SENS - 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	5.85%	5.49%	4.93%	7.80%	6.08%	6.10%	7.68	8.67	7.23	9.21
Weekly	13.88%	17.59%	12.38%	18.16%	13.38%	13.43%	7.14	9.33	6.24	10.66
Monthly	30.54%	48.67%	25.66%	40.02%	27.84%	27.97%	6.18	10.78	4.68	14.24
Quarterly	92.90%	157.86%	39.60%	73.99%	48.23%	48.44%	5.04	13.22	3.11	21.41
Annual	—	—	—	—	96.45%	96.88%	3.11	21.41	1.19	56.17
Option Time Horizon	—	—	—	—	37.10%	37.26%	5.63	11.83	3.89	17.14

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $8.16 | Strike (K): $10.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.6250 (Bid $0.4000 / Ask $0.8500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 96.45% (CRR binomial tree, American, n=20 steps) | BS IV: 96.72% (European Black-Scholes) | Yahoo IV (Annual): 96.88% → 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 3.31. Further, an Excess Kurtosis of 36.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.48%	4	0.16%	0.16%
-17.48% to -13.09%	13	0.52%	0.68%
-13.09% to -8.71%	69	2.76%	3.44%
-8.71% to -4.32%	282	11.29%	14.73%
-4.32% to 0.07%	1054	42.19%	56.93%
0.07% to 4.46%	716	28.66%	85.59%
4.46% to 8.85%	252	10.09%	95.68%
8.85% to 13.24%	61	2.44%	98.12%
13.24% to 17.62%	25	1.00%	99.12%
Greater than 17.62%	22	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.78%	5.92%	82.19%	68.27%
±2σ	-11.63%	11.77%	96.56%	95.45%
±3σ	-17.48%	17.62%	98.96%	99.73%

Descriptive Statistics

Mean	0.072%
Standard Error	0.117%
Median	-0.368%
Mode	0.000%
Standard Deviation	5.851%
Sample Variance	34.229%
Kurtosis	36.47
Skewness	3.31
Range	114.397%
Minimum	-33.699%
Maximum	80.698%
Count	2498

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.360%	1076	43.07%	1.878%
Negative	-3.441%	1311	52.48%	-1.806%
Zero	0.000%	111	4.44%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.48%
20	1 Month	7.19%
60	1 Quarter	6.74%
250	1 Year	7.19%
750	3 Years	7.59%
1,250	5 Years	7.80%
2,500	10 Years	7.61%
5,000	20 Years	7.61%
12,500	50 Years	7.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.40. Further, an Excess Kurtosis of 61.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.79%	0	0.00%	0.00%
-8.79% to -4.67%	0	0.00%	0.00%
-4.67% to -0.55%	0	0.00%	0.00%
-0.55% to 3.57%	294	11.76%	11.76%
3.57% to 7.69%	1296	51.86%	63.63%
7.69% to 11.81%	587	23.49%	87.11%
11.81% to 15.93%	191	7.64%	94.76%
15.93% to 20.04%	67	2.68%	97.44%
20.04% to 24.16%	29	1.16%	98.60%
Greater than 24.16%	35	1.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.20%	13.18%	88.24%	68.27%
±2σ	-3.30%	18.67%	96.60%	95.45%
±3σ	-8.79%	24.16%	98.60%	99.73%

Descriptive Statistics

Mean	7.687%
Standard Error	0.110%
Median	6.438%
Mode	7.143%
Standard Deviation	5.492%
Sample Variance	30.158%
Kurtosis	61.32
Skewness	5.40
Range	100.634%
Minimum	0.717%
Maximum	101.351%
Count	2499

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.687%	2499	100.00%	7.687%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.57. Further, an Excess Kurtosis of 7.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.24%	18	0.72%	0.72%
-14.24% to -10.54%	26	1.04%	1.76%
-10.54% to -6.85%	86	3.44%	5.20%
-6.85% to -3.15%	318	12.73%	17.93%
-3.15% to 0.54%	784	31.37%	49.30%
0.54% to 4.24%	830	33.21%	82.51%
4.24% to 7.94%	311	12.44%	94.96%
7.94% to 11.63%	88	3.52%	98.48%
11.63% to 15.33%	26	1.04%	99.52%
Greater than 15.33%	12	0.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.38%	5.47%	76.07%	68.27%
±2σ	-9.31%	10.40%	95.32%	95.45%
±3σ	-14.24%	15.33%	98.80%	99.73%

