ROKU - 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	4.67%	3.25%	3.77%	5.55%	3.19%	3.26%	86.26	91.95	83.55	94.93
Weekly	11.64%	11.85%	10.70%	13.31%	7.03%	7.17%	83.01	95.55	77.38	102.51
Monthly	23.75%	22.63%	20.89%	28.60%	14.63%	14.93%	76.94	103.10	66.46	119.34
Quarterly	37.61%	38.36%	35.32%	49.76%	25.35%	25.86%	69.12	114.75	53.64	147.86
Annual	—	—	—	—	50.70%	51.72%	53.64	147.86	32.31	245.49
Option Time Horizon	—	—	—	—	19.50%	19.89%	73.28	108.24	60.30	131.54

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $89.06 | Strike (K): $90.00 (first OTM call ≥ spot) | Observed Mid-Price: $6.7000 (Bid $6.4000 / Ask $7.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 50.70% (CRR binomial tree, American, n=20 steps) | BS IV: 50.60% (European Black-Scholes) | Yahoo IV (Annual): 51.72% → 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 1.27. Further, an Excess Kurtosis of 14.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.85%	13	0.62%	0.62%
-13.85% to -10.35%	16	0.76%	1.38%
-10.35% to -6.84%	59	2.80%	4.17%
-6.84% to -3.34%	251	11.90%	16.07%
-3.34% to 0.17%	763	36.18%	52.25%
0.17% to 3.67%	677	32.10%	84.35%
3.67% to 7.18%	228	10.81%	95.16%
7.18% to 10.68%	60	2.84%	98.01%
10.68% to 14.19%	27	1.28%	99.29%
Greater than 14.19%	15	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.50%	4.84%	79.61%	68.27%
±2σ	-9.18%	9.52%	95.64%	95.45%
±3σ	-13.85%	14.19%	98.67%	99.73%

Descriptive Statistics

Mean	0.169%
Standard Error	0.102%
Median	0.010%
Mode	0.000%
Standard Deviation	4.673%
Sample Variance	21.839%
Kurtosis	14.56
Skewness	1.27
Range	78.746%
Minimum	-23.810%
Maximum	54.936%
Count	2109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.295%	1055	50.02%	1.648%
Negative	-2.970%	1050	49.79%	-1.479%
Zero	0.000%	4	0.19%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.85%
20	1 Month	5.35%
60	1 Quarter	4.43%
250	1 Year	4.76%
750	3 Years	4.83%
1,250	5 Years	5.55%
2,500	10 Years	5.88%
5,000	20 Years	5.88%
12,500	50 Years	5.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.46. Further, an Excess Kurtosis of 26.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.11%	0	0.00%	0.00%
-4.11% to -1.67%	0	0.00%	0.00%
-1.67% to 0.77%	0	0.00%	0.00%
0.77% to 3.21%	359	17.01%	17.01%
3.21% to 5.65%	947	44.88%	61.90%
5.65% to 8.09%	487	23.08%	84.98%
8.09% to 10.53%	190	9.00%	93.98%
10.53% to 12.97%	67	3.18%	97.16%
12.97% to 15.41%	27	1.28%	98.44%
Greater than 15.41%	33	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.39%	8.90%	84.55%	68.27%
±2σ	-0.86%	12.15%	96.16%	95.45%
±3σ	-4.11%	15.41%	98.44%	99.73%

Descriptive Statistics

Mean	5.648%
Standard Error	0.071%
Median	4.885%
Mode	4.388%
Standard Deviation	3.253%
Sample Variance	10.580%
Kurtosis	26.10
Skewness	3.46
Range	48.159%
Minimum	1.047%
Maximum	49.206%
Count	2110

