U - 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	4.86%	3.39%	4.16%	6.37%	4.77%	4.85%	17.40	19.14	16.59	20.08
Weekly	10.62%	9.78%	10.95%	15.21%	10.50%	10.69%	16.43	20.27	14.79	22.51
Monthly	20.89%	20.86%	22.28%	32.24%	21.85%	22.24%	14.67	22.71	11.79	28.25
Quarterly	36.02%	24.71%	39.11%	61.34%	37.84%	38.53%	12.50	26.65	8.56	38.90
Annual	—	—	—	—	75.69%	77.05%	8.56	38.90	4.02	82.92
Option Time Horizon	—	—	—	—	29.11%	29.64%	13.64	24.42	10.20	32.67

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $18.25 | Strike (K): $19.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.8600 (Bid $1.8000 / Ask $1.9200) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 75.69% (CRR binomial tree, American, n=20 steps) | BS IV: 76.34% (European Black-Scholes) | Yahoo IV (Annual): 77.05% → 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 0.07. Further, an Excess Kurtosis of 6.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.56%	5	0.37%	0.37%
-14.56% to -10.91%	9	0.66%	1.03%
-10.91% to -7.27%	53	3.89%	4.92%
-7.27% to -3.62%	177	13.01%	17.93%
-3.62% to 0.02%	455	33.43%	51.36%
0.02% to 3.67%	421	30.93%	82.29%
3.67% to 7.31%	162	11.90%	94.20%
7.31% to 10.96%	54	3.97%	98.16%
10.96% to 14.60%	14	1.03%	99.19%
Greater than 14.60%	11	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.84%	4.88%	75.68%	68.27%
±2σ	-9.70%	9.74%	95.59%	95.45%
±3σ	-14.56%	14.60%	98.82%	99.73%

Descriptive Statistics

Mean	0.022%
Standard Error	0.132%
Median	-0.127%
Mode	-2.496%
Standard Deviation	4.860%
Sample Variance	23.618%
Kurtosis	6.03
Skewness	0.07
Range	67.461%
Minimum	-37.046%
Maximum	30.415%
Count	1361

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.577%	662	48.64%	1.740%
Negative	-3.359%	696	51.14%	-1.718%
Zero	0.000%	3	0.22%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.07%
20	1 Month	10.74%
60	1 Quarter	7.06%
250	1 Year	6.57%
750	3 Years	5.84%
1,250	5 Years	6.37%
2,500	10 Years	6.46%
5,000	20 Years	6.46%
12,500	50 Years	6.46%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.43. Further, an Excess Kurtosis of 11.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.97%	0	0.00%	0.00%
-3.97% to -1.42%	0	0.00%	0.00%
-1.42% to 1.12%	0	0.00%	0.00%
1.12% to 3.67%	272	19.97%	19.97%
3.67% to 6.21%	552	40.53%	60.50%
6.21% to 8.75%	305	22.39%	82.89%
8.75% to 11.30%	138	10.13%	93.02%
11.30% to 13.84%	53	3.89%	96.92%
13.84% to 16.39%	21	1.54%	98.46%
Greater than 16.39%	21	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.82%	9.60%	80.76%	68.27%
±2σ	-0.58%	12.99%	95.74%	95.45%
±3σ	-3.97%	16.38%	98.46%	99.73%

Descriptive Statistics

Mean	6.209%
Standard Error	0.092%
Median	5.432%
Mode	4.224%
Standard Deviation	3.392%
Sample Variance	11.504%
Kurtosis	11.79
Skewness	2.43
Range	36.542%
Minimum	1.548%
Maximum	38.090%
Count	1362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.209%	1362	100.00%	6.209%
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 0.23. 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 -12.32%	8	0.59%	0.59%
-12.32% to -9.20%	14	1.03%	1.62%
-9.20% to -6.08%	50	3.67%	5.29%
-6.08% to -2.95%	190	13.95%	19.24%
-2.95% to 0.17%	437	32.09%	51.32%
0.17% to 3.29%	397	29.15%	80.47%
3.29% to 6.41%	176	12.92%	93.39%
6.41% to 9.54%	67	4.92%	98.31%
9.54% to 12.66%	18	1.32%	99.63%
Greater than 12.66%	5	0.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.00%	4.33%	72.91%	68.27%
±2σ	-8.16%	8.49%	94.71%	95.45%
±3σ	-12.32%	12.66%	99.05%	99.73%