Descriptive Statistics

Mean	0.544%
Standard Error	0.099%
Median	0.619%
Mode	0.000%
Standard Deviation	4.928%
Sample Variance	24.285%
Kurtosis	7.24
Skewness	-0.57
Range	77.331%
Minimum	-43.860%
Maximum	33.471%
Count	2499

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.703%	1370	54.82%	2.030%
Negative	-3.665%	1013	40.54%	-1.486%
Zero	0.000%	116	4.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.62. Further, an Excess Kurtosis of 17.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.20%	2	0.39%	0.39%
-41.20% to -30.79%	2	0.39%	0.77%
-30.79% to -20.38%	7	1.35%	2.12%
-20.38% to -9.98%	69	13.29%	15.41%
-9.98% to 0.43%	205	39.50%	54.91%
0.43% to 10.84%	168	32.37%	87.28%
10.84% to 21.24%	44	8.48%	95.76%
21.24% to 31.65%	11	2.12%	97.88%
31.65% to 42.05%	3	0.58%	98.46%
Greater than 42.05%	8	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.45%	14.30%	83.43%	68.27%
±2σ	-27.32%	28.18%	96.72%	95.45%
±3σ	-41.20%	42.05%	98.07%	99.73%

Descriptive Statistics

Mean	0.429%
Standard Error	0.609%
Median	-1.090%
Mode	0.000%
Standard Deviation	13.875%
Sample Variance	192.511%
Kurtosis	17.29
Skewness	2.62
Range	163.903%
Minimum	-42.973%
Maximum	120.930%
Count	519

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.292%	235	45.28%	4.660%
Negative	-7.899%	278	53.56%	-4.231%
Zero	0.000%	6	1.16%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.31%
12	1 Quarter	15.08%
52	1 Year	16.79%
156	3 Years	17.76%
260	5 Years	18.16%
520	10 Years	17.82%
1,040	20 Years	17.82%
2,600	50 Years	17.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.77. Further, an Excess Kurtosis of 32.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.98%	0	0.00%	0.00%
-32.98% to -19.79%	0	0.00%	0.00%
-19.79% to -6.59%	0	0.00%	0.00%
-6.59% to 6.60%	23	4.42%	4.42%
6.60% to 19.79%	336	64.62%	69.04%
19.79% to 32.98%	104	20.00%	89.04%
32.98% to 46.17%	35	6.73%	95.77%
46.17% to 59.36%	8	1.54%	97.31%
59.36% to 72.55%	4	0.77%	98.08%
Greater than 72.55%	10	1.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.20%	37.38%	92.50%	68.27%
±2σ	-15.39%	54.96%	96.54%	95.45%
±3σ	-32.98%	72.55%	98.08%	99.73%

Descriptive Statistics

Mean	19.788%
Standard Error	0.771%
Median	15.127%
Mode	7.692%
Standard Deviation	17.588%
Sample Variance	309.333%
Kurtosis	32.78
Skewness	4.77
Range	186.331%
Minimum	3.273%
Maximum	189.604%
Count	520

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.788%	520	100.00%	19.788%
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 0.72. Further, an Excess Kurtosis of 7.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.69%	5	0.96%	0.96%
-35.69% to -26.40%	4	0.77%	1.73%
-26.40% to -17.12%	17	3.27%	5.00%
-17.12% to -7.83%	55	10.58%	15.58%
-7.83% to 1.45%	180	34.62%	50.19%
1.45% to 10.74%	173	33.27%	83.46%
10.74% to 20.02%	61	11.73%	95.19%
20.02% to 29.31%	17	3.27%	98.46%
29.31% to 38.59%	4	0.77%	99.23%
Greater than 38.59%	4	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.93%	13.83%	79.04%	68.27%
±2σ	-23.31%	26.21%	95.96%	95.45%
±3σ	-35.69%	38.59%	98.27%	99.73%

