QS - 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	6.74%	4.83%	4.97%	7.09%	5.09%	5.06%	6.59	7.29	6.26	7.67
Weekly	17.27%	18.63%	15.06%	17.25%	11.20%	11.13%	6.20	7.75	5.54	8.67
Monthly	45.53%	59.85%	26.82%	37.47%	23.30%	23.17%	5.49	8.75	4.35	11.04
Quarterly	75.69%	200.71%	51.37%	75.49%	40.36%	40.14%	4.63	10.38	3.09	15.54
Annual	—	—	—	—	80.73%	80.27%	3.09	15.54	1.38	34.83
Option Time Horizon	—	—	—	—	30.47%	30.30%	5.11	9.40	3.77	12.75

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $6.93 | Strike (K): $7.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.8200 (Bid $0.7900 / Ask $0.8500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 80.73% (CRR binomial tree, American, n=20 steps) | BS IV: 80.26% (European Black-Scholes) | Yahoo IV (Annual): 80.27% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.98. Further, an Excess Kurtosis of 29.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.05%	3	0.21%	0.21%
-20.05% to -14.99%	7	0.50%	0.71%
-14.99% to -9.93%	26	1.85%	2.56%
-9.93% to -4.88%	170	12.10%	14.66%
-4.88% to 0.18%	580	41.28%	55.94%
0.18% to 5.24%	438	31.17%	87.12%
5.24% to 10.30%	120	8.54%	95.66%
10.30% to 15.36%	29	2.06%	97.72%
15.36% to 20.41%	13	0.93%	98.65%
Greater than 20.41%	19	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.56%	6.93%	83.13%	68.27%
±2σ	-13.31%	13.67%	96.16%	95.45%
±3σ	-20.05%	20.41%	98.43%	99.73%

Descriptive Statistics

Mean	0.182%
Standard Error	0.180%
Median	-0.369%
Mode	0.000%
Standard Deviation	6.744%
Sample Variance	45.478%
Kurtosis	29.00
Skewness	2.98
Range	128.241%
Minimum	-40.841%
Maximum	87.400%
Count	1405

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.742%	643	45.77%	2.170%
Negative	-3.759%	743	52.88%	-1.988%
Zero	0.000%	19	1.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.19%
20	1 Month	5.20%
60	1 Quarter	5.69%
250	1 Year	7.96%
750	3 Years	6.70%
1,250	5 Years	7.09%
2,500	10 Years	7.65%
5,000	20 Years	7.65%
12,500	50 Years	7.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.23. Further, an Excess Kurtosis of 20.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.04%	0	0.00%	0.00%
-7.04% to -3.42%	0	0.00%	0.00%
-3.42% to 0.20%	1	0.07%	0.07%
0.20% to 3.82%	200	14.22%	14.30%
3.82% to 7.45%	674	47.94%	62.23%
7.45% to 11.07%	329	23.40%	85.63%
11.07% to 14.69%	115	8.18%	93.81%
14.69% to 18.31%	40	2.84%	96.66%
18.31% to 21.94%	21	1.49%	98.15%
Greater than 21.94%	26	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.62%	12.28%	87.34%	68.27%
±2σ	-2.21%	17.11%	96.02%	95.45%
±3σ	-7.04%	21.94%	98.15%	99.73%

Descriptive Statistics

Mean	7.446%
Standard Error	0.129%
Median	6.130%
Mode	5.263%
Standard Deviation	4.830%
Sample Variance	23.326%
Kurtosis	20.16
Skewness	3.23
Range	63.163%
Minimum	0.102%
Maximum	63.265%
Count	1406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.446%	1406	100.00%	7.446%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.56. Further, an Excess Kurtosis of 4.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.59%	14	1.00%	1.00%
-14.59% to -10.86%	13	0.92%	1.92%
-10.86% to -7.14%	50	3.56%	5.48%
-7.14% to -3.41%	164	11.66%	17.14%
-3.41% to 0.32%	444	31.58%	48.72%
0.32% to 4.04%	465	33.07%	81.79%
4.04% to 7.77%	186	13.23%	95.02%
7.77% to 11.49%	44	3.13%	98.15%
11.49% to 15.22%	20	1.42%	99.57%
Greater than 15.22%	6	0.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.65%	5.28%	76.32%	68.27%
±2σ	-9.62%	10.25%	94.67%	95.45%
±3σ	-14.59%	15.22%	98.58%	99.73%