Descriptive Statistics

Mean	0.168%
Standard Error	0.113%
Median	0.074%
Mode	0.000%
Standard Deviation	4.163%
Sample Variance	17.331%
Kurtosis	3.03
Skewness	0.23
Range	47.309%
Minimum	-17.068%
Maximum	30.241%
Count	1362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.203%	694	50.95%	1.632%
Negative	-3.007%	663	48.68%	-1.464%
Zero	0.000%	5	0.37%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 1.12 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.78%	2	0.71%	0.71%
-31.78% to -23.82%	3	1.06%	1.77%
-23.82% to -15.86%	8	2.83%	4.59%
-15.86% to -7.89%	44	15.55%	20.14%
-7.89% to 0.07%	90	31.80%	51.94%
0.07% to 8.04%	84	29.68%	81.63%
8.04% to 16.00%	34	12.01%	93.64%
16.00% to 23.97%	9	3.18%	96.82%
23.97% to 31.93%	8	2.83%	99.65%
Greater than 31.93%	1	0.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.55%	10.69%	72.44%	68.27%
±2σ	-21.16%	21.31%	93.99%	95.45%
±3σ	-31.78%	31.93%	98.94%	99.73%

Descriptive Statistics

Mean	0.073%
Standard Error	0.631%
Median	-0.254%
Mode	-7.901%
Standard Deviation	10.619%
Sample Variance	112.763%
Kurtosis	1.12
Skewness	0.29
Range	66.519%
Minimum	-33.000%
Maximum	33.519%
Count	283

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.362%	136	48.06%	4.019%
Negative	-7.596%	147	51.94%	-3.946%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	25.94%
12	1 Quarter	15.85%
52	1 Year	15.36%
156	3 Years	13.97%
260	5 Years	15.21%
520	10 Years	15.36%
1,040	20 Years	15.36%
2,600	50 Years	15.36%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.50. Further, an Excess Kurtosis of 10.40 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%	0	0.00%	0.00%
-12.56% to -5.22%	0	0.00%	0.00%
-5.22% to 2.11%	0	0.00%	0.00%
2.11% to 9.45%	51	17.96%	17.96%
9.45% to 16.79%	125	44.01%	61.97%
16.79% to 24.13%	65	22.89%	84.86%
24.13% to 31.46%	23	8.10%	92.96%
31.46% to 38.80%	10	3.52%	96.48%
38.80% to 46.14%	5	1.76%	98.24%
Greater than 46.14%	5	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.01%	26.57%	83.10%	68.27%
±2σ	-2.78%	36.36%	95.77%	95.45%
±3σ	-12.56%	46.14%	98.24%	99.73%

Descriptive Statistics

Mean	16.789%
Standard Error	0.581%
Median	14.285%
Mode	20.420%
Standard Deviation	9.784%
Sample Variance	95.718%
Kurtosis	10.40
Skewness	2.50
Range	79.218%
Minimum	5.210%
Maximum	84.428%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.789%	284	100.00%	16.789%
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 0.92. Further, an Excess Kurtosis of 3.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.69%	0	0.00%	0.00%
-31.69% to -23.47%	3	1.06%	1.06%
-23.47% to -15.26%	11	3.87%	4.93%
-15.26% to -7.05%	40	14.08%	19.01%
-7.05% to 1.17%	98	34.51%	53.52%
1.17% to 9.38%	85	29.93%	83.45%
9.38% to 17.60%	33	11.62%	95.07%
17.60% to 25.81%	7	2.46%	97.54%
25.81% to 34.02%	2	0.70%	98.24%
Greater than 34.02%	5	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.78%	12.12%	75.35%	68.27%
±2σ	-20.74%	23.07%	95.07%	95.45%
±3σ	-31.69%	34.02%	98.24%	99.73%