Descriptive Statistics

Mean	1.453%
Standard Error	0.543%
Median	1.382%
Mode	0.000%
Standard Deviation	12.380%
Sample Variance	153.258%
Kurtosis	7.95
Skewness	0.72
Range	143.469%
Minimum	-54.737%
Maximum	88.732%
Count	520

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.147%	284	54.62%	4.996%
Negative	-8.009%	230	44.23%	-3.542%
Zero	0.000%	6	1.15%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.58. Further, an Excess Kurtosis of 10.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -89.86%	0	0.00%	0.00%
-89.86% to -66.95%	0	0.00%	0.00%
-66.95% to -44.05%	2	1.67%	1.67%
-44.05% to -21.14%	13	10.83%	12.50%
-21.14% to 1.76%	60	50.00%	62.50%
1.76% to 24.66%	31	25.83%	88.33%
24.66% to 47.57%	8	6.67%	95.00%
47.57% to 70.47%	1	0.83%	95.83%
70.47% to 93.38%	3	2.50%	98.33%
Greater than 93.38%	2	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.78%	32.30%	85.00%	68.27%
±2σ	-59.32%	62.84%	95.00%	95.45%
±3σ	-89.86%	93.38%	98.33%	99.73%

Descriptive Statistics

Mean	1.760%
Standard Error	2.788%
Median	-5.186%
Mode	-54.714%
Standard Deviation	30.539%
Sample Variance	932.617%
Kurtosis	10.54
Skewness	2.58
Range	226.503%
Minimum	-54.714%
Maximum	171.789%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.368%	48	40.00%	10.547%
Negative	-14.646%	72	60.00%	-8.788%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	34.79%
12	1 Year	33.79%
36	3 Years	39.78%
60	5 Years	40.02%
120	10 Years	41.31%
240	20 Years	41.31%
600	50 Years	41.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.66. Further, an Excess Kurtosis of 17.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -95.42%	0	0.00%	0.00%
-95.42% to -58.92%	0	0.00%	0.00%
-58.92% to -22.42%	0	0.00%	0.00%
-22.42% to 14.08%	3	2.48%	2.48%
14.08% to 50.58%	86	71.07%	73.55%
50.58% to 87.08%	20	16.53%	90.08%
87.08% to 123.58%	4	3.31%	93.39%
123.58% to 160.08%	2	1.65%	95.04%
160.08% to 196.58%	3	2.48%	97.52%
Greater than 196.58%	3	2.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.91%	99.25%	92.56%	68.27%
±2σ	-46.75%	147.91%	95.04%	95.45%
±3σ	-95.42%	196.58%	97.52%	99.73%

Descriptive Statistics

Mean	50.579%
Standard Error	4.424%
Median	36.975%
Mode	42.857%
Standard Deviation	48.666%
Sample Variance	2368.404%
Kurtosis	17.39
Skewness	3.66
Range	361.622%
Minimum	7.692%
Maximum	369.314%
Count	121

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.579%	121	100.00%	50.579%
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 0.91. Further, an Excess Kurtosis of 4.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.70%	0	0.00%	0.00%
-71.70% to -52.46%	2	1.65%	1.65%
-52.46% to -33.21%	4	3.31%	4.96%
-33.21% to -13.97%	19	15.70%	20.66%
-13.97% to 5.28%	35	28.93%	49.59%
5.28% to 24.52%	44	36.36%	85.95%
24.52% to 43.76%	12	9.92%	95.87%
43.76% to 63.01%	1	0.83%	96.69%
63.01% to 82.25%	2	1.65%	98.35%
Greater than 82.25%	2	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.38%	30.93%	79.34%	68.27%
±2σ	-46.04%	56.59%	94.21%	95.45%
±3σ	-71.70%	82.25%	98.35%	99.73%

Descriptive Statistics

Mean	5.275%
Standard Error	2.333%
Median	5.917%
Mode	0.000%
Standard Deviation	25.659%
Sample Variance	658.371%
Kurtosis	4.30
Skewness	0.91
Range	188.532%
Minimum	-64.557%
Maximum	123.975%
Count	121

