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	4.85%	3.37%	4.16%	6.38%	5.50%	5.49%	17.47	19.50	16.54	20.61
Weekly	10.61%	9.71%	10.95%	15.20%	12.12%	12.09%	16.35	20.84	14.49	23.52
Monthly	20.73%	21.11%	22.15%	32.25%	25.22%	25.17%	14.35	23.76	11.15	30.57
Quarterly	35.97%	24.61%	38.94%	61.51%	43.68%	43.60%	11.93	28.57	7.71	44.22
Annual	—	—	—	—	87.37%	87.21%	7.71	44.22	3.22	105.94
Option Time Horizon	—	—	—	—	32.98%	32.92%	13.27	25.67	9.55	35.70

Calculation Notes: Computed at 2026-03-23T16:42 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $18.46 | Strike (K): $19.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.2400 (Bid $2.2000 / Ask $2.2800) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 87.37% (CRR binomial tree, American, n=20 steps) | BS IV: 87.63% (European Black-Scholes) | Yahoo IV (Annual): 87.21% → 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 5.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.52%	5	0.36%	0.36%
-14.52% to -10.89%	9	0.65%	1.01%
-10.89% to -7.25%	54	3.91%	4.92%
-7.25% to -3.61%	180	13.02%	17.95%
-3.61% to 0.02%	461	33.36%	51.30%
0.02% to 3.66%	428	30.97%	82.27%
3.66% to 7.30%	166	12.01%	94.28%
7.30% to 10.93%	53	3.84%	98.12%
10.93% to 14.57%	15	1.09%	99.20%
Greater than 14.57%	11	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.83%	4.87%	75.54%	68.27%
±2σ	-9.67%	9.72%	95.66%	95.45%
±3σ	-14.52%	14.57%	98.84%	99.73%

Descriptive Statistics

Mean	0.024%
Standard Error	0.130%
Median	-0.122%
Mode	0.000%
Standard Deviation	4.849%
Sample Variance	23.509%
Kurtosis	5.99
Skewness	0.07
Range	67.461%
Minimum	-37.046%
Maximum	30.415%
Count	1382

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.575%	673	48.70%	1.741%
Negative	-3.365%	705	51.01%	-1.717%
Zero	0.000%	4	0.29%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.94%
20	1 Month	6.60%
60	1 Quarter	7.62%
250	1 Year	6.53%
750	3 Years	5.86%
1,250	5 Years	6.38%
2,500	10 Years	6.47%
5,000	20 Years	6.47%
12,500	50 Years	6.47%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.91%	0	0.00%	0.00%
-3.91% to -1.38%	0	0.00%	0.00%
-1.38% to 1.15%	0	0.00%	0.00%
1.15% to 3.68%	279	20.17%	20.17%
3.68% to 6.21%	554	40.06%	60.23%
6.21% to 8.74%	315	22.78%	83.01%
8.74% to 11.28%	138	9.98%	92.99%
11.28% to 13.81%	55	3.98%	96.96%
13.81% to 16.34%	20	1.45%	98.41%
Greater than 16.34%	22	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.84%	9.59%	80.62%	68.27%
±2σ	-0.53%	12.96%	95.81%	95.45%
±3σ	-3.91%	16.34%	98.41%	99.73%

Descriptive Statistics

Mean	6.214%
Standard Error	0.091%
Median	5.445%
Mode	4.224%
Standard Deviation	3.374%
Sample Variance	11.383%
Kurtosis	11.87
Skewness	2.43
Range	36.542%
Minimum	1.548%
Maximum	38.090%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.214%	1383	100.00%	6.214%
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 0.22. Further, an Excess Kurtosis of 2.99 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.33%	8	0.58%	0.58%
-12.33% to -9.21%	14	1.01%	1.59%
-9.21% to -6.09%	53	3.83%	5.42%
-6.09% to -2.97%	190	13.74%	19.16%
-2.97% to 0.15%	441	31.89%	51.05%
0.15% to 3.27%	409	29.57%	80.62%
3.27% to 6.39%	178	12.87%	93.49%
6.39% to 9.51%	67	4.84%	98.34%
9.51% to 12.63%	18	1.30%	99.64%
Greater than 12.63%	5	0.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.01%	4.31%	73.10%	68.27%
±2σ	-8.17%	8.47%	94.72%	95.45%
±3σ	-12.33%	12.63%	99.06%	99.73%

Descriptive Statistics

Mean	0.154%
Standard Error	0.112%
Median	0.071%
Mode	0.000%
Standard Deviation	4.160%
Sample Variance	17.308%
Kurtosis	2.99
Skewness	0.22
Range	47.309%
Minimum	-17.068%
Maximum	30.241%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.194%	704	50.90%	1.626%
Negative	-3.020%	674	48.73%	-1.472%
Zero	0.000%	5	0.36%	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 1.08 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.75%	2	0.70%	0.70%
-31.75% to -23.79%	3	1.05%	1.74%
-23.79% to -15.83%	8	2.79%	4.53%
-15.83% to -7.87%	45	15.68%	20.21%
-7.87% to 0.09%	91	31.71%	51.92%
0.09% to 8.04%	84	29.27%	81.18%
8.04% to 16.00%	36	12.54%	93.73%
16.00% to 23.96%	9	3.14%	96.86%
23.96% to 31.92%	7	2.44%	99.30%
Greater than 31.92%	2	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.53%	10.70%	72.47%	68.27%
±2σ	-21.14%	21.31%	94.08%	95.45%
±3σ	-31.75%	31.92%	98.95%	99.73%