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.648%	2110	100.00%	5.648%
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 -0.33. Further, an Excess Kurtosis of 5.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.27%	17	0.81%	0.81%
-11.27% to -8.44%	21	1.00%	1.80%
-8.44% to -5.61%	68	3.22%	5.02%
-5.61% to -2.78%	275	13.03%	18.06%
-2.78% to 0.05%	663	31.42%	49.48%
0.05% to 2.88%	672	31.85%	81.33%
2.88% to 5.70%	275	13.03%	94.36%
5.70% to 8.53%	93	4.41%	98.77%
8.53% to 11.36%	19	0.90%	99.67%
Greater than 11.36%	7	0.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.72%	3.82%	74.93%	68.27%
±2σ	-7.49%	7.59%	95.12%	95.45%
±3σ	-11.26%	11.36%	98.86%	99.73%

Descriptive Statistics

Mean	0.048%
Standard Error	0.082%
Median	0.092%
Mode	0.000%
Standard Deviation	3.771%
Sample Variance	14.222%
Kurtosis	5.44
Skewness	-0.33
Range	59.261%
Minimum	-32.766%
Maximum	26.495%
Count	2110

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.753%	1072	50.81%	1.399%
Negative	-2.761%	1032	48.91%	-1.350%
Zero	0.000%	6	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.82. Further, an Excess Kurtosis of 26.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.03%	0	0.00%	0.00%
-34.03% to -25.29%	5	1.14%	1.14%
-25.29% to -16.56%	7	1.60%	2.74%
-16.56% to -7.83%	69	15.75%	18.49%
-7.83% to 0.90%	150	34.25%	52.74%
0.90% to 9.63%	140	31.96%	84.70%
9.63% to 18.36%	49	11.19%	95.89%
18.36% to 27.09%	10	2.28%	98.17%
27.09% to 35.83%	4	0.91%	99.09%
Greater than 35.83%	4	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.74%	12.54%	79.00%	68.27%
±2σ	-22.38%	24.18%	96.58%	95.45%
±3σ	-34.03%	35.83%	99.09%	99.73%

Descriptive Statistics

Mean	0.900%
Standard Error	0.556%
Median	0.272%
Mode	2.004%
Standard Deviation	11.642%
Sample Variance	135.526%
Kurtosis	26.16
Skewness	2.82
Range	154.518%
Minimum	-33.680%
Maximum	120.838%
Count	438

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.348%	226	51.60%	4.307%
Negative	-7.073%	211	48.17%	-3.407%
Zero	0.000%	1	0.23%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.59%
12	1 Quarter	9.93%
52	1 Year	11.08%
156	3 Years	11.43%
260	5 Years	13.31%
520	10 Years	14.29%
1,040	20 Years	14.29%
2,600	50 Years	14.29%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.16. Further, an Excess Kurtosis of 48.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.87%	0	0.00%	0.00%
-19.87% to -10.99%	0	0.00%	0.00%
-10.99% to -2.10%	0	0.00%	0.00%
-2.10% to 6.79%	43	9.79%	9.79%
6.79% to 15.68%	242	55.13%	64.92%
15.68% to 24.56%	101	23.01%	87.93%
24.56% to 33.45%	30	6.83%	94.76%
33.45% to 42.34%	9	2.05%	96.81%
42.34% to 51.23%	8	1.82%	98.63%
Greater than 51.23%	6	1.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.83%	27.53%	90.66%	68.27%
±2σ	-8.02%	39.38%	96.36%	95.45%
±3σ	-19.87%	51.23%	98.63%	99.73%

Descriptive Statistics

Mean	15.676%
Standard Error	0.566%
Median	12.520%
Mode	7.756%
Standard Deviation	11.850%
Sample Variance	140.429%
Kurtosis	48.44
Skewness	5.16
Range	151.783%
Minimum	4.076%
Maximum	155.859%
Count	439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.676%	439	100.00%	15.676%
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 0.32. Further, an Excess Kurtosis of 4.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.68%	3	0.68%	0.68%
-31.68% to -23.66%	4	0.91%	1.59%
-23.66% to -15.63%	13	2.96%	4.56%
-15.63% to -7.61%	60	13.67%	18.22%
-7.61% to 0.41%	152	34.62%	52.85%
0.41% to 8.43%	127	28.93%	81.78%
8.43% to 16.45%	58	13.21%	94.99%
16.45% to 24.48%	14	3.19%	98.18%
24.48% to 32.50%	4	0.91%	99.09%
Greater than 32.50%	4	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.29%	11.11%	75.40%	68.27%
±2σ	-20.98%	21.80%	95.44%	95.45%
±3σ	-31.68%	32.50%	98.41%	99.73%