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.817%	72	59.50%	11.792%
Negative	-17.141%	46	38.02%	-6.516%
Zero	0.000%	3	2.48%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.90. Further, an Excess Kurtosis of 26.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -269.20%	0	0.00%	0.00%
-269.20% to -199.53%	0	0.00%	0.00%
-199.53% to -129.85%	0	0.00%	0.00%
-129.85% to -60.18%	0	0.00%	0.00%
-60.18% to 9.49%	29	70.73%	70.73%
9.49% to 79.17%	10	24.39%	95.12%
79.17% to 148.84%	0	0.00%	95.12%
148.84% to 218.51%	1	2.44%	97.56%
218.51% to 288.19%	0	0.00%	97.56%
Greater than 288.19%	1	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-83.41%	102.39%	95.12%	68.27%
±2σ	-176.30%	195.29%	97.56%	95.45%
±3σ	-269.20%	288.19%	97.56%	99.73%

Descriptive Statistics

Mean	9.492%
Standard Error	14.508%
Median	-8.219%
Mode	-52.361%
Standard Deviation	92.898%
Sample Variance	8630.114%
Kurtosis	26.99
Skewness	4.90
Range	587.750%
Minimum	-52.361%
Maximum	535.389%
Count	41

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	61.653%	16	39.02%	24.059%
Negative	-23.890%	25	60.98%	-14.567%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	40.51%
12	3 Years	74.43%
20	5 Years	73.99%
40	10 Years	90.33%
80	20 Years	88.94%
200	50 Years	88.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.81. Further, an Excess Kurtosis of 26.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -357.01%	0	0.00%	0.00%
-357.01% to -238.62%	0	0.00%	0.00%
-238.62% to -120.22%	0	0.00%	0.00%
-120.22% to -1.82%	0	0.00%	0.00%
-1.82% to 116.58%	32	76.19%	76.19%
116.58% to 234.97%	7	16.67%	92.86%
234.97% to 353.37%	1	2.38%	95.24%
353.37% to 471.77%	1	2.38%	97.62%
471.77% to 590.17%	0	0.00%	97.62%
Greater than 590.17%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-41.29%	274.44%	95.24%	68.27%
±2σ	-199.15%	432.31%	97.62%	95.45%
±3σ	-357.01%	590.17%	97.62%	99.73%

Descriptive Statistics

Mean	116.577%
Standard Error	24.359%
Median	76.136%
Mode	7.692%
Standard Deviation	157.864%
Sample Variance	24920.926%
Kurtosis	26.56
Skewness	4.81
Range	1006.594%
Minimum	7.692%
Maximum	1014.286%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	116.577%	42	100.00%	116.577%
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 0.25. Further, an Excess Kurtosis of 0.74 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -104.93%	0	0.00%	0.00%
-104.93% to -75.23%	1	2.38%	2.38%
-75.23% to -45.53%	1	2.38%	4.76%
-45.53% to -15.82%	4	9.52%	14.29%
-15.82% to 13.88%	19	45.24%	59.52%
13.88% to 43.58%	9	21.43%	80.95%
43.58% to 73.28%	4	9.52%	90.48%
73.28% to 102.98%	3	7.14%	97.62%
102.98% to 132.68%	1	2.38%	100.00%
Greater than 132.68%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.73%	53.48%	76.19%	68.27%
±2σ	-65.33%	93.08%	95.24%	95.45%
±3σ	-104.93%	132.68%	100.00%	99.73%

Descriptive Statistics

Mean	13.876%
Standard Error	6.111%
Median	8.715%
Mode	-84.388%
Standard Deviation	39.602%
Sample Variance	1568.294%
Kurtosis	0.74
Skewness	0.25
Range	196.100%
Minimum	-84.388%
Maximum	111.712%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.441%	27	64.29%	22.141%
Negative	-23.141%	15	35.71%	-8.265%
Zero	0.000%	0	0.00%	0.000%

SENS Deep Analytical Report