BYND - 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	7.27%	7.54%	5.27%	7.83%	9.82%	9.74%	0.64	0.78	0.58	0.86
Weekly	12.61%	25.08%	13.77%	19.16%	21.61%	21.45%	0.57	0.88	0.46	1.09
Monthly	22.95%	154.90%	25.06%	43.30%	44.99%	44.65%	0.45	1.11	0.29	1.74
Quarterly	28.66%	261.88%	54.03%	74.71%	77.92%	77.34%	0.32	1.54	0.15	3.36
Annual	—	—	—	—	155.84%	154.69%	0.15	3.36	0.03	15.96
Option Time Horizon	—	—	—	—	58.82%	58.39%	0.39	1.27	0.22	2.29

Calculation Notes: Computed at 2026-03-23T16:42 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $0.71 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0850 (Bid $0.0800 / Ask $0.0900) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 155.84% (CRR binomial tree, American, n=20 steps) | BS IV: 156.89% (European Black-Scholes) | Yahoo IV (Annual): 154.69% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.95. Further, an Excess Kurtosis of 151.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.87%	7	0.40%	0.40%
-21.87% to -16.41%	4	0.23%	0.64%
-16.41% to -10.96%	18	1.04%	1.68%
-10.96% to -5.50%	165	9.53%	11.21%
-5.50% to -0.05%	735	42.46%	53.67%
-0.05% to 5.41%	621	35.88%	89.54%
5.41% to 10.87%	124	7.16%	96.71%
10.87% to 16.32%	33	1.91%	98.61%
16.32% to 21.78%	13	0.75%	99.36%
Greater than 21.78%	11	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.32%	7.23%	87.41%	68.27%
±2σ	-14.59%	14.50%	97.57%	95.45%
±3σ	-21.87%	21.78%	98.96%	99.73%

Descriptive Statistics

Mean	-0.046%
Standard Error	0.175%
Median	-0.417%
Mode	0.000%
Standard Deviation	7.274%
Sample Variance	52.905%
Kurtosis	151.19
Skewness	7.95
Range	194.765%
Minimum	-48.507%
Maximum	146.258%
Count	1731

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.270%	781	45.12%	1.927%
Negative	-3.652%	935	54.02%	-1.973%
Zero	0.000%	15	0.87%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.10%
20	1 Month	8.99%
60	1 Quarter	8.54%
250	1 Year	11.11%
750	3 Years	8.24%
1,250	5 Years	7.83%
2,500	10 Years	7.60%
5,000	20 Years	7.60%
12,500	50 Years	7.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 11.90. Further, an Excess Kurtosis of 239.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.16%	0	0.00%	0.00%
-15.16% to -9.50%	0	0.00%	0.00%
-9.50% to -3.84%	0	0.00%	0.00%
-3.84% to 1.81%	1	0.06%	0.06%
1.81% to 7.47%	1151	66.45%	66.51%
7.47% to 13.13%	440	25.40%	91.92%
13.13% to 18.79%	87	5.02%	96.94%
18.79% to 24.44%	22	1.27%	98.21%
24.44% to 30.10%	10	0.58%	98.79%
Greater than 30.10%	21	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.07%	15.02%	94.40%	68.27%
±2σ	-7.61%	22.56%	97.92%	95.45%
±3σ	-15.16%	30.10%	98.79%	99.73%

Descriptive Statistics

Mean	7.472%
Standard Error	0.181%
Median	6.017%
Mode	6.667%
Standard Deviation	7.543%
Sample Variance	56.891%
Kurtosis	239.81
Skewness	11.90
Range	191.881%
Minimum	1.630%
Maximum	193.511%
Count	1732

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.472%	1732	100.00%	7.472%
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 1.39. Further, an Excess Kurtosis of 29.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.44%	13	0.75%	0.75%
-15.44% to -11.49%	16	0.92%	1.67%
-11.49% to -7.54%	51	2.94%	4.62%
-7.54% to -3.58%	160	9.24%	13.86%
-3.58% to 0.37%	605	34.93%	48.79%
0.37% to 4.32%	632	36.49%	85.28%
4.32% to 8.28%	193	11.14%	96.42%
8.28% to 12.23%	40	2.31%	98.73%
12.23% to 16.18%	14	0.81%	99.54%
Greater than 16.18%	8	0.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.90%	5.64%	81.81%	68.27%
±2σ	-10.17%	10.91%	96.13%	95.45%
±3σ	-15.44%	16.18%	98.79%	99.73%