Descriptive Statistics

Mean	0.410%
Standard Error	0.511%
Median	-0.233%
Mode	-14.688%
Standard Deviation	10.696%
Sample Variance	114.412%
Kurtosis	4.47
Skewness	0.32
Range	113.254%
Minimum	-54.952%
Maximum	58.302%
Count	439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.347%	212	48.29%	4.031%
Negative	-7.003%	227	51.71%	-3.621%
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 1.54. Further, an Excess Kurtosis of 4.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.69%	0	0.00%	0.00%
-67.69% to -49.87%	0	0.00%	0.00%
-49.87% to -32.06%	1	0.99%	0.99%
-32.06% to -14.25%	22	21.78%	22.77%
-14.25% to 3.56%	33	32.67%	55.45%
3.56% to 21.38%	30	29.70%	85.15%
21.38% to 39.19%	5	4.95%	90.10%
39.19% to 57.00%	8	7.92%	98.02%
57.00% to 74.81%	0	0.00%	98.02%
Greater than 74.81%	2	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.18%	27.32%	72.28%	68.27%
±2σ	-43.94%	51.06%	98.02%	95.45%
±3σ	-67.69%	74.81%	98.02%	99.73%

Descriptive Statistics

Mean	3.565%
Standard Error	2.363%
Median	1.658%
Mode	-32.770%
Standard Deviation	23.750%
Sample Variance	564.053%
Kurtosis	4.41
Skewness	1.54
Range	148.177%
Minimum	-32.770%
Maximum	115.407%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.363%	56	55.45%	10.182%
Negative	-14.849%	45	44.55%	-6.616%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	21.11%
12	1 Year	21.14%
36	3 Years	25.53%
60	5 Years	28.60%
120	10 Years	32.92%
240	20 Years	32.92%
600	50 Years	32.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.78. Further, an Excess Kurtosis of 13.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.27%	0	0.00%	0.00%
-28.27% to -11.30%	0	0.00%	0.00%
-11.30% to 5.67%	0	0.00%	0.00%
5.67% to 22.64%	14	13.73%	13.73%
22.64% to 39.61%	45	44.12%	57.84%
39.61% to 56.58%	25	24.51%	82.35%
56.58% to 73.55%	13	12.75%	95.10%
73.55% to 90.52%	3	2.94%	98.04%
90.52% to 107.48%	1	0.98%	99.02%
Greater than 107.48%	1	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.98%	62.23%	83.33%	68.27%
±2σ	-5.65%	84.86%	96.08%	95.45%
±3σ	-28.27%	107.48%	99.02%	99.73%

Descriptive Statistics

Mean	39.607%
Standard Error	2.240%
Median	34.208%
Mode	9.247%
Standard Deviation	22.626%
Sample Variance	511.958%
Kurtosis	13.62
Skewness	2.78
Range	169.833%
Minimum	9.247%
Maximum	179.080%
Count	102

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.607%	102	100.00%	39.607%
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 0.08. Further, an Excess Kurtosis of -0.10 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.90%	0	0.00%	0.00%
-61.90% to -46.23%	1	0.98%	0.98%
-46.23% to -30.57%	7	6.86%	7.84%
-30.57% to -14.90%	10	9.80%	17.65%
-14.90% to 0.76%	40	39.22%	56.86%
0.76% to 16.43%	22	21.57%	78.43%
16.43% to 32.09%	13	12.75%	91.18%
32.09% to 47.76%	8	7.84%	99.02%
47.76% to 63.42%	1	0.98%	100.00%
Greater than 63.42%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.12%	21.65%	69.61%	68.27%
±2σ	-41.01%	42.54%	96.08%	95.45%
±3σ	-61.90%	63.42%	100.00%	99.73%

