79.91%	68.27%
±2σ	-1.19%	17.14%	95.76%	95.45%
±3σ	-5.78%	21.72%	98.53%	99.73%

Descriptive Statistics

Mean	7.973%
Standard Error	0.135%
Median	6.885%
Mode	4.762%
Standard Deviation	4.583%
Sample Variance	21.006%
Kurtosis	15.52
Skewness	2.61
Range	56.085%
Minimum	1.602%
Maximum	57.687%
Count	1155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.973%	1155	100.00%	7.973%
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 0.13. Further, an Excess Kurtosis of 1.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.19%	4	0.35%	0.35%
-14.19% to -10.59%	16	1.39%	1.73%
-10.59% to -6.99%	53	4.59%	6.32%
-6.99% to -3.40%	154	13.33%	19.65%
-3.40% to 0.20%	369	31.95%	51.60%
0.20% to 3.80%	348	30.13%	81.73%
3.80% to 7.39%	137	11.86%	93.59%
7.39% to 10.99%	43	3.72%	97.32%
10.99% to 14.59%	26	2.25%	99.57%
Greater than 14.59%	5	0.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.60%	5.00%	72.81%	68.27%
±2σ	-9.39%	9.79%	93.77%	95.45%
±3σ	-14.19%	14.59%	99.22%	99.73%

Descriptive Statistics

Mean	0.200%
Standard Error	0.141%
Median	0.000%
Mode	0.000%
Standard Deviation	4.796%
Sample Variance	23.006%
Kurtosis	1.17
Skewness	0.13
Range	38.750%
Minimum	-18.750%
Maximum	20.000%
Count	1155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.877%	562	48.66%	1.886%
Negative	-3.574%	545	47.19%	-1.686%
Zero	0.000%	48	4.16%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.66. Further, an Excess Kurtosis of 2.76 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.36%	0	0.00%	0.00%
-35.36% to -26.60%	2	0.83%	0.83%
-26.60% to -17.84%	11	4.58%	5.42%
-17.84% to -9.07%	32	13.33%	18.75%
-9.07% to -0.31%	80	33.33%	52.08%
-0.31% to 8.46%	73	30.42%	82.50%
8.46% to 17.22%	28	11.67%	94.17%
17.22% to 25.98%	8	3.33%	97.50%
25.98% to 34.75%	4	1.67%	99.17%
Greater than 34.75%	2	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.99%	11.38%	75.00%	68.27%
±2σ	-23.68%	23.06%	94.58%	95.45%
±3σ	-35.36%	34.75%	99.17%	99.73%

Descriptive Statistics

Mean	-0.309%
Standard Error	0.754%
Median	-0.847%
Mode	0.000%
Standard Deviation	11.685%
Sample Variance	136.537%
Kurtosis	2.76
Skewness	0.66
Range	92.745%
Minimum	-35.075%
Maximum	57.670%
Count	240

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.261%	108	45.00%	4.167%
Negative	-8.460%	127	52.92%	-4.477%
Zero	0.000%	5	2.08%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	19.07%
12	1 Quarter	12.44%
52	1 Year	12.73%
156	3 Years	17.45%
260	5 Years	17.99%
520	10 Years	17.99%
1,040	20 Years	17.99%
2,600	50 Years	17.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.18. Further, an Excess Kurtosis of 9.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.97%	0	0.00%	0.00%
-14.97% to -6.19%	0	0.00%	0.00%
-6.19% to 2.59%	0	0.00%	0.00%
2.59% to 11.38%	54	22.41%	22.41%
11.38% to 20.16%	91	37.76%	60.17%
20.16% to 28.94%	50	20.75%	80.91%
28.94% to 37.73%	29	12.03%	92.95%
37.73% to 46.51%	12	4.98%	97.93%
46.51% to 55.29%	2	0.83%	98.76%
Greater than 55.29%	3	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.45%	31.87%	77.59%	68.27%
±2σ	-3.26%	43.58%	96.68%	95.45%
±3σ	-14.98%	55.29%	98.76%	99.73%

Descriptive Statistics

Mean	20.158%
Standard Error	0.754%
Median	17.833%
Mode	16.667%
Standard Deviation	11.711%
Sample Variance	137.142%
Kurtosis	9.64
Skewness	2.18
Range	96.400%
Minimum	4.651%
Maximum	101.051%
Count	241

