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	5.12%	4.27%	4.55%	6.28%	4.17%	4.15%	20.07	21.81	19.25	22.74
Weekly	11.72%	10.46%	11.16%	15.04%	9.18%	9.14%	19.09	22.93	17.41	25.14
Monthly	26.18%	29.02%	22.41%	30.91%	19.11%	19.03%	17.28	25.33	14.27	30.66
Quarterly	55.44%	73.71%	43.82%	55.40%	33.10%	32.96%	15.02	29.13	10.79	40.56
Annual	—	—	—	—	66.20%	65.92%	10.79	40.56	5.57	78.63
Option Time Horizon	—	—	—	—	24.99%	24.88%	16.29	26.86	12.69	34.48

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $20.92 | Strike (K): $21.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.0750 (Bid $1.9500 / Ask $2.2000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 66.20% (CRR binomial tree, American, n=20 steps) | BS IV: 65.59% (European Black-Scholes) | Yahoo IV (Annual): 65.92% → 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 8.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.22%	13	0.33%	0.33%
-15.22% to -11.38%	36	0.93%	1.26%
-11.38% to -7.54%	134	3.45%	4.71%
-7.54% to -3.70%	512	13.18%	17.88%
-3.70% to 0.15%	1373	35.33%	53.22%
0.15% to 3.99%	1154	29.70%	82.91%
3.99% to 7.83%	448	11.53%	94.44%
7.83% to 11.67%	117	3.01%	97.45%
11.67% to 15.52%	61	1.57%	99.02%
Greater than 15.52%	38	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.98%	5.27%	76.09%	68.27%
±2σ	-10.10%	10.39%	95.08%	95.45%
±3σ	-15.22%	15.52%	98.69%	99.73%

Descriptive Statistics

Mean	0.146%
Standard Error	0.082%
Median	-0.054%
Mode	0.000%
Standard Deviation	5.123%
Sample Variance	26.245%
Kurtosis	8.28
Skewness	0.97
Range	84.371%
Minimum	-23.246%
Maximum	61.125%
Count	3886

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.882%	1883	48.46%	1.881%
Negative	-3.445%	1957	50.36%	-1.735%
Zero	0.000%	46	1.18%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.87%
20	1 Month	5.51%
60	1 Quarter	5.36%
250	1 Year	6.20%
750	3 Years	5.72%
1,250	5 Years	6.28%
2,500	10 Years	6.41%
5,000	20 Years	6.92%
12,500	50 Years	6.92%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.01%	0	0.00%	0.00%
-6.01% to -2.81%	0	0.00%	0.00%
-2.81% to 0.39%	0	0.00%	0.00%
0.39% to 3.59%	671	17.26%	17.26%
3.59% to 6.79%	1750	45.02%	62.28%
6.79% to 9.99%	885	22.77%	85.05%
9.99% to 13.19%	325	8.36%	93.41%
13.19% to 16.39%	136	3.50%	96.91%
16.39% to 19.59%	55	1.41%	98.33%
Greater than 19.59%	65	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.52%	11.05%	83.92%	68.27%
±2σ	-1.75%	15.32%	96.04%	95.45%
±3σ	-6.01%	19.59%	98.33%	99.73%

Descriptive Statistics

Mean	6.788%
Standard Error	0.068%
Median	5.791%
Mode	6.250%
Standard Deviation	4.267%
Sample Variance	18.205%
Kurtosis	29.56
Skewness	3.38
Range	78.760%
Minimum	0.807%
Maximum	79.567%
Count	3887

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.788%	3887	100.00%	6.788%
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 Fairly Symmetrical with a Skewness factor of 0.10. Further, an Excess Kurtosis of 4.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.44%	23	0.59%	0.59%
-13.44% to -10.03%	46	1.18%	1.78%
-10.03% to -6.62%	131	3.37%	5.15%
-6.62% to -3.20%	518	13.33%	18.47%
-3.20% to 0.21%	1241	31.93%	50.40%
0.21% to 3.62%	1255	32.29%	82.69%
3.62% to 7.03%	465	11.96%	94.65%
7.03% to 10.44%	139	3.58%	98.22%
10.44% to 13.85%	32	0.82%	99.05%
Greater than 13.85%	37	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.34%	4.75%	76.18%	68.27%
±2σ	-8.89%	9.30%	94.80%	95.45%
±3σ	-13.44%	13.85%	98.46%	99.73%