Descriptive Statistics

Mean	0.085%
Standard Error	0.626%
Median	-0.254%
Mode	-7.901%
Standard Deviation	10.612%
Sample Variance	112.624%
Kurtosis	1.08
Skewness	0.29
Range	66.519%
Minimum	-33.000%
Maximum	33.519%
Count	287

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.405%	138	48.08%	4.041%
Negative	-7.622%	149	51.92%	-3.957%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.86%
12	1 Quarter	17.61%
52	1 Year	15.51%
156	3 Years	14.08%
260	5 Years	15.20%
520	10 Years	15.37%
1,040	20 Years	15.37%
2,600	50 Years	15.37%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 10.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.34%	0	0.00%	0.00%
-12.34% to -5.06%	0	0.00%	0.00%
-5.06% to 2.23%	0	0.00%	0.00%
2.23% to 9.51%	52	18.06%	18.06%
9.51% to 16.79%	127	44.10%	62.15%
16.79% to 24.08%	66	22.92%	85.07%
24.08% to 31.36%	23	7.99%	93.06%
31.36% to 38.64%	9	3.12%	96.18%
38.64% to 45.93%	6	2.08%	98.26%
Greater than 45.93%	5	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.08%	26.51%	83.33%	68.27%
±2σ	-2.63%	36.22%	95.83%	95.45%
±3σ	-12.34%	45.93%	98.26%	99.73%

Descriptive Statistics

Mean	16.794%
Standard Error	0.572%
Median	14.386%
Mode	20.420%
Standard Deviation	9.711%
Sample Variance	94.309%
Kurtosis	10.60
Skewness	2.52
Range	79.218%
Minimum	5.210%
Maximum	84.428%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.794%	288	100.00%	16.794%
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 0.90. Further, an Excess Kurtosis of 3.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.72%	0	0.00%	0.00%
-31.72% to -23.50%	3	1.04%	1.04%
-23.50% to -15.29%	11	3.82%	4.86%
-15.29% to -7.07%	42	14.58%	19.44%
-7.07% to 1.14%	98	34.03%	53.47%
1.14% to 9.36%	86	29.86%	83.33%
9.36% to 17.57%	34	11.81%	95.14%
17.57% to 25.79%	7	2.43%	97.57%
25.79% to 34.00%	2	0.69%	98.26%
Greater than 34.00%	5	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.81%	12.10%	75.00%	68.27%
±2σ	-20.77%	23.05%	95.14%	95.45%
±3σ	-31.72%	34.00%	98.26%	99.73%

Descriptive Statistics

Mean	1.142%
Standard Error	0.645%
Median	0.577%
Mode	-1.851%
Standard Deviation	10.954%
Sample Variance	119.984%
Kurtosis	3.14
Skewness	0.90
Range	77.495%
Minimum	-26.853%
Maximum	50.642%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.668%	152	52.78%	4.575%
Negative	-7.323%	135	46.88%	-3.433%
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 0.30 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -62.42%	0	0.00%	0.00%
-62.42% to -46.87%	0	0.00%	0.00%
-46.87% to -31.32%	4	6.06%	6.06%
-31.32% to -15.78%	11	16.67%	22.73%
-15.78% to -0.23%	19	28.79%	51.52%
-0.23% to 15.32%	17	25.76%	77.27%
15.32% to 30.86%	9	13.64%	90.91%
30.86% to 46.41%	5	7.58%	98.48%
46.41% to 61.96%	1	1.52%	100.00%
Greater than 61.96%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.96%	20.50%	72.73%	68.27%
±2σ	-41.69%	41.23%	96.97%	95.45%
±3σ	-62.42%	61.96%	100.00%	99.73%

Descriptive Statistics

Mean	-0.230%
Standard Error	2.552%
Median	-0.798%
Mode	-6.801%
Standard Deviation	20.729%
Sample Variance	429.686%
Kurtosis	0.30
Skewness	0.49
Range	99.994%
Minimum	-39.813%
Maximum	60.181%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.227%	32	48.48%	7.868%
Negative	-15.719%	34	51.52%	-8.098%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	38.90%
12	1 Year	33.80%
36	3 Years	30.71%
60	5 Years	32.25%
120	10 Years	32.40%
240	20 Years	32.40%
600	50 Years	32.40%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.08. Further, an Excess Kurtosis of 7.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.65%	0	0.00%	0.00%
-22.65% to -6.81%	0	0.00%	0.00%
-6.81% to 9.02%	0	0.00%	0.00%
9.02% to 24.85%	11	16.42%	16.42%
24.85% to 40.68%	30	44.78%	61.19%
40.68% to 56.51%	13	19.40%	80.60%
56.51% to 72.34%	9	13.43%	94.03%
72.34% to 88.18%	3	4.48%	98.51%
88.18% to 104.01%	0	0.00%	98.51%
Greater than 104.01%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.57%	61.79%	79.10%	68.27%
±2σ	-1.54%	82.90%	95.52%	95.45%
±3σ	-22.65%	104.01%	98.51%	99.73%

