DQ - 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	5.13%	4.27%	4.56%	6.41%	4.24%	4.32%	23.34	25.41	22.37	26.51
Weekly	11.74%	10.48%	11.18%	15.31%	9.34%	9.51%	22.18	26.73	20.20	29.35
Monthly	26.22%	29.04%	22.46%	31.52%	19.44%	19.79%	20.05	29.58	16.50	35.92
Quarterly	55.35%	73.90%	43.81%	54.98%	33.68%	34.28%	17.39	34.10	12.42	47.75
Annual	—	—	—	—	67.35%	68.56%	12.42	47.75	6.33	93.66
Option Time Horizon	—	—	—	—	25.91%	26.37%	18.79	31.55	14.50	40.88

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $24.35 | Strike (K): $25.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3000 (Bid $1.9500 / Ask $2.6500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 67.35% (CRR binomial tree, American, n=20 steps) | BS IV: 67.68% (European Black-Scholes) | Yahoo IV (Annual): 68.56% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.97. Further, an Excess Kurtosis of 8.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.24%	13	0.34%	0.34%
-15.24% to -11.40%	36	0.93%	1.27%
-11.40% to -7.55%	134	3.47%	4.73%
-7.55% to -3.70%	506	13.09%	17.83%
-3.70% to 0.15%	1367	35.37%	53.20%
0.15% to 4.00%	1149	29.73%	82.92%
4.00% to 7.85%	445	11.51%	94.44%
7.85% to 11.70%	116	3.00%	97.44%
11.70% to 15.55%	62	1.60%	99.04%
Greater than 15.55%	37	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.98%	5.28%	76.09%	68.27%
±2σ	-10.11%	10.41%	95.06%	95.45%
±3σ	-15.24%	15.55%	98.71%	99.73%

Descriptive Statistics

Mean	0.151%
Standard Error	0.083%
Median	-0.054%
Mode	0.000%
Standard Deviation	5.132%
Sample Variance	26.337%
Kurtosis	8.26
Skewness	0.97
Range	84.371%
Minimum	-23.246%
Maximum	61.125%
Count	3865

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.891%	1874	48.49%	1.887%
Negative	-3.447%	1946	50.35%	-1.736%
Zero	0.000%	45	1.16%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.39%
20	1 Month	5.52%
60	1 Quarter	5.31%
250	1 Year	6.30%
750	3 Years	5.72%
1,250	5 Years	6.41%
2,500	10 Years	6.40%
5,000	20 Years	6.93%
12,500	50 Years	6.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.38. Further, an Excess Kurtosis of 29.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.02%	0	0.00%	0.00%
-6.02% to -2.82%	0	0.00%	0.00%
-2.82% to 0.39%	0	0.00%	0.00%
0.39% to 3.59%	667	17.25%	17.25%
3.59% to 6.80%	1742	45.06%	62.31%
6.80% to 10.00%	884	22.87%	85.18%
10.00% to 13.21%	318	8.23%	93.40%
13.21% to 16.41%	135	3.49%	96.90%
16.41% to 19.62%	55	1.42%	98.32%
Greater than 19.62%	65	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.52%	11.07%	83.86%	68.27%
±2σ	-1.75%	15.35%	96.02%	95.45%
±3σ	-6.02%	19.62%	98.32%	99.73%

Descriptive Statistics

Mean	6.798%
Standard Error	0.069%
Median	5.802%
Mode	6.250%
Standard Deviation	4.274%
Sample Variance	18.268%
Kurtosis	29.48
Skewness	3.38
Range	78.760%
Minimum	0.807%
Maximum	79.567%
Count	3866

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.798%	3866	100.00%	6.798%
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 0.10. Further, an Excess Kurtosis of 4.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.47%	22	0.57%	0.57%
-13.47% to -10.05%	47	1.22%	1.78%
-10.05% to -6.63%	128	3.31%	5.10%
-6.63% to -3.21%	518	13.40%	18.49%
-3.21% to 0.21%	1234	31.92%	50.41%
0.21% to 3.62%	1249	32.31%	82.72%
3.62% to 7.04%	461	11.92%	94.65%
7.04% to 10.46%	139	3.60%	98.24%
10.46% to 13.88%	31	0.80%	99.04%
Greater than 13.88%	37	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.35%	4.76%	76.23%	68.27%
±2σ	-8.91%	9.32%	94.80%	95.45%
±3σ	-13.47%	13.88%	98.47%	99.73%

