DOCU - 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	3.58%	2.46%	2.88%	4.39%	4.00%	4.07%	42.74	46.29	41.06	48.18
Weekly	7.71%	8.19%	8.39%	10.73%	8.80%	8.95%	40.73	48.57	37.30	53.04
Monthly	13.96%	14.12%	14.67%	22.73%	18.32%	18.63%	37.03	53.42	30.83	64.17
Quarterly	31.64%	30.44%	32.18%	39.73%	31.74%	32.28%	32.38	61.09	23.58	83.91
Annual	—	—	—	—	63.47%	64.55%	23.58	83.91	12.50	158.30
Option Time Horizon	—	—	—	—	20.75%	21.10%	36.15	54.74	29.37	67.36

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $44.48 | Strike (K): $47.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.7600 (Bid $2.3700 / Ask $3.1500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 63.47% (CRR binomial tree, American, n=20 steps) | BS IV: 64.20% (European Black-Scholes) | Yahoo IV (Annual): 64.55% → 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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.65. Further, an Excess Kurtosis of 16.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.65%	9	0.46%	0.46%
-10.65% to -7.97%	18	0.92%	1.37%
-7.97% to -5.29%	63	3.21%	4.58%
-5.29% to -2.61%	235	11.97%	16.55%
-2.61% to 0.07%	656	33.40%	49.95%
0.07% to 2.75%	661	33.66%	83.60%
2.75% to 5.43%	238	12.12%	95.72%
5.43% to 8.12%	57	2.90%	98.63%
8.12% to 10.80%	11	0.56%	99.19%
Greater than 10.80%	16	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.50%	3.65%	78.67%	68.27%
±2σ	-7.08%	7.22%	96.33%	95.45%
±3σ	-10.65%	10.80%	98.73%	99.73%

Descriptive Statistics

Mean	0.072%
Standard Error	0.081%
Median	0.075%
Mode	0.000%
Standard Deviation	3.575%
Sample Variance	12.778%
Kurtosis	16.74
Skewness	-0.65
Range	70.081%
Minimum	-42.225%
Maximum	27.856%
Count	1964

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.423%	1002	51.02%	1.236%
Negative	-2.387%	958	48.78%	-1.164%
Zero	0.000%	4	0.20%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.51%
20	1 Month	4.96%
60	1 Quarter	4.00%
250	1 Year	3.83%
750	3 Years	3.59%
1,250	5 Years	4.39%
2,500	10 Years	4.53%
5,000	20 Years	4.53%
12,500	50 Years	4.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.10. Further, an Excess Kurtosis of 9.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.05%	0	0.00%	0.00%
-3.05% to -1.21%	0	0.00%	0.00%
-1.21% to 0.63%	0	0.00%	0.00%
0.63% to 2.47%	428	21.78%	21.78%
2.47% to 4.31%	778	39.59%	61.37%
4.31% to 6.15%	423	21.53%	82.90%
6.15% to 7.99%	185	9.41%	92.32%
7.99% to 9.84%	79	4.02%	96.34%
9.84% to 11.68%	37	1.88%	98.22%
Greater than 11.68%	35	1.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.86%	6.77%	79.75%	68.27%
±2σ	-0.60%	9.22%	95.57%	95.45%
±3σ	-3.05%	11.68%	98.22%	99.73%

Descriptive Statistics

Mean	4.311%
Standard Error	0.055%
Median	3.711%
Mode	2.469%
Standard Deviation	2.455%
Sample Variance	6.025%
Kurtosis	9.08
Skewness	2.10
Range	28.909%
Minimum	0.779%
Maximum	29.688%
Count	1965

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.311%	1965	100.00%	4.311%
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 0.16. Further, an Excess Kurtosis of 2.14 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.65%	9	0.46%	0.46%
-8.65% to -6.49%	23	1.17%	1.63%
-6.49% to -4.32%	75	3.82%	5.45%
-4.32% to -2.16%	263	13.38%	18.83%
-2.16% to 0.01%	639	32.52%	51.35%
0.01% to 2.17%	596	30.33%	81.68%
2.17% to 4.33%	237	12.06%	93.74%
4.33% to 6.50%	81	4.12%	97.86%
6.50% to 8.66%	30	1.53%	99.39%
Greater than 8.66%	12	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.88%	2.89%	73.59%	68.27%
±2σ	-5.76%	5.77%	94.45%	95.45%
±3σ	-8.65%	8.66%	98.93%	99.73%