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.158%	241	100.00%	20.158%
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 3.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.55%	1	0.41%	0.41%
-34.55% to -25.50%	2	0.83%	1.24%
-25.50% to -16.45%	7	2.90%	4.15%
-16.45% to -7.40%	38	15.77%	19.92%
-7.40% to 1.65%	81	33.61%	53.53%
1.65% to 10.70%	72	29.88%	83.40%
10.70% to 19.75%	22	9.13%	92.53%
19.75% to 28.80%	12	4.98%	97.51%
28.80% to 37.84%	4	1.66%	99.17%
Greater than 37.84%	2	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.42%	13.71%	75.52%	68.27%
±2σ	-22.49%	25.78%	94.19%	95.45%
±3σ	-34.55%	37.84%	98.76%	99.73%

Descriptive Statistics

Mean	1.646%
Standard Error	0.777%
Median	0.334%
Mode	0.000%
Standard Deviation	12.066%
Sample Variance	145.596%
Kurtosis	3.03
Skewness	0.78
Range	98.353%
Minimum	-35.135%
Maximum	63.218%
Count	241

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.092%	125	51.87%	5.234%
Negative	-7.862%	110	45.64%	-3.588%
Zero	0.000%	6	2.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.27. Further, an Excess Kurtosis of 3.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.85%	0	0.00%	0.00%
-79.85% to -60.16%	0	0.00%	0.00%
-60.16% to -40.48%	2	3.64%	3.64%
-40.48% to -20.79%	11	20.00%	23.64%
-20.79% to -1.10%	16	29.09%	52.73%
-1.10% to 18.59%	19	34.55%	87.27%
18.59% to 38.28%	3	5.45%	92.73%
38.28% to 57.97%	2	3.64%	96.36%
57.97% to 77.66%	1	1.82%	98.18%
Greater than 77.66%	1	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.35%	25.15%	74.55%	68.27%
±2σ	-53.60%	51.41%	96.36%	95.45%
±3σ	-79.85%	77.66%	98.18%	99.73%

Descriptive Statistics

Mean	-1.097%
Standard Error	3.540%
Median	-3.797%
Mode	-47.410%
Standard Deviation	26.252%
Sample Variance	689.173%
Kurtosis	3.50
Skewness	1.27
Range	148.197%
Minimum	-47.410%
Maximum	100.787%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.900%	25	45.45%	9.046%
Negative	-19.236%	29	52.73%	-10.143%
Zero	0.000%	1	1.82%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.46%
12	1 Year	25.58%
36	3 Years	38.91%
60	5 Years	38.78%
120	10 Years	38.78%
240	20 Years	38.78%
600	50 Years	38.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.39. Further, an Excess Kurtosis of 1.92 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.71%	0	0.00%	0.00%
-28.71% to -9.39%	0	0.00%	0.00%
-9.39% to 9.92%	0	0.00%	0.00%
9.92% to 29.24%	10	17.86%	17.86%
29.24% to 48.56%	21	37.50%	55.36%
48.56% to 67.87%	16	28.57%	83.93%
67.87% to 87.19%	5	8.93%	92.86%
87.19% to 106.50%	0	0.00%	92.86%
106.50% to 125.82%	3	5.36%	98.21%
Greater than 125.82%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.80%	74.31%	80.36%	68.27%
±2σ	-2.95%	100.07%	92.86%	95.45%
±3σ	-28.71%	125.82%	98.21%	99.73%

Descriptive Statistics

Mean	48.556%
Standard Error	3.442%
Median	42.389%
Mode	13.815%
Standard Deviation	25.755%
Sample Variance	663.321%
Kurtosis	1.92
Skewness	1.39
Range	113.458%
Minimum	13.815%
Maximum	127.273%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.556%	56	100.00%	48.556%
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 -73.70%	0	0.00%	0.00%
-73.70% to -53.50%	0	0.00%	0.00%
-53.50% to -33.30%	2	3.57%	3.57%
-33.30% to -13.10%	7	12.50%	16.07%
-13.10% to 7.11%	23	41.07%	57.14%
7.11% to 27.31%	14	25.00%	82.14%
27.31% to 47.51%	5	8.93%	91.07%
47.51% to 67.71%	3	5.36%	96.43%
67.71% to 87.91%	1	1.79%	98.21%
Greater than 87.91%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.83%	34.04%	75.00%	68.27%
±2σ	-46.77%	60.98%	92.86%	95.45%
±3σ	-73.70%	87.91%	98.21%	99.73%