Descriptive Statistics

Mean	40.681%
Standard Error	2.579%
Median	34.032%
Mode	12.922%
Standard Deviation	21.109%
Sample Variance	445.610%
Kurtosis	7.31
Skewness	2.08
Range	130.117%
Minimum	12.922%
Maximum	143.039%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.681%	67	100.00%	40.681%
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 0.75. Further, an Excess Kurtosis of 0.58 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.72%	0	0.00%	0.00%
-61.72% to -45.10%	0	0.00%	0.00%
-45.10% to -28.49%	2	2.99%	2.99%
-28.49% to -11.87%	15	22.39%	25.37%
-11.87% to 4.74%	19	28.36%	53.73%
4.74% to 21.36%	17	25.37%	79.10%
21.36% to 37.98%	9	13.43%	92.54%
37.98% to 54.59%	2	2.99%	95.52%
54.59% to 71.21%	3	4.48%	100.00%
Greater than 71.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.41%	26.90%	73.13%	68.27%
±2σ	-39.56%	49.05%	95.52%	95.45%
±3σ	-61.72%	71.21%	100.00%	99.73%

Descriptive Statistics

Mean	4.744%
Standard Error	2.707%
Median	1.428%
Mode	-36.393%
Standard Deviation	22.154%
Sample Variance	490.786%
Kurtosis	0.58
Skewness	0.75
Range	102.383%
Minimum	-36.393%
Maximum	65.990%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.235%	36	53.73%	10.872%
Negative	-13.247%	31	46.27%	-6.129%
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 -109.15%	0	0.00%	0.00%
-109.15% to -82.17%	0	0.00%	0.00%
-82.17% to -55.20%	0	0.00%	0.00%
-55.20% to -28.22%	7	31.82%	31.82%
-28.22% to -1.24%	5	22.73%	54.55%
-1.24% to 25.73%	5	22.73%	77.27%
25.73% to 52.71%	2	9.09%	86.36%
52.71% to 79.68%	3	13.64%	100.00%
79.68% to 106.66%	0	0.00%	100.00%
Greater than 106.66%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-37.21%	34.72%	72.73%	68.27%
±2σ	-73.18%	70.69%	100.00%	95.45%
±3σ	-109.15%	106.66%	100.00%	99.73%

Descriptive Statistics

Mean	-1.244%
Standard Error	7.668%
Median	-13.096%
Mode	-44.655%
Standard Deviation	35.968%
Sample Variance	1293.720%
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	-29.607%	12	54.55%	-16.149%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	63.19%
12	3 Years	62.60%
20	5 Years	61.51%
40	10 Years	61.90%
80	20 Years	61.90%
200	50 Years	61.90%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. 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 11.25%	0	0.00%	0.00%
11.25% to 29.70%	0	0.00%	0.00%
29.70% to 48.16%	1	4.35%	4.35%
48.16% to 66.61%	5	21.74%	26.09%
66.61% to 85.06%	6	26.09%	52.17%
85.06% to 103.52%	8	34.78%	86.96%
103.52% to 121.97%	1	4.35%	91.30%
121.97% to 140.43%	1	4.35%	95.65%
140.43% to 158.88%	1	4.35%	100.00%
Greater than 158.88%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	60.46%	109.67%	69.57%	68.27%
±2σ	35.85%	134.28%	95.65%	95.45%
±3σ	11.25%	158.88%	100.00%	99.73%

Descriptive Statistics

Mean	85.065%
Standard Error	5.131%
Median	84.744%
Mode	47.391%
Standard Deviation	24.606%
Sample Variance	605.446%
Kurtosis	0.25
Skewness	0.67
Range	95.648%
Minimum	47.391%
Maximum	143.039%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	85.065%	23	100.00%	85.065%
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 -103.87%	0	0.00%	0.00%
-103.87% to -74.66%	0	0.00%	0.00%
-74.66% to -45.45%	0	0.00%	0.00%
-45.45% to -16.25%	7	30.43%	30.43%
-16.25% to 12.96%	5	21.74%	52.17%
12.96% to 42.17%	4	17.39%	69.57%
42.17% to 71.38%	5	21.74%	91.30%
71.38% to 100.58%	2	8.70%	100.00%
100.58% to 129.79%	0	0.00%	100.00%
Greater than 129.79%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.98%	51.91%	65.22%	68.27%
±2σ	-64.92%	90.85%	100.00%	95.45%
±3σ	-103.87%	129.79%	100.00%	99.73%

Descriptive Statistics

Mean	12.962%
Standard Error	8.120%
Median	-0.071%
Mode	-41.449%
Standard Deviation	38.943%
Sample Variance	1516.552%
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	49.451%	11	47.83%	23.650%
Negative	-20.487%	12	52.17%	-10.689%
Zero	0.000%	0	0.00%	0.000%

U Deep Analytical Report