Descriptive Statistics

Mean	0.207%
Standard Error	0.073%
Median	0.175%
Mode	0.000%
Standard Deviation	4.558%
Sample Variance	20.773%
Kurtosis	4.75
Skewness	0.10
Range	71.806%
Minimum	-38.660%
Maximum	33.146%
Count	3866

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.323%	2016	52.15%	1.733%
Negative	-3.272%	1803	46.64%	-1.526%
Zero	0.000%	47	1.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.81. Further, an Excess Kurtosis of 2.42 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.45%	3	0.37%	0.37%
-34.45% to -25.65%	1	0.12%	0.50%
-25.65% to -16.85%	26	3.24%	3.74%
-16.85% to -8.04%	143	17.83%	21.57%
-8.04% to 0.76%	267	33.29%	54.86%
0.76% to 9.56%	223	27.81%	82.67%
9.56% to 18.36%	80	9.98%	92.64%
18.36% to 27.16%	35	4.36%	97.01%
27.16% to 35.97%	17	2.12%	99.13%
Greater than 35.97%	7	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.98%	12.49%	75.94%	68.27%
±2σ	-22.71%	24.23%	93.77%	95.45%
±3σ	-34.45%	35.96%	98.75%	99.73%

Descriptive Statistics

Mean	0.757%
Standard Error	0.414%
Median	-0.388%
Mode	-9.777%
Standard Deviation	11.736%
Sample Variance	137.739%
Kurtosis	2.42
Skewness	0.81
Range	100.181%
Minimum	-38.668%
Maximum	61.513%
Count	802

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.663%	388	48.38%	4.675%
Negative	-7.607%	413	51.50%	-3.917%
Zero	0.000%	1	0.12%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.88%
12	1 Quarter	11.11%
52	1 Year	14.72%
156	3 Years	13.91%
260	5 Years	15.31%
520	10 Years	15.25%
1,040	20 Years	16.51%
2,600	50 Years	16.51%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.24. Further, an Excess Kurtosis of 8.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.63%	0	0.00%	0.00%
-13.63% to -5.77%	0	0.00%	0.00%
-5.77% to 2.09%	0	0.00%	0.00%
2.09% to 9.94%	151	18.80%	18.80%
9.94% to 17.80%	349	43.46%	62.27%
17.80% to 25.66%	177	22.04%	84.31%
25.66% to 33.51%	67	8.34%	92.65%
33.51% to 41.37%	32	3.99%	96.64%
41.37% to 49.23%	14	1.74%	98.38%
Greater than 49.23%	13	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.32%	28.28%	80.70%	68.27%
±2σ	-3.15%	38.75%	95.14%	95.45%
±3σ	-13.63%	49.23%	98.38%	99.73%

Descriptive Statistics

Mean	17.800%
Standard Error	0.370%
Median	15.076%
Mode	12.500%
Standard Deviation	10.476%
Sample Variance	109.755%
Kurtosis	8.16
Skewness	2.24
Range	88.735%
Minimum	3.912%
Maximum	92.647%
Count	803

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.800%	803	100.00%	17.800%
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 0.42. Further, an Excess Kurtosis of 2.51 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.90%	3	0.37%	0.37%
-32.90% to -24.51%	9	1.12%	1.49%
-24.51% to -16.12%	36	4.48%	5.98%
-16.12% to -7.74%	102	12.70%	18.68%
-7.74% to 0.65%	261	32.50%	51.18%
0.65% to 9.04%	235	29.27%	80.45%
9.04% to 17.42%	114	14.20%	94.65%
17.42% to 25.81%	25	3.11%	97.76%
25.81% to 34.20%	13	1.62%	99.38%
Greater than 34.20%	5	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.53%	11.83%	75.72%	68.27%
±2σ	-21.71%	23.01%	94.65%	95.45%
±3σ	-32.90%	34.20%	99.00%	99.73%