Descriptive Statistics

Mean	0.315%
Standard Error	0.132%
Median	0.404%
Mode	0.000%
Standard Deviation	4.968%
Sample Variance	24.684%
Kurtosis	4.05
Skewness	-0.56
Range	54.236%
Minimum	-32.973%
Maximum	21.263%
Count	1406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.602%	755	53.70%	1.934%
Negative	-3.625%	628	44.67%	-1.619%
Zero	0.000%	23	1.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.81. Further, an Excess Kurtosis of 16.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.70%	1	0.34%	0.34%
-50.70% to -37.75%	1	0.34%	0.68%
-37.75% to -24.79%	2	0.68%	1.37%
-24.79% to -11.84%	35	11.99%	13.36%
-11.84% to 1.12%	136	46.58%	59.93%
1.12% to 14.07%	77	26.37%	86.30%
14.07% to 27.03%	27	9.25%	95.55%
27.03% to 39.98%	6	2.05%	97.60%
39.98% to 52.94%	2	0.68%	98.29%
Greater than 52.94%	5	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.16%	18.39%	82.88%	68.27%
±2σ	-33.43%	35.67%	96.23%	95.45%
±3σ	-50.70%	52.94%	97.95%	99.73%

Descriptive Statistics

Mean	1.118%
Standard Error	1.011%
Median	-1.009%
Mode	-56.632%
Standard Deviation	17.274%
Sample Variance	298.401%
Kurtosis	16.76
Skewness	2.81
Range	183.905%
Minimum	-56.632%
Maximum	127.273%
Count	292

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.873%	131	44.86%	5.775%
Negative	-8.498%	160	54.80%	-4.656%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.72%
12	1 Quarter	12.95%
52	1 Year	19.36%
156	3 Years	16.59%
260	5 Years	17.25%
520	10 Years	19.49%
1,040	20 Years	19.49%
2,600	50 Years	19.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.22. Further, an Excess Kurtosis of 25.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.36%	0	0.00%	0.00%
-34.36% to -20.39%	0	0.00%	0.00%
-20.39% to -6.42%	0	0.00%	0.00%
-6.42% to 7.55%	14	4.78%	4.78%
7.55% to 21.52%	177	60.41%	65.19%
21.52% to 35.50%	72	24.57%	89.76%
35.50% to 49.47%	15	5.12%	94.88%
49.47% to 63.44%	7	2.39%	97.27%
63.44% to 77.41%	3	1.02%	98.29%
Greater than 77.41%	5	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.90%	40.15%	90.44%	68.27%
±2σ	-15.73%	58.78%	96.59%	95.45%
±3σ	-34.36%	77.41%	98.29%	99.73%

Descriptive Statistics

Mean	21.525%
Standard Error	1.088%
Median	16.699%
Mode	10.638%
Standard Deviation	18.628%
Sample Variance	346.989%
Kurtosis	25.07
Skewness	4.22
Range	159.593%
Minimum	0.508%
Maximum	160.101%
Count	293

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.525%	293	100.00%	21.525%
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 1.81. Further, an Excess Kurtosis of 17.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.91%	2	0.68%	0.68%
-43.91% to -32.62%	3	1.02%	1.71%
-32.62% to -21.32%	6	2.05%	3.75%
-21.32% to -10.03%	32	10.92%	14.68%
-10.03% to 1.26%	108	36.86%	51.54%
1.26% to 12.55%	99	33.79%	85.32%
12.55% to 23.85%	31	10.58%	95.90%
23.85% to 35.14%	9	3.07%	98.98%
35.14% to 46.43%	1	0.34%	99.32%
Greater than 46.43%	2	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.80%	16.32%	80.55%	68.27%
±2σ	-28.85%	31.38%	96.25%	95.45%
±3σ	-43.91%	46.43%	98.63%	99.73%