Descriptive Statistics

Mean	1.168%
Standard Error	0.650%
Median	0.577%
Mode	-1.851%
Standard Deviation	10.952%
Sample Variance	119.953%
Kurtosis	3.21
Skewness	0.92
Range	77.495%
Minimum	-26.853%
Maximum	50.642%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.643%	150	52.82%	4.565%
Negative	-7.253%	133	46.83%	-3.397%
Zero	0.000%	1	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.49. Further, an Excess Kurtosis of 0.26 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -62.92%	0	0.00%	0.00%
-62.92% to -47.26%	0	0.00%	0.00%
-47.26% to -31.59%	4	6.15%	6.15%
-31.59% to -15.93%	11	16.92%	23.08%
-15.93% to -0.26%	19	29.23%	52.31%
-0.26% to 15.40%	16	24.62%	76.92%
15.40% to 31.07%	9	13.85%	90.77%
31.07% to 46.74%	5	7.69%	98.46%
46.74% to 62.40%	1	1.54%	100.00%
Greater than 62.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.15%	20.63%	72.31%	68.27%
±2σ	-42.03%	41.51%	96.92%	95.45%
±3σ	-62.92%	62.40%	100.00%	99.73%

Descriptive Statistics

Mean	-0.260%
Standard Error	2.591%
Median	-1.202%
Mode	-6.801%
Standard Deviation	20.887%
Sample Variance	436.254%
Kurtosis	0.26
Skewness	0.49
Range	99.994%
Minimum	-39.813%
Maximum	60.181%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.692%	31	47.69%	7.961%
Negative	-15.716%	34	52.31%	-8.221%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	38.76%
12	1 Year	33.86%
36	3 Years	30.59%
60	5 Years	32.24%
120	10 Years	32.50%
240	20 Years	32.50%
600	50 Years	32.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.11. Further, an Excess Kurtosis of 7.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.78%	0	0.00%	0.00%
-21.78% to -6.14%	0	0.00%	0.00%
-6.14% to 9.51%	0	0.00%	0.00%
9.51% to 25.15%	11	16.67%	16.67%
25.15% to 40.80%	29	43.94%	60.61%
40.80% to 56.44%	13	19.70%	80.30%
56.44% to 72.08%	9	13.64%	93.94%
72.08% to 87.73%	3	4.55%	98.48%
87.73% to 103.37%	0	0.00%	98.48%
Greater than 103.37%	1	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.94%	61.65%	77.27%	68.27%
±2σ	-0.92%	82.51%	96.97%	95.45%
±3σ	-21.78%	103.37%	98.48%	99.73%

Descriptive Statistics

Mean	40.795%
Standard Error	2.568%
Median	34.565%
Mode	12.922%
Standard Deviation	20.858%
Sample Variance	435.077%
Kurtosis	7.73
Skewness	2.11
Range	130.117%
Minimum	12.922%
Maximum	143.039%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.795%	66	100.00%	40.795%
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 0.73. Further, an Excess Kurtosis of 0.52 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.96%	0	0.00%	0.00%
-61.96% to -45.25%	0	0.00%	0.00%
-45.25% to -28.54%	2	3.03%	3.03%
-28.54% to -11.82%	15	22.73%	25.76%
-11.82% to 4.89%	18	27.27%	53.03%
4.89% to 21.60%	18	27.27%	80.30%
21.60% to 38.31%	8	12.12%	92.42%
38.31% to 55.02%	2	3.03%	95.45%
55.02% to 71.74%	3	4.55%	100.00%
Greater than 71.74%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.40%	27.17%	72.73%	68.27%
±2σ	-39.68%	49.45%	95.45%	95.45%
±3σ	-61.96%	71.74%	100.00%	99.73%