Descriptive Statistics

Mean	0.207%
Standard Error	0.073%
Median	0.175%
Mode	0.000%
Standard Deviation	4.548%
Sample Variance	20.685%
Kurtosis	4.77
Skewness	0.10
Range	71.806%
Minimum	-38.660%
Maximum	33.146%
Count	3887

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.315%	2027	52.15%	1.729%
Negative	-3.264%	1812	46.62%	-1.522%
Zero	0.000%	48	1.24%	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 2.44 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.42%	3	0.37%	0.37%
-34.42% to -25.63%	1	0.12%	0.50%
-25.63% to -16.84%	26	3.23%	3.72%
-16.84% to -8.05%	143	17.74%	21.46%
-8.05% to 0.73%	268	33.25%	54.71%
0.73% to 9.52%	226	28.04%	82.75%
9.52% to 18.31%	80	9.93%	92.68%
18.31% to 27.10%	35	4.34%	97.02%
27.10% to 35.89%	17	2.11%	99.13%
Greater than 35.89%	7	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.98%	12.45%	75.93%	68.27%
±2σ	-22.70%	24.17%	93.80%	95.45%
±3σ	-34.42%	35.89%	98.76%	99.73%

Descriptive Statistics

Mean	0.735%
Standard Error	0.413%
Median	-0.410%
Mode	-9.777%
Standard Deviation	11.717%
Sample Variance	137.287%
Kurtosis	2.44
Skewness	0.81
Range	100.181%
Minimum	-38.668%
Maximum	61.513%
Count	806

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.646%	389	48.26%	4.655%
Negative	-7.596%	416	51.61%	-3.921%
Zero	0.000%	1	0.12%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.61%
12	1 Quarter	11.56%
52	1 Year	14.31%
156	3 Years	13.81%
260	5 Years	15.04%
520	10 Years	15.24%
1,040	20 Years	16.48%
2,600	50 Years	16.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.25. Further, an Excess Kurtosis of 8.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.62%	0	0.00%	0.00%
-13.62% to -5.78%	0	0.00%	0.00%
-5.78% to 2.07%	0	0.00%	0.00%
2.07% to 9.92%	150	18.59%	18.59%
9.92% to 17.77%	353	43.74%	62.33%
17.77% to 25.62%	178	22.06%	84.39%
25.62% to 33.47%	67	8.30%	92.69%
33.47% to 41.31%	32	3.97%	96.65%
41.31% to 49.16%	14	1.73%	98.39%
Greater than 49.16%	13	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.30%	28.23%	80.79%	68.27%
±2σ	-3.16%	38.70%	95.17%	95.45%
±3σ	-13.62%	49.16%	98.39%	99.73%

Descriptive Statistics

Mean	17.769%
Standard Error	0.368%
Median	15.058%
Mode	12.500%
Standard Deviation	10.464%
Sample Variance	109.492%
Kurtosis	8.19
Skewness	2.25
Range	88.735%
Minimum	3.912%
Maximum	92.647%
Count	807

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.769%	807	100.00%	17.769%
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 -32.83%	3	0.37%	0.37%
-32.83% to -24.45%	9	1.12%	1.49%
-24.45% to -16.08%	36	4.46%	5.95%
-16.08% to -7.71%	102	12.64%	18.59%
-7.71% to 0.66%	262	32.47%	51.05%
0.66% to 9.04%	237	29.37%	80.42%
9.04% to 17.41%	115	14.25%	94.67%
17.41% to 25.78%	25	3.10%	97.77%
25.78% to 34.15%	13	1.61%	99.38%
Greater than 34.15%	5	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.50%	11.83%	75.71%	68.27%
±2σ	-21.66%	22.99%	94.67%	95.45%
±3σ	-32.83%	34.15%	99.01%	99.73%