Descriptive Statistics

Mean	1.261%
Standard Error	0.880%
Median	0.870%
Mode	-7.143%
Standard Deviation	15.057%
Sample Variance	226.705%
Kurtosis	17.67
Skewness	1.81
Range	182.793%
Minimum	-55.911%
Maximum	126.882%
Count	293

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.520%	153	52.22%	5.493%
Negative	-8.921%	139	47.44%	-4.232%
Zero	0.000%	1	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.29. Further, an Excess Kurtosis of 25.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -131.37%	0	0.00%	0.00%
-131.37% to -97.22%	0	0.00%	0.00%
-97.22% to -63.08%	0	0.00%	0.00%
-63.08% to -28.93%	6	8.96%	8.96%
-28.93% to 5.22%	40	59.70%	68.66%
5.22% to 39.37%	13	19.40%	88.06%
39.37% to 73.52%	6	8.96%	97.01%
73.52% to 107.67%	1	1.49%	98.51%
107.67% to 141.81%	0	0.00%	98.51%
Greater than 141.81%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-40.31%	50.75%	88.06%	68.27%
±2σ	-85.84%	96.28%	98.51%	95.45%
±3σ	-131.37%	141.81%	98.51%	99.73%

Descriptive Statistics

Mean	5.221%
Standard Error	5.563%
Median	-3.972%
Mode	-48.194%
Standard Deviation	45.531%
Sample Variance	2073.110%
Kurtosis	25.82
Skewness	4.29
Range	346.499%
Minimum	-48.194%
Maximum	298.305%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.312%	26	38.81%	14.867%
Negative	-15.764%	41	61.19%	-9.647%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.20%
12	1 Year	49.21%
36	3 Years	37.27%
60	5 Years	37.47%
120	10 Years	48.07%
240	20 Years	48.07%
600	50 Years	48.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.91. Further, an Excess Kurtosis of 17.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -122.85%	0	0.00%	0.00%
-122.85% to -77.96%	0	0.00%	0.00%
-77.96% to -33.08%	0	0.00%	0.00%
-33.08% to 11.81%	2	2.94%	2.94%
11.81% to 56.69%	43	63.24%	66.18%
56.69% to 101.58%	19	27.94%	94.12%
101.58% to 146.46%	1	1.47%	95.59%
146.46% to 191.35%	1	1.47%	97.06%
191.35% to 236.23%	0	0.00%	97.06%
Greater than 236.23%	2	2.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.15%	116.54%	94.12%	68.27%
±2σ	-63.00%	176.38%	97.06%	95.45%
±3σ	-122.85%	236.23%	97.06%	99.73%

Descriptive Statistics

Mean	56.692%
Standard Error	7.257%
Median	39.471%
Mode	2.156%
Standard Deviation	59.846%
Sample Variance	3581.592%
Kurtosis	17.54
Skewness	3.91
Range	361.449%
Minimum	2.156%
Maximum	363.605%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	56.692%	68	100.00%	56.692%
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 -0.15. Further, an Excess Kurtosis of 0.70 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -76.36%	0	0.00%	0.00%
-76.36% to -56.24%	1	1.47%	1.47%
-56.24% to -36.12%	5	7.35%	8.82%
-36.12% to -16.00%	9	13.24%	22.06%
-16.00% to 4.12%	20	29.41%	51.47%
4.12% to 24.23%	17	25.00%	76.47%
24.23% to 44.35%	13	19.12%	95.59%
44.35% to 64.47%	2	2.94%	98.53%
64.47% to 84.59%	1	1.47%	100.00%
Greater than 84.59%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.71%	30.94%	70.59%	68.27%
±2σ	-49.53%	57.77%	95.59%	95.45%
±3σ	-76.36%	84.59%	100.00%	99.73%