Descriptive Statistics

Mean	0.762%
Standard Error	2.068%
Median	-1.948%
Mode	-53.440%
Standard Deviation	20.887%
Sample Variance	436.286%
Kurtosis	-0.10
Skewness	0.08
Range	101.691%
Minimum	-53.440%
Maximum	48.251%
Count	102

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.808%	46	45.10%	8.482%
Negative	-14.061%	56	54.90%	-7.720%
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 -0.19 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -102.36%	0	0.00%	0.00%
-102.36% to -74.16%	0	0.00%	0.00%
-74.16% to -45.95%	1	2.94%	2.94%
-45.95% to -17.74%	8	23.53%	26.47%
-17.74% to 10.47%	10	29.41%	55.88%
10.47% to 38.68%	7	20.59%	76.47%
38.68% to 66.89%	5	14.71%	91.18%
66.89% to 95.10%	2	5.88%	97.06%
95.10% to 123.31%	1	2.94%	100.00%
Greater than 123.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.14%	48.08%	70.59%	68.27%
±2σ	-64.75%	85.70%	94.12%	95.45%
±3σ	-102.36%	123.31%	100.00%	99.73%

Descriptive Statistics

Mean	10.472%
Standard Error	6.450%
Median	2.242%
Mode	-46.195%
Standard Deviation	37.612%
Sample Variance	1414.670%
Kurtosis	-0.19
Skewness	0.60
Range	145.508%
Minimum	-46.195%
Maximum	99.313%
Count	34

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.690%	19	55.88%	20.503%
Negative	-22.737%	15	44.12%	-10.031%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	35.07%
12	3 Years	48.90%
20	5 Years	49.76%
40	10 Years	60.77%
80	20 Years	60.77%
200	50 Years	60.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.53. Further, an Excess Kurtosis of 3.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.29%	0	0.00%	0.00%
-35.29% to -6.52%	0	0.00%	0.00%
-6.52% to 22.25%	0	0.00%	0.00%
22.25% to 51.02%	8	22.86%	22.86%
51.02% to 79.78%	12	34.29%	57.14%
79.78% to 108.55%	9	25.71%	82.86%
108.55% to 137.32%	4	11.43%	94.29%
137.32% to 166.09%	1	2.86%	97.14%
166.09% to 194.86%	0	0.00%	97.14%
Greater than 194.86%	1	2.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	41.43%	118.14%	74.29%	68.27%
±2σ	3.07%	156.50%	94.29%	95.45%
±3σ	-35.29%	194.86%	97.14%	99.73%

Descriptive Statistics

Mean	79.783%
Standard Error	6.484%
Median	77.897%
Mode	24.691%
Standard Deviation	38.358%
Sample Variance	1471.307%
Kurtosis	3.87
Skewness	1.53
Range	192.102%
Minimum	24.691%
Maximum	216.793%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	79.783%	35	100.00%	79.783%
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 0.78. Further, an Excess Kurtosis of 0.02 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -104.91%	0	0.00%	0.00%
-104.91% to -78.42%	0	0.00%	0.00%
-78.42% to -51.93%	0	0.00%	0.00%
-51.93% to -25.44%	8	22.86%	22.86%
-25.44% to 1.05%	11	31.43%	54.29%
1.05% to 27.54%	10	28.57%	82.86%
27.54% to 54.03%	2	5.71%	88.57%
54.03% to 80.52%	2	5.71%	94.29%
80.52% to 107.01%	2	5.71%	100.00%
Greater than 107.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.27%	36.37%	71.43%	68.27%
±2σ	-69.59%	71.69%	94.29%	95.45%
±3σ	-104.91%	107.01%	100.00%	99.73%

Descriptive Statistics

Mean	1.053%
Standard Error	5.970%
Median	-1.598%
Mode	-49.680%
Standard Deviation	35.320%
Sample Variance	1247.476%
Kurtosis	0.02
Skewness	0.78
Range	136.503%
Minimum	-49.680%
Maximum	86.823%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.355%	17	48.57%	14.744%
Negative	-26.620%	18	51.43%	-13.690%
Zero	0.000%	0	0.00%	0.000%

ROKU Deep Analytical Report