Descriptive Statistics

Mean	0.369%
Standard Error	0.127%
Median	0.450%
Mode	0.000%
Standard Deviation	5.271%
Sample Variance	27.782%
Kurtosis	29.82
Skewness	1.39
Range	108.534%
Minimum	-36.188%
Maximum	72.346%
Count	1732

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.477%	944	54.50%	1.895%
Negative	-3.436%	769	44.40%	-1.526%
Zero	0.000%	19	1.10%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.08. Further, an Excess Kurtosis of 6.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.35%	1	0.28%	0.28%
-38.35% to -28.89%	2	0.56%	0.84%
-28.89% to -19.43%	9	2.51%	3.34%
-19.43% to -9.98%	48	13.37%	16.71%
-9.98% to -0.52%	139	38.72%	55.43%
-0.52% to 8.94%	97	27.02%	82.45%
8.94% to 18.39%	43	11.98%	94.43%
18.39% to 27.85%	12	3.34%	97.77%
27.85% to 37.31%	3	0.84%	98.61%
Greater than 37.31%	5	1.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.13%	12.09%	76.88%	68.27%
±2σ	-25.74%	24.70%	95.82%	95.45%
±3σ	-38.35%	37.31%	98.33%	99.73%

Descriptive Statistics

Mean	-0.520%
Standard Error	0.666%
Median	-1.702%
Mode	-7.662%
Standard Deviation	12.610%
Sample Variance	159.014%
Kurtosis	6.04
Skewness	1.08
Range	130.770%
Minimum	-55.957%
Maximum	74.813%
Count	359

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.881%	153	42.62%	4.211%
Negative	-8.245%	206	57.38%	-4.731%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	22.60%
12	1 Quarter	19.86%
52	1 Year	28.48%
156	3 Years	20.41%
260	5 Years	19.16%
520	10 Years	18.77%
1,040	20 Years	18.77%
2,600	50 Years	18.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.48. Further, an Excess Kurtosis of 74.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.90%	0	0.00%	0.00%
-53.90% to -35.09%	0	0.00%	0.00%
-35.09% to -16.27%	0	0.00%	0.00%
-16.27% to 2.54%	0	0.00%	0.00%
2.54% to 21.35%	252	70.00%	70.00%
21.35% to 40.17%	81	22.50%	92.50%
40.17% to 58.98%	15	4.17%	96.67%
58.98% to 77.79%	6	1.67%	98.33%
77.79% to 96.61%	2	0.56%	98.89%
Greater than 96.61%	4	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.73%	46.44%	95.28%	68.27%
±2σ	-28.81%	71.52%	97.78%	95.45%
±3σ	-53.90%	96.60%	98.89%	99.73%

Descriptive Statistics

Mean	21.353%
Standard Error	1.322%
Median	16.267%
Mode	12.590%
Standard Deviation	25.084%
Sample Variance	629.210%
Kurtosis	74.89
Skewness	7.48
Range	322.770%
Minimum	4.452%
Maximum	327.222%
Count	360

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.353%	360	100.00%	21.353%
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 2.39. Further, an Excess Kurtosis of 21.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.03%	1	0.28%	0.28%
-39.03% to -28.71%	4	1.11%	1.39%
-28.71% to -18.39%	8	2.22%	3.61%
-18.39% to -8.06%	45	12.50%	16.11%
-8.06% to 2.26%	129	35.83%	51.94%
2.26% to 12.59%	122	33.89%	85.83%
12.59% to 22.91%	37	10.28%	96.11%
22.91% to 33.23%	8	2.22%	98.33%
33.23% to 43.56%	3	0.83%	99.17%
Greater than 43.56%	3	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.50%	16.03%	80.56%	68.27%
±2σ	-25.27%	29.79%	95.83%	95.45%
±3σ	-39.03%	43.56%	98.89%	99.73%