Descriptive Statistics

Mean	4.115%
Standard Error	3.253%
Median	3.748%
Mode	-74.617%
Standard Deviation	26.825%
Sample Variance	719.602%
Kurtosis	0.70
Skewness	-0.15
Range	155.569%
Minimum	-74.617%
Maximum	80.952%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.071%	40	58.82%	12.395%
Negative	-20.852%	27	39.71%	-8.279%
Zero	0.000%	1	1.47%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.21. Further, an Excess Kurtosis of 5.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -213.44%	0	0.00%	0.00%
-213.44% to -156.68%	0	0.00%	0.00%
-156.68% to -99.92%	0	0.00%	0.00%
-99.92% to -43.15%	2	9.09%	9.09%
-43.15% to 13.61%	13	59.09%	68.18%
13.61% to 70.37%	3	13.64%	81.82%
70.37% to 127.14%	3	13.64%	95.45%
127.14% to 183.90%	0	0.00%	95.45%
183.90% to 240.66%	0	0.00%	95.45%
Greater than 240.66%	1	4.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-62.08%	89.30%	81.82%	68.27%
±2σ	-137.76%	164.98%	95.45%	95.45%
±3σ	-213.44%	240.67%	95.45%	99.73%

Descriptive Statistics

Mean	13.610%
Standard Error	16.136%
Median	-17.112%
Mode	-60.781%
Standard Deviation	75.685%
Sample Variance	5728.201%
Kurtosis	5.63
Skewness	2.21
Range	331.544%
Minimum	-60.781%
Maximum	270.763%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	74.866%	9	40.91%	30.627%
Negative	-28.797%	13	59.09%	-17.016%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	128.98%
12	3 Years	87.14%
20	5 Years	75.49%
40	10 Years	119.04%
80	20 Years	119.04%
200	50 Years	119.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.12. Further, an Excess Kurtosis of 18.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -453.62%	0	0.00%	0.00%
-453.62% to -303.08%	0	0.00%	0.00%
-303.08% to -152.55%	0	0.00%	0.00%
-152.55% to -2.01%	0	0.00%	0.00%
-2.01% to 148.52%	17	73.91%	73.91%
148.52% to 299.06%	5	21.74%	95.65%
299.06% to 449.59%	0	0.00%	95.65%
449.59% to 600.12%	0	0.00%	95.65%
600.12% to 750.66%	0	0.00%	95.65%
Greater than 750.66%	1	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-52.19%	349.23%	95.65%	68.27%
±2σ	-252.90%	549.94%	95.65%	95.45%
±3σ	-453.62%	750.66%	95.65%	99.73%

Descriptive Statistics

Mean	148.521%
Standard Error	41.851%
Median	100.827%
Mode	38.386%
Standard Deviation	200.712%
Sample Variance	40285.434%
Kurtosis	18.29
Skewness	4.12
Range	986.444%
Minimum	38.386%
Maximum	1024.830%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	148.521%	23	100.00%	148.521%
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 0.65. Further, an Excess Kurtosis of 0.97 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -140.68%	0	0.00%	0.00%
-140.68% to -102.15%	0	0.00%	0.00%
-102.15% to -63.63%	1	4.35%	4.35%
-63.63% to -25.11%	3	13.04%	17.39%
-25.11% to 13.42%	7	30.43%	47.83%
13.42% to 51.94%	8	34.78%	82.61%
51.94% to 90.46%	2	8.70%	91.30%
90.46% to 128.99%	1	4.35%	95.65%
128.99% to 167.51%	1	4.35%	100.00%
Greater than 167.51%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-37.95%	64.78%	69.57%	68.27%
±2σ	-89.31%	116.15%	95.65%	95.45%
±3σ	-140.68%	167.51%	100.00%	99.73%

Descriptive Statistics

Mean	13.417%
Standard Error	10.710%
Median	20.963%
Mode	-72.731%
Standard Deviation	51.365%
Sample Variance	2638.372%
Kurtosis	0.97
Skewness	0.65
Range	220.241%
Minimum	-72.731%
Maximum	147.510%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.994%	15	65.22%	26.735%
Negative	-38.292%	8	34.78%	-13.319%
Zero	0.000%	0	0.00%	0.000%

QS Deep Analytical Report