Descriptive Statistics

Mean	0.005%
Standard Error	0.065%
Median	-0.075%
Mode	0.000%
Standard Deviation	2.885%
Sample Variance	8.321%
Kurtosis	2.14
Skewness	0.16
Range	27.741%
Minimum	-13.151%
Maximum	14.590%
Count	1965

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.176%	956	48.65%	1.059%
Negative	-2.064%	1003	51.04%	-1.054%
Zero	0.000%	6	0.30%	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 3.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.80%	3	0.74%	0.74%
-22.80% to -17.01%	5	1.23%	1.96%
-17.01% to -11.23%	18	4.41%	6.37%
-11.23% to -5.44%	49	12.01%	18.38%
-5.44% to 0.34%	121	29.66%	48.04%
0.34% to 6.12%	142	34.80%	82.84%
6.12% to 11.91%	51	12.50%	95.34%
11.91% to 17.69%	12	2.94%	98.28%
17.69% to 23.48%	3	0.74%	99.02%
Greater than 23.48%	4	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.37%	8.05%	77.70%	68.27%
±2σ	-15.08%	15.76%	94.85%	95.45%
±3σ	-22.79%	23.48%	98.28%	99.73%

Descriptive Statistics

Mean	0.341%
Standard Error	0.382%
Median	0.673%
Mode	-0.682%
Standard Deviation	7.712%
Sample Variance	59.474%
Kurtosis	3.91
Skewness	-0.29
Range	73.676%
Minimum	-42.791%
Maximum	30.885%
Count	408

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.559%	219	53.68%	2.984%
Negative	-5.705%	189	46.32%	-2.643%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.55%
12	1 Quarter	10.05%
52	1 Year	9.22%
156	3 Years	8.73%
260	5 Years	10.73%
520	10 Years	10.84%
1,040	20 Years	10.84%
2,600	50 Years	10.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.92. Further, an Excess Kurtosis of 28.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.94%	0	0.00%	0.00%
-12.94% to -6.80%	0	0.00%	0.00%
-6.80% to -0.66%	0	0.00%	0.00%
-0.66% to 5.49%	51	12.47%	12.47%
5.49% to 11.62%	217	53.06%	65.53%
11.62% to 17.77%	84	20.54%	86.06%
17.77% to 23.91%	29	7.09%	93.15%
23.91% to 30.05%	14	3.42%	96.58%
30.05% to 36.19%	7	1.71%	98.29%
Greater than 36.19%	7	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.44%	19.81%	88.02%	68.27%
±2σ	-4.75%	28.00%	96.09%	95.45%
±3σ	-12.94%	36.19%	98.29%	99.73%

Descriptive Statistics

Mean	11.625%
Standard Error	0.405%
Median	9.619%
Mode	6.579%
Standard Deviation	8.187%
Sample Variance	67.020%
Kurtosis	28.45
Skewness	3.92
Range	91.405%
Minimum	2.801%
Maximum	94.206%
Count	409

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.625%	409	100.00%	11.625%
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 2.27. Further, an Excess Kurtosis of 16.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.83%	0	0.00%	0.00%
-24.83% to -18.54%	4	0.98%	0.98%
-18.54% to -12.25%	12	2.93%	3.91%
-12.25% to -5.96%	42	10.27%	14.18%
-5.96% to 0.33%	171	41.81%	55.99%
0.33% to 6.62%	114	27.87%	83.86%
6.62% to 12.91%	41	10.02%	93.89%
12.91% to 19.20%	16	3.91%	97.80%
19.20% to 25.50%	5	1.22%	99.02%
Greater than 25.50%	4	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.06%	8.72%	81.17%	68.27%
±2σ	-16.45%	17.11%	95.35%	95.45%
±3σ	-24.83%	25.50%	99.02%	99.73%