Descriptive Statistics

Mean	2.261%
Standard Error	0.725%
Median	1.527%
Mode	5.263%
Standard Deviation	13.765%
Sample Variance	189.464%
Kurtosis	21.88
Skewness	2.39
Range	170.686%
Minimum	-39.768%
Maximum	130.918%
Count	360

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.975%	205	56.94%	5.680%
Negative	-7.993%	154	42.78%	-3.419%
Zero	0.000%	1	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 0.21 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.25%	0	0.00%	0.00%
-72.25% to -55.03%	0	0.00%	0.00%
-55.03% to -37.82%	4	4.88%	4.88%
-37.82% to -20.60%	14	17.07%	21.95%
-20.60% to -3.38%	31	37.80%	59.76%
-3.38% to 13.83%	16	19.51%	79.27%
13.83% to 31.05%	9	10.98%	90.24%
31.05% to 48.27%	5	6.10%	96.34%
48.27% to 65.48%	3	3.66%	100.00%
Greater than 65.48%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.34%	19.57%	71.95%	68.27%
±2σ	-49.29%	42.53%	95.12%	95.45%
±3σ	-72.25%	65.48%	100.00%	99.73%

Descriptive Statistics

Mean	-3.384%
Standard Error	2.535%
Median	-8.948%
Mode	-43.177%
Standard Deviation	22.955%
Sample Variance	526.913%
Kurtosis	0.21
Skewness	0.78
Range	104.657%
Minimum	-43.177%
Maximum	61.480%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.990%	28	34.15%	7.850%
Negative	-17.060%	54	65.85%	-11.235%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	41.21%
12	1 Year	70.82%
36	3 Years	48.58%
60	5 Years	43.30%
120	10 Years	43.27%
240	20 Years	43.27%
600	50 Years	43.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 8.66. Further, an Excess Kurtosis of 77.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -397.68%	0	0.00%	0.00%
-397.68% to -281.50%	0	0.00%	0.00%
-281.50% to -165.32%	0	0.00%	0.00%
-165.32% to -49.15%	0	0.00%	0.00%
-49.15% to 67.03%	65	78.31%	78.31%
67.03% to 183.21%	17	20.48%	98.80%
183.21% to 299.39%	0	0.00%	98.80%
299.39% to 415.56%	0	0.00%	98.80%
415.56% to 531.74%	0	0.00%	98.80%
Greater than 531.74%	1	1.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-87.87%	221.94%	98.80%	68.27%
±2σ	-242.78%	376.84%	98.80%	95.45%
±3σ	-397.68%	531.74%	98.80%	99.73%

Descriptive Statistics

Mean	67.031%
Standard Error	17.003%
Median	46.795%
Mode	10.440%
Standard Deviation	154.904%
Sample Variance	23995.187%
Kurtosis	77.40
Skewness	8.66
Range	1427.560%
Minimum	10.440%
Maximum	1438.000%
Count	83

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	67.031%	83	100.00%	67.031%
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 0.11. Further, an Excess Kurtosis of 0.21 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.01%	0	0.00%	0.00%
-67.01% to -48.21%	1	1.20%	1.20%
-48.21% to -29.41%	4	4.82%	6.02%
-29.41% to -10.62%	14	16.87%	22.89%
-10.62% to 8.18%	19	22.89%	45.78%
8.18% to 26.98%	28	33.73%	79.52%
26.98% to 45.77%	13	15.66%	95.18%
45.77% to 64.57%	2	2.41%	97.59%
64.57% to 83.36%	2	2.41%	100.00%
Greater than 83.36%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.88%	33.24%	67.47%	68.27%
±2σ	-41.95%	58.30%	95.18%	95.45%
±3σ	-67.01%	83.36%	100.00%	99.73%

Descriptive Statistics

Mean	8.178%
Standard Error	2.751%
Median	10.016%
Mode	-55.820%
Standard Deviation	25.062%
Sample Variance	628.094%
Kurtosis	0.21
Skewness	0.11
Range	131.841%
Minimum	-55.820%
Maximum	76.021%
Count	83