Descriptive Statistics

Mean	0.664%
Standard Error	0.393%
Median	0.437%
Mode	0.000%
Standard Deviation	11.163%
Sample Variance	124.607%
Kurtosis	2.51
Skewness	0.42
Range	94.584%
Minimum	-37.981%
Maximum	56.603%
Count	807

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.744%	411	50.93%	4.453%
Negative	-7.841%	390	48.33%	-3.789%
Zero	0.000%	6	0.74%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.31. Further, an Excess Kurtosis of 12.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.50%	0	0.00%	0.00%
-75.50% to -55.87%	0	0.00%	0.00%
-55.87% to -36.23%	5	2.70%	2.70%
-36.23% to -16.60%	30	16.22%	18.92%
-16.60% to 3.03%	72	38.92%	57.84%
3.03% to 22.66%	51	27.57%	85.41%
22.66% to 42.30%	16	8.65%	94.05%
42.30% to 61.93%	8	4.32%	98.38%
61.93% to 81.56%	1	0.54%	98.92%
Greater than 81.56%	2	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.14%	29.21%	75.68%	68.27%
±2σ	-49.32%	55.38%	97.84%	95.45%
±3σ	-75.50%	81.56%	98.92%	99.73%

Descriptive Statistics

Mean	3.031%
Standard Error	1.925%
Median	-0.852%
Mode	-39.211%
Standard Deviation	26.176%
Sample Variance	685.188%
Kurtosis	12.52
Skewness	2.31
Range	222.812%
Minimum	-39.211%
Maximum	183.601%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.757%	89	48.11%	10.467%
Negative	-14.329%	96	51.89%	-7.436%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.31%
12	1 Year	29.25%
36	3 Years	29.16%
60	5 Years	30.91%
120	10 Years	32.20%
240	20 Years	36.11%
600	50 Years	36.11%

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 -44.06%	0	0.00%	0.00%
-44.06% to -22.30%	0	0.00%	0.00%
-22.30% to -0.53%	0	0.00%	0.00%
-0.53% to 21.23%	22	11.83%	11.83%
21.23% to 43.00%	100	53.76%	65.59%
43.00% to 64.76%	39	20.97%	86.56%
64.76% to 86.53%	16	8.60%	95.16%
86.53% to 108.29%	5	2.69%	97.85%
108.29% to 130.06%	2	1.08%	98.92%
Greater than 130.06%	2	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.98%	72.02%	88.17%	68.27%
±2σ	-15.04%	101.04%	97.31%	95.45%
±3σ	-44.06%	130.05%	98.92%	99.73%

Descriptive Statistics

Mean	42.998%
Standard Error	2.128%
Median	35.359%
Mode	12.185%
Standard Deviation	29.019%
Sample Variance	842.109%
Kurtosis	28.01
Skewness	4.13
Range	273.624%
Minimum	12.185%
Maximum	285.809%
Count	186

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	42.998%	186	100.00%	42.998%
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 0.44. Further, an Excess Kurtosis of 0.54 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.87%	0	0.00%	0.00%
-64.87% to -48.06%	2	1.08%	1.08%
-48.06% to -31.25%	5	2.69%	3.76%
-31.25% to -14.45%	33	17.74%	21.51%
-14.45% to 2.36%	60	32.26%	53.76%
2.36% to 19.17%	50	26.88%	80.65%
19.17% to 35.98%	20	10.75%	91.40%
35.98% to 52.78%	10	5.38%	96.77%
52.78% to 69.59%	6	3.23%	100.00%
Greater than 69.59%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.05%	24.77%	72.04%	68.27%
±2σ	-42.46%	47.18%	94.09%	95.45%
±3σ	-64.87%	69.59%	100.00%	99.73%