Descriptive Statistics

Mean	0.331%
Standard Error	0.415%
Median	-0.717%
Mode	-5.543%
Standard Deviation	8.388%
Sample Variance	70.358%
Kurtosis	16.88
Skewness	2.27
Range	99.041%
Minimum	-23.534%
Maximum	75.507%
Count	409

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.594%	186	45.48%	2.999%
Negative	-4.915%	222	54.28%	-2.668%
Zero	0.000%	1	0.24%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.26. Further, an Excess Kurtosis of 0.82 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.77%	0	0.00%	0.00%
-40.77% to -30.30%	2	2.13%	2.13%
-30.30% to -19.83%	3	3.19%	5.32%
-19.83% to -9.36%	17	18.09%	23.40%
-9.36% to 1.11%	25	26.60%	50.00%
1.11% to 11.58%	30	31.91%	81.91%
11.58% to 22.05%	9	9.57%	91.49%
22.05% to 32.52%	4	4.26%	95.74%
32.52% to 42.99%	4	4.26%	100.00%
Greater than 42.99%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.85%	15.07%	76.60%	68.27%
±2σ	-26.81%	29.03%	93.62%	95.45%
±3σ	-40.77%	42.99%	100.00%	99.73%

Descriptive Statistics

Mean	1.111%
Standard Error	1.440%
Median	0.800%
Mode	-38.176%
Standard Deviation	13.961%
Sample Variance	194.922%
Kurtosis	0.82
Skewness	0.26
Range	76.838%
Minimum	-38.176%
Maximum	38.662%
Count	94

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.558%	48	51.06%	5.902%
Negative	-9.790%	46	48.94%	-4.791%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	21.04%
12	1 Year	17.84%
36	3 Years	19.50%
60	5 Years	22.73%
120	10 Years	23.07%
240	20 Years	23.07%
600	50 Years	23.07%

High-to-Low 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 4.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.69%	0	0.00%	0.00%
-15.69% to -5.10%	0	0.00%	0.00%
-5.10% to 5.49%	0	0.00%	0.00%
5.49% to 16.08%	24	25.26%	25.26%
16.08% to 26.67%	34	35.79%	61.05%
26.67% to 37.27%	20	21.05%	82.11%
37.27% to 47.86%	9	9.47%	91.58%
47.86% to 58.45%	5	5.26%	96.84%
58.45% to 69.04%	1	1.05%	97.89%
Greater than 69.04%	2	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.55%	40.80%	82.11%	68.27%
±2σ	-1.57%	54.92%	95.79%	95.45%
±3σ	-15.69%	69.04%	97.89%	99.73%

Descriptive Statistics

Mean	26.674%
Standard Error	1.449%
Median	22.824%
Mode	10.514%
Standard Deviation	14.122%
Sample Variance	199.431%
Kurtosis	4.39
Skewness	1.76
Range	79.312%
Minimum	10.514%
Maximum	89.826%
Count	95

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.674%	95	100.00%	26.674%
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 1.09. Further, an Excess Kurtosis of 3.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.05%	0	0.00%	0.00%
-43.05% to -32.04%	0	0.00%	0.00%
-32.04% to -21.04%	5	5.26%	5.26%
-21.04% to -10.04%	13	13.68%	18.95%
-10.04% to 0.97%	34	35.79%	54.74%
0.97% to 11.97%	27	28.42%	83.16%
11.97% to 22.97%	11	11.58%	94.74%
22.97% to 33.98%	3	3.16%	97.89%
33.98% to 44.98%	0	0.00%	97.89%
Greater than 44.98%	2	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.70%	15.64%	80.00%	68.27%
±2σ	-28.38%	30.31%	95.79%	95.45%
±3σ	-43.05%	44.98%	97.89%	99.73%