Descriptive Statistics

Mean	7.105%
Standard Error	3.600%
Median	3.808%
Mode	-49.804%
Standard Deviation	26.936%
Sample Variance	725.570%
Kurtosis	1.20
Skewness	0.86
Range	142.228%
Minimum	-49.804%
Maximum	92.424%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.667%	31	55.36%	13.655%
Negative	-14.673%	25	44.64%	-6.550%
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 3.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -152.71%	0	0.00%	0.00%
-152.71% to -115.10%	0	0.00%	0.00%
-115.10% to -77.49%	0	0.00%	0.00%
-77.49% to -39.88%	3	15.79%	15.79%
-39.88% to -2.27%	9	47.37%	63.16%
-2.27% to 35.33%	5	26.32%	89.47%
35.33% to 72.94%	0	0.00%	89.47%
72.94% to 110.55%	0	0.00%	89.47%
110.55% to 148.16%	2	10.53%	100.00%
Greater than 148.16%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-52.42%	47.87%	84.21%	68.27%
±2σ	-102.57%	98.02%	89.47%	95.45%
±3σ	-152.71%	148.16%	100.00%	99.73%

Descriptive Statistics

Mean	-2.275%
Standard Error	11.504%
Median	-10.256%
Mode	-64.337%
Standard Deviation	50.146%
Sample Variance	2514.624%
Kurtosis	3.06
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	-26.306%	13	68.42%	-17.999%
Zero	0.000%	1	5.26%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	36.66%
12	3 Years	64.66%
20	5 Years	66.22%
40	10 Years	66.22%
80	20 Years	66.22%
200	50 Years	66.22%

High-to-Low 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 1.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -91.28%	0	0.00%	0.00%
-91.28% to -43.81%	0	0.00%	0.00%
-43.81% to 3.65%	0	0.00%	0.00%
3.65% to 51.12%	4	20.00%	20.00%
51.12% to 98.58%	8	40.00%	60.00%
98.58% to 146.05%	3	15.00%	75.00%
146.05% to 193.51%	4	20.00%	95.00%
193.51% to 240.98%	0	0.00%	95.00%
240.98% to 288.44%	1	5.00%	100.00%
Greater than 288.44%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	35.30%	161.87%	80.00%	68.27%
±2σ	-27.99%	225.16%	95.00%	95.45%
±3σ	-91.28%	288.44%	100.00%	99.73%

Descriptive Statistics

Mean	98.583%
Standard Error	14.151%
Median	70.726%
Mode	23.625%
Standard Deviation	63.287%
Sample Variance	4005.233%
Kurtosis	1.73
Skewness	1.29
Range	252.237%
Minimum	23.625%
Maximum	275.862%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	98.583%	20	100.00%	98.583%
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 1.26. Further, an Excess Kurtosis of 2.98 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 -95.58%	0	0.00%	0.00%
-95.58% to -56.02%	1	5.00%	5.00%
-56.02% to -16.46%	2	10.00%	15.00%
-16.46% to 23.11%	9	45.00%	60.00%
23.11% to 62.67%	5	25.00%	85.00%
62.67% to 102.23%	2	10.00%	95.00%
102.23% to 141.79%	0	0.00%	95.00%
141.79% to 181.36%	1	5.00%	100.00%
Greater than 181.36%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.64%	75.86%	75.00%	68.27%
±2σ	-82.39%	128.61%	95.00%	95.45%
±3σ	-135.14%	181.36%	100.00%	99.73%

Descriptive Statistics

Mean	23.106%
Standard Error	11.795%
Median	10.743%
Mode	-56.777%
Standard Deviation	52.750%
Sample Variance	2782.607%
Kurtosis	2.98
Skewness	1.26
Range	235.493%
Minimum	-56.777%
Maximum	178.716%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.850%	14	70.00%	30.695%
Negative	-25.298%	6	30.00%	-7.589%
Zero	0.000%	0	0.00%	0.000%

BLND Deep Analytical Report