Descriptive Statistics

Mean	2.362%
Standard Error	1.643%
Median	1.124%
Mode	-0.284%
Standard Deviation	22.410%
Sample Variance	502.221%
Kurtosis	0.54
Skewness	0.44
Range	126.517%
Minimum	-63.946%
Maximum	62.571%
Count	186

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.770%	96	51.61%	9.688%
Negative	-15.141%	90	48.39%	-7.326%
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 1.73. Further, an Excess Kurtosis of 3.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -154.91%	0	0.00%	0.00%
-154.91% to -113.33%	0	0.00%	0.00%
-113.33% to -71.75%	0	0.00%	0.00%
-71.75% to -30.18%	12	19.35%	19.35%
-30.18% to 11.40%	29	46.77%	66.13%
11.40% to 52.98%	10	16.13%	82.26%
52.98% to 94.56%	7	11.29%	93.55%
94.56% to 136.13%	1	1.61%	95.16%
136.13% to 177.71%	1	1.61%	96.77%
Greater than 177.71%	2	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-44.03%	66.84%	77.42%	68.27%
±2σ	-99.47%	122.27%	95.16%	95.45%
±3σ	-154.91%	177.71%	96.77%	99.73%

Descriptive Statistics

Mean	11.402%
Standard Error	7.040%
Median	-3.450%
Mode	-53.608%
Standard Deviation	55.436%
Sample Variance	3073.187%
Kurtosis	3.68
Skewness	1.73
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	-25.197%	33	53.23%	-13.411%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	57.13%
12	3 Years	55.02%
20	5 Years	55.40%
40	10 Years	62.92%
80	20 Years	72.94%
200	50 Years	72.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.72. Further, an Excess Kurtosis of 9.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -123.30%	0	0.00%	0.00%
-123.30% to -68.02%	0	0.00%	0.00%
-68.02% to -12.74%	0	0.00%	0.00%
-12.74% to 42.54%	8	12.70%	12.70%
42.54% to 97.82%	32	50.79%	63.49%
97.82% to 153.10%	14	22.22%	85.71%
153.10% to 208.38%	6	9.52%	95.24%
208.38% to 263.66%	0	0.00%	95.24%
263.66% to 318.94%	1	1.59%	96.83%
Greater than 318.94%	2	3.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.12%	171.53%	93.65%	68.27%
±2σ	-49.59%	245.24%	95.24%	95.45%
±3σ	-123.30%	318.94%	96.83%	99.73%

Descriptive Statistics

Mean	97.823%
Standard Error	9.286%
Median	73.584%
Mode	29.185%
Standard Deviation	73.706%
Sample Variance	5432.622%
Kurtosis	9.00
Skewness	2.72
Range	393.603%
Minimum	29.185%
Maximum	422.788%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	97.823%	63	100.00%	97.823%
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 0.57. Further, an Excess Kurtosis of -0.05 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -123.41%	0	0.00%	0.00%
-123.41% to -90.55%	0	0.00%	0.00%
-90.55% to -57.69%	3	4.76%	4.76%
-57.69% to -24.82%	14	22.22%	26.98%
-24.82% to 8.04%	17	26.98%	53.97%
8.04% to 40.90%	17	26.98%	80.95%
40.90% to 73.76%	6	9.52%	90.48%
73.76% to 106.63%	4	6.35%	96.83%
106.63% to 139.49%	2	3.17%	100.00%
Greater than 139.49%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.78%	51.86%	68.25%	68.27%
±2σ	-79.60%	95.67%	96.83%	95.45%
±3σ	-123.41%	139.49%	100.00%	99.73%

Descriptive Statistics

Mean	8.038%
Standard Error	5.520%
Median	4.530%
Mode	-68.684%
Standard Deviation	43.817%
Sample Variance	1919.971%
Kurtosis	-0.05
Skewness	0.57
Range	184.425%
Minimum	-68.684%
Maximum	115.741%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.056%	35	55.56%	21.142%
Negative	-29.485%	28	44.44%	-13.104%
Zero	0.000%	0	0.00%	0.000%

DQ Deep Analytical Report