Descriptive Statistics

Mean	0.967%
Standard Error	1.505%
Median	-0.570%
Mode	-27.710%
Standard Deviation	14.671%
Sample Variance	215.235%
Kurtosis	3.37
Skewness	1.09
Range	90.588%
Minimum	-27.710%
Maximum	62.878%
Count	95

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.593%	44	46.32%	5.833%
Negative	-9.064%	51	53.68%	-4.866%
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 1.00. Further, an Excess Kurtosis of 2.21 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.11%	0	0.00%	0.00%
-90.11% to -66.38%	0	0.00%	0.00%
-66.38% to -42.65%	1	3.12%	3.12%
-42.65% to -18.92%	6	18.75%	21.88%
-18.92% to 4.81%	11	34.38%	56.25%
4.81% to 28.54%	8	25.00%	81.25%
28.54% to 52.27%	4	12.50%	93.75%
52.27% to 76.00%	1	3.12%	96.88%
76.00% to 99.73%	0	0.00%	96.88%
Greater than 99.73%	1	3.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.83%	36.45%	75.00%	68.27%
±2σ	-58.47%	68.09%	96.88%	95.45%
±3σ	-90.11%	99.73%	96.88%	99.73%

Descriptive Statistics

Mean	4.810%
Standard Error	5.593%
Median	-3.788%
Mode	-54.806%
Standard Deviation	31.639%
Sample Variance	1001.022%
Kurtosis	2.21
Skewness	1.00
Range	161.804%
Minimum	-54.806%
Maximum	106.998%
Count	32

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.104%	14	43.75%	14.483%
Negative	-17.197%	18	56.25%	-9.673%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	26.47%
12	3 Years	34.93%
20	5 Years	39.73%
40	10 Years	42.80%
80	20 Years	42.80%
200	50 Years	42.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.81. Further, an Excess Kurtosis of 4.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.97%	0	0.00%	0.00%
-37.97% to -15.14%	0	0.00%	0.00%
-15.14% to 7.69%	0	0.00%	0.00%
7.69% to 30.52%	9	27.27%	27.27%
30.52% to 53.34%	10	30.30%	57.58%
53.34% to 76.17%	8	24.24%	81.82%
76.17% to 99.00%	4	12.12%	93.94%
99.00% to 121.82%	1	3.03%	96.97%
121.82% to 144.65%	0	0.00%	96.97%
Greater than 144.65%	1	3.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.91%	83.78%	87.88%	68.27%
±2σ	-7.53%	114.22%	96.97%	95.45%
±3σ	-37.96%	144.65%	96.97%	99.73%

Descriptive Statistics

Mean	53.343%
Standard Error	5.298%
Median	45.815%
Mode	10.514%
Standard Deviation	30.436%
Sample Variance	926.342%
Kurtosis	4.99
Skewness	1.81
Range	156.130%
Minimum	10.514%
Maximum	166.644%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.343%	33	100.00%	53.343%
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 1.45. 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 -92.61%	0	0.00%	0.00%
-92.61% to -68.47%	0	0.00%	0.00%
-68.47% to -44.34%	1	3.03%	3.03%
-44.34% to -20.20%	6	18.18%	21.21%
-20.20% to 3.93%	10	30.30%	51.52%
3.93% to 28.07%	10	30.30%	81.82%
28.07% to 52.20%	4	12.12%	93.94%
52.20% to 76.33%	1	3.03%	96.97%
76.33% to 100.47%	0	0.00%	96.97%
Greater than 100.47%	1	3.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.25%	36.11%	81.82%	68.27%
±2σ	-60.43%	68.29%	96.97%	95.45%
±3σ	-92.61%	100.47%	96.97%	99.73%

Descriptive Statistics

Mean	3.932%
Standard Error	5.602%
Median	2.393%
Mode	-52.410%
Standard Deviation	32.179%
Sample Variance	1035.505%
Kurtosis	4.23
Skewness	1.45
Range	172.868%
Minimum	-52.410%
Maximum	120.458%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.937%	18	54.55%	13.602%
Negative	-21.275%	15	45.45%	-9.671%
Zero	0.000%	0	0.00%	0.000%

DOCU Deep Analytical Report