Descriptive Statistics

Mean	0.650%
Standard Error	0.395%
Median	0.398%
Mode	0.000%
Standard Deviation	11.182%
Sample Variance	125.029%
Kurtosis	2.51
Skewness	0.42
Range	94.584%
Minimum	-37.981%
Maximum	56.603%
Count	803

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.768%	408	50.81%	4.455%
Negative	-7.853%	389	48.44%	-3.804%
Zero	0.000%	6	0.75%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.30. Further, an Excess Kurtosis of 12.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.52%	0	0.00%	0.00%
-75.52% to -55.86%	0	0.00%	0.00%
-55.86% to -36.20%	5	2.72%	2.72%
-36.20% to -16.54%	30	16.30%	19.02%
-16.54% to 3.13%	72	39.13%	58.15%
3.13% to 22.79%	50	27.17%	85.33%
22.79% to 42.45%	16	8.70%	94.02%
42.45% to 62.12%	8	4.35%	98.37%
62.12% to 81.78%	1	0.54%	98.91%
Greater than 81.78%	2	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.09%	29.34%	76.09%	68.27%
±2σ	-49.31%	55.56%	97.83%	95.45%
±3σ	-75.52%	81.78%	98.91%	99.73%

Descriptive Statistics

Mean	3.127%
Standard Error	1.933%
Median	-0.806%
Mode	-39.211%
Standard Deviation	26.217%
Sample Variance	687.346%
Kurtosis	12.47
Skewness	2.30
Range	222.812%
Minimum	-39.211%
Maximum	183.601%
Count	184

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.757%	89	48.37%	10.524%
Negative	-14.326%	95	51.63%	-7.397%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.78%
12	1 Year	29.27%
36	3 Years	29.38%
60	5 Years	31.52%
120	10 Years	32.22%
240	20 Years	36.21%
600	50 Years	36.21%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.13. Further, an Excess Kurtosis of 28.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.00%	0	0.00%	0.00%
-44.00% to -22.22%	0	0.00%	0.00%
-22.22% to -0.43%	0	0.00%	0.00%
-0.43% to 21.35%	21	11.35%	11.35%
21.35% to 43.13%	100	54.05%	65.41%
43.13% to 64.91%	39	21.08%	86.49%
64.91% to 86.69%	16	8.65%	95.14%
86.69% to 108.48%	5	2.70%	97.84%
108.48% to 130.26%	2	1.08%	98.92%
Greater than 130.26%	2	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.09%	72.17%	88.11%	68.27%
±2σ	-14.96%	101.22%	97.30%	95.45%
±3σ	-44.00%	130.26%	98.92%	99.73%

Descriptive Statistics

Mean	43.129%
Standard Error	2.135%
Median	35.397%
Mode	12.185%
Standard Deviation	29.043%
Sample Variance	843.477%
Kurtosis	28.01
Skewness	4.13
Range	273.624%
Minimum	12.185%
Maximum	285.809%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.129%	185	100.00%	43.129%
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 0.45. Further, an Excess Kurtosis of 0.53 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.08%	0	0.00%	0.00%
-65.08% to -48.23%	2	1.08%	1.08%
-48.23% to -31.39%	4	2.16%	3.24%
-31.39% to -14.54%	34	18.38%	21.62%
-14.54% to 2.30%	59	31.89%	53.51%
2.30% to 19.14%	50	27.03%	80.54%
19.14% to 35.99%	20	10.81%	91.35%
35.99% to 52.83%	10	5.41%	96.76%
52.83% to 69.68%	6	3.24%	100.00%
Greater than 69.68%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.16%	24.76%	71.89%	68.27%
±2σ	-42.62%	47.22%	94.59%	95.45%
±3σ	-65.08%	69.68%	100.00%	99.73%