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.753%	56	67.47%	14.677%
Negative	-19.977%	27	32.53%	-6.499%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.09. Further, an Excess Kurtosis of -1.07 proves the distribution possesses Thin Tails (Platykurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -99.71%	0	0.00%	0.00%
-99.71% to -78.22%	0	0.00%	0.00%
-78.22% to -56.72%	2	7.41%	7.41%
-56.72% to -35.22%	5	18.52%	25.93%
-35.22% to -13.73%	5	18.52%	44.44%
-13.73% to 7.77%	8	29.63%	74.07%
7.77% to 29.27%	6	22.22%	96.30%
29.27% to 50.76%	1	3.70%	100.00%
50.76% to 72.26%	0	0.00%	100.00%
Greater than 72.26%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-42.39%	14.94%	59.26%	68.27%
±2σ	-71.05%	43.60%	100.00%	95.45%
±3σ	-99.71%	72.26%	100.00%	99.73%

Descriptive Statistics

Mean	-13.726%
Standard Error	5.516%
Median	-10.351%
Mode	-65.291%
Standard Deviation	28.662%
Sample Variance	821.501%
Kurtosis	-1.07
Skewness	-0.09
Range	96.043%
Minimum	-65.291%
Maximum	30.752%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.185%	9	33.33%	6.062%
Negative	-29.682%	18	66.67%	-19.788%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	113.65%
12	3 Years	85.39%
20	5 Years	74.71%
40	10 Years	72.58%
80	20 Years	72.58%
200	50 Years	72.58%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.63. Further, an Excess Kurtosis of 22.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -623.33%	0	0.00%	0.00%
-623.33% to -426.92%	0	0.00%	0.00%
-426.92% to -230.50%	0	0.00%	0.00%
-230.50% to -34.09%	0	0.00%	0.00%
-34.09% to 162.31%	23	82.14%	82.14%
162.31% to 358.73%	3	10.71%	92.86%
358.73% to 555.13%	1	3.57%	96.43%
555.13% to 751.54%	0	0.00%	96.43%
751.54% to 947.96%	0	0.00%	96.43%
Greater than 947.96%	1	3.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-99.56%	424.19%	92.86%	68.27%
±2σ	-361.44%	686.08%	96.43%	95.45%
±3σ	-623.33%	947.95%	96.43%	99.73%

Descriptive Statistics

Mean	162.315%
Standard Error	49.491%
Median	95.627%
Mode	47.449%
Standard Deviation	261.880%
Sample Variance	68581.139%
Kurtosis	22.75
Skewness	4.63
Range	1390.551%
Minimum	47.449%
Maximum	1438.000%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	162.315%	28	100.00%	162.315%
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 0.99. Further, an Excess Kurtosis of 1.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -135.69%	0	0.00%	0.00%
-135.69% to -95.17%	0	0.00%	0.00%
-95.17% to -54.66%	1	3.57%	3.57%
-54.66% to -14.14%	5	17.86%	21.43%
-14.14% to 26.38%	12	42.86%	64.29%
26.38% to 66.90%	4	14.29%	78.57%
66.90% to 107.42%	5	17.86%	96.43%
107.42% to 147.94%	0	0.00%	96.43%
147.94% to 188.46%	1	3.57%	100.00%
Greater than 188.46%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.64%	80.41%	78.57%	68.27%
±2σ	-81.67%	134.44%	96.43%	95.45%
±3σ	-135.69%	188.46%	100.00%	99.73%

Descriptive Statistics

Mean	26.384%
Standard Error	10.210%
Median	10.806%
Mode	-76.592%
Standard Deviation	54.026%
Sample Variance	2918.847%
Kurtosis	1.61
Skewness	0.99
Range	263.024%
Minimum	-76.592%
Maximum	186.432%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.525%	18	64.29%	33.766%
Negative	-20.671%	10	35.71%	-7.382%
Zero	0.000%	0	0.00%	0.000%

BYND Deep Analytical Report