Descriptive Statistics

Mean	4.887%
Standard Error	2.743%
Median	2.096%
Mode	-36.393%
Standard Deviation	22.283%
Sample Variance	496.542%
Kurtosis	0.52
Skewness	0.73
Range	102.201%
Minimum	-36.393%
Maximum	65.808%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.230%	36	54.55%	11.034%
Negative	-13.525%	30	45.45%	-6.148%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.60. Further, an Excess Kurtosis of -0.88 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -109.35%	0	0.00%	0.00%
-109.35% to -82.33%	0	0.00%	0.00%
-82.33% to -55.32%	0	0.00%	0.00%
-55.32% to -28.31%	7	31.82%	31.82%
-28.31% to -1.29%	5	22.73%	54.55%
-1.29% to 25.72%	5	22.73%	77.27%
25.72% to 52.73%	2	9.09%	86.36%
52.73% to 79.75%	3	13.64%	100.00%
79.75% to 106.76%	0	0.00%	100.00%
Greater than 106.76%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-37.31%	34.73%	72.73%	68.27%
±2σ	-73.33%	70.74%	100.00%	95.45%
±3σ	-109.35%	106.76%	100.00%	99.73%

Descriptive Statistics

Mean	-1.292%
Standard Error	7.679%
Median	-13.096%
Mode	-44.655%
Standard Deviation	36.018%
Sample Variance	1297.319%
Kurtosis	-0.88
Skewness	0.60
Range	114.622%
Minimum	-44.655%
Maximum	69.967%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.793%	10	45.45%	14.906%
Negative	-29.696%	12	54.55%	-16.198%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	62.36%
12	3 Years	62.32%
20	5 Years	61.34%
40	10 Years	61.75%
80	20 Years	61.75%
200	50 Years	61.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.72. Further, an Excess Kurtosis of 0.25 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than 10.49%	0	0.00%	0.00%
10.49% to 29.02%	0	0.00%	0.00%
29.02% to 47.55%	1	4.35%	4.35%
47.55% to 66.08%	4	17.39%	21.74%
66.08% to 84.61%	7	30.43%	52.17%
84.61% to 103.14%	8	34.78%	86.96%
103.14% to 121.67%	1	4.35%	91.30%
121.67% to 140.20%	1	4.35%	95.65%
140.20% to 158.73%	1	4.35%	100.00%
Greater than 158.73%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	59.91%	109.32%	69.57%	68.27%
±2σ	35.20%	134.03%	95.65%	95.45%
±3σ	10.49%	158.73%	100.00%	99.73%

Descriptive Statistics

Mean	84.613%
Standard Error	5.152%
Median	84.198%
Mode	47.391%
Standard Deviation	24.707%
Sample Variance	610.444%
Kurtosis	0.25
Skewness	0.72
Range	95.648%
Minimum	47.391%
Maximum	143.039%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	84.613%	23	100.00%	84.613%
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 0.26. Further, an Excess Kurtosis of -1.39 proves the distribution possesses Thin Tails (Platykurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -104.25%	0	0.00%	0.00%
-104.25% to -74.91%	0	0.00%	0.00%
-74.91% to -45.58%	0	0.00%	0.00%
-45.58% to -16.25%	7	30.43%	30.43%
-16.25% to 13.08%	5	21.74%	52.17%
13.08% to 42.41%	4	17.39%	69.57%
42.41% to 71.75%	5	21.74%	91.30%
71.75% to 101.08%	2	8.70%	100.00%
101.08% to 130.41%	0	0.00%	100.00%
Greater than 130.41%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.03%	52.19%	65.22%	68.27%
±2σ	-65.14%	91.30%	100.00%	95.45%
±3σ	-104.25%	130.41%	100.00%	99.73%

Descriptive Statistics

Mean	13.082%
Standard Error	8.155%
Median	-0.071%
Mode	-41.449%
Standard Deviation	39.109%
Sample Variance	1529.491%
Kurtosis	-1.39
Skewness	0.26
Range	119.730%
Minimum	-41.449%
Maximum	78.281%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.703%	11	47.83%	23.771%
Negative	-20.487%	12	52.17%	-10.689%
Zero	0.000%	0	0.00%	0.000%

U Deep Analytical Report