Descriptive Statistics

Mean	2.301%
Standard Error	1.651%
Median	0.852%
Mode	-0.284%
Standard Deviation	22.459%
Sample Variance	504.387%
Kurtosis	0.53
Skewness	0.45
Range	126.517%
Minimum	-63.946%
Maximum	62.571%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.825%	95	51.35%	9.667%
Negative	-15.141%	90	48.65%	-7.366%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.72. Further, an Excess Kurtosis of 3.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -154.42%	0	0.00%	0.00%
-154.42% to -112.91%	0	0.00%	0.00%
-112.91% to -71.39%	0	0.00%	0.00%
-71.39% to -29.88%	12	19.35%	19.35%
-29.88% to 11.63%	29	46.77%	66.13%
11.63% to 53.15%	10	16.13%	82.26%
53.15% to 94.66%	7	11.29%	93.55%
94.66% to 136.17%	1	1.61%	95.16%
136.17% to 177.69%	1	1.61%	96.77%
Greater than 177.69%	2	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-43.72%	66.98%	77.42%	68.27%
±2σ	-99.07%	122.33%	95.16%	95.45%
±3σ	-154.42%	177.69%	96.77%	99.73%

Descriptive Statistics

Mean	11.633%
Standard Error	7.030%
Median	-1.749%
Mode	-53.608%
Standard Deviation	55.351%
Sample Variance	3063.750%
Kurtosis	3.69
Skewness	1.72
Range	271.309%
Minimum	-53.608%
Maximum	217.701%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.050%	29	46.77%	24.814%
Negative	-24.764%	33	53.23%	-13.181%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	55.03%
12	3 Years	54.32%
20	5 Years	54.98%
40	10 Years	62.71%
80	20 Years	72.80%
200	50 Years	72.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.69. Further, an Excess Kurtosis of 8.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -124.07%	0	0.00%	0.00%
-124.07% to -68.64%	0	0.00%	0.00%
-68.64% to -13.22%	0	0.00%	0.00%
-13.22% to 42.21%	8	12.70%	12.70%
42.21% to 97.63%	32	50.79%	63.49%
97.63% to 153.06%	14	22.22%	85.71%
153.06% to 208.48%	6	9.52%	95.24%
208.48% to 263.91%	0	0.00%	95.24%
263.91% to 319.34%	1	1.59%	96.83%
Greater than 319.34%	2	3.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.73%	171.53%	92.06%	68.27%
±2σ	-50.17%	245.44%	95.24%	95.45%
±3σ	-124.07%	319.34%	96.83%	99.73%

Descriptive Statistics

Mean	97.633%
Standard Error	9.311%
Median	73.584%
Mode	17.257%
Standard Deviation	73.901%
Sample Variance	5461.291%
Kurtosis	8.92
Skewness	2.69
Range	405.531%
Minimum	17.257%
Maximum	422.788%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	97.633%	63	100.00%	97.633%
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 0.59. Further, an Excess Kurtosis of -0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -123.66%	0	0.00%	0.00%
-123.66% to -90.81%	0	0.00%	0.00%
-90.81% to -57.95%	2	3.17%	3.17%
-57.95% to -25.09%	14	22.22%	25.40%
-25.09% to 7.77%	19	30.16%	55.56%
7.77% to 40.62%	16	25.40%	80.95%
40.62% to 73.48%	6	9.52%	90.48%
73.48% to 106.34%	4	6.35%	96.83%
106.34% to 139.20%	2	3.17%	100.00%
Greater than 139.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.04%	51.58%	68.25%	68.27%
±2σ	-79.85%	95.39%	96.83%	95.45%
±3σ	-123.66%	139.20%	100.00%	99.73%

Descriptive Statistics

Mean	7.767%
Standard Error	5.519%
Median	1.150%
Mode	-68.684%
Standard Deviation	43.810%
Sample Variance	1919.287%
Kurtosis	-0.03
Skewness	0.59
Range	184.425%
Minimum	-68.684%
Maximum	115.741%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.568%	35	55.56%	20.871%
Negative	-29.485%	28	44.44%	-13.104%
Zero	0.000%	0	0.00%	0.000%

DQ Deep Analytical Report