NOW - 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	2.57%	1.91%	2.16%	3.29%	3.22%	3.28%	100.97	107.68	97.77	111.20
Weekly	5.37%	4.79%	5.38%	7.97%	7.09%	7.21%	97.14	111.93	90.49	120.15
Monthly	9.45%	8.40%	9.48%	16.31%	14.75%	15.01%	89.97	120.84	77.63	140.05
Quarterly	15.51%	14.48%	15.68%	27.25%	25.55%	26.00%	80.76	134.63	62.55	173.82
Annual	—	—	—	—	51.10%	51.99%	62.55	173.82	37.52	289.76
Option Time Horizon	—	—	—	—	19.66%	20.00%	85.66	126.92	70.38	154.49

Calculation Notes: Computed at 2026-02-22T14:17 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $104.27 | Strike (K): $105.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.0500 (Bid $7.9000 / Ask $8.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 51.10% (CRR binomial tree, American, n=20 steps) | BS IV: 50.83% (European Black-Scholes) | Yahoo IV (Annual): 51.99% → 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 Fairly Symmetrical with a Skewness factor of 0.12. Further, an Excess Kurtosis of 4.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.58%	27	0.79%	0.79%
-7.58% to -5.65%	36	1.05%	1.84%
-5.65% to -3.73%	143	4.17%	6.01%
-3.73% to -1.80%	375	10.94%	16.94%
-1.80% to 0.12%	1086	31.67%	48.61%
0.12% to 2.05%	1199	34.97%	83.58%
2.05% to 3.97%	391	11.40%	94.98%
3.97% to 5.90%	104	3.03%	98.02%
5.90% to 7.82%	40	1.17%	99.18%
Greater than 7.82%	28	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.45%	2.69%	77.40%	68.27%
±2σ	-5.01%	5.26%	94.93%	95.45%
±3σ	-7.58%	7.82%	98.40%	99.73%

Descriptive Statistics

Mean	0.122%
Standard Error	0.044%
Median	0.177%
Mode	-1.606%
Standard Deviation	2.567%
Sample Variance	6.590%
Kurtosis	4.46
Skewness	0.12
Range	31.144%
Minimum	-15.656%
Maximum	15.488%
Count	3429

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.788%	1850	53.95%	0.965%
Negative	-1.834%	1575	45.93%	-0.842%
Zero	0.000%	4	0.12%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.34%
20	1 Month	5.39%
60	1 Quarter	3.77%
250	1 Year	3.30%
750	3 Years	2.89%
1,250	5 Years	3.29%
2,500	10 Years	3.22%
5,000	20 Years	3.39%
12,500	50 Years	3.39%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.37. Further, an Excess Kurtosis of 10.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.52%	0	0.00%	0.00%
-2.52% to -1.09%	0	0.00%	0.00%
-1.09% to 0.35%	0	0.00%	0.00%
0.35% to 1.78%	640	18.66%	18.66%
1.78% to 3.21%	1543	44.99%	63.64%
3.21% to 4.64%	691	20.15%	83.79%
4.64% to 6.08%	289	8.43%	92.22%
6.08% to 7.51%	140	4.08%	96.30%
7.51% to 8.94%	67	1.95%	98.25%
Greater than 8.94%	60	1.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.30%	5.12%	82.97%	68.27%
±2σ	-0.61%	7.03%	95.25%	95.45%
±3σ	-2.52%	8.94%	98.25%	99.73%

Descriptive Statistics

Mean	3.211%
Standard Error	0.033%
Median	2.665%
Mode	1.695%
Standard Deviation	1.910%
Sample Variance	3.649%
Kurtosis	10.46
Skewness	2.37
Range	21.778%
Minimum	0.625%
Maximum	22.403%
Count	3430

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.211%	3430	100.00%	3.211%
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 3.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.50%	15	0.44%	0.44%
-6.50% to -4.87%	43	1.25%	1.69%
-4.87% to -3.25%	112	3.27%	4.96%
-3.25% to -1.63%	447	13.03%	17.99%
-1.63% to -0.01%	1184	34.52%	52.51%
-0.01% to 1.61%	1030	30.03%	82.54%
1.61% to 3.23%	382	11.14%	93.67%
3.23% to 4.86%	132	3.85%	97.52%
4.86% to 6.48%	55	1.60%	99.13%
Greater than 6.48%	30	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.17%	2.15%	76.01%	68.27%
±2σ	-4.33%	4.31%	94.17%	95.45%
±3σ	-6.50%	6.48%	98.69%	99.73%

Descriptive Statistics

Mean	-0.009%
Standard Error	0.037%
Median	-0.122%
Mode	-0.398%
Standard Deviation	2.162%
Sample Variance	4.674%
Kurtosis	3.05
Skewness	0.33
Range	25.793%
Minimum	-12.222%
Maximum	13.571%
Count	3430

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.651%	1617	47.14%	0.778%
Negative	-1.492%	1810	52.77%	-0.787%
Zero	0.000%	3	0.09%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.14. Further, an Excess Kurtosis of 1.63 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.54%	3	0.42%	0.42%
-15.54% to -11.51%	13	1.83%	2.25%
-11.51% to -7.48%	32	4.49%	6.74%
-7.48% to -3.45%	80	11.24%	17.98%
-3.45% to 0.57%	218	30.62%	48.60%
0.57% to 4.60%	233	32.72%	81.32%
4.60% to 8.63%	92	12.92%	94.24%
8.63% to 12.66%	31	4.35%	98.60%
12.66% to 16.68%	8	1.12%	99.72%
Greater than 16.68%	2	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.80%	5.94%	74.44%	68.27%
±2σ	-10.17%	11.31%	93.54%	95.45%
±3σ	-15.54%	16.68%	99.30%	99.73%

Descriptive Statistics

Mean	0.574%
Standard Error	0.201%
Median	0.768%
Mode	-2.535%
Standard Deviation	5.370%
Sample Variance	28.835%
Kurtosis	1.63
Skewness	-0.14
Range	47.917%
Minimum	-23.919%
Maximum	23.998%
Count	712

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.062%	404	56.74%	2.305%
Negative	-4.002%	308	43.26%	-1.731%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.63%
12	1 Quarter	9.77%
52	1 Year	8.04%
156	3 Years	6.98%
260	5 Years	7.97%
520	10 Years	7.63%
1,040	20 Years	8.02%
2,600	50 Years	8.02%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.80. Further, an Excess Kurtosis of 4.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.00%	0	0.00%	0.00%
-6.00% to -2.40%	0	0.00%	0.00%
-2.40% to 1.19%	0	0.00%	0.00%
1.19% to 4.78%	140	19.64%	19.64%
4.78% to 8.37%	320	44.88%	64.52%
8.37% to 11.96%	126	17.67%	82.19%
11.96% to 15.55%	69	9.68%	91.87%
15.55% to 19.15%	28	3.93%	95.79%
19.15% to 22.74%	18	2.52%	98.32%
Greater than 22.74%	12	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.58%	13.16%	80.36%	68.27%
±2σ	-1.21%	17.95%	94.11%	95.45%
±3σ	-6.00%	22.74%	98.32%	99.73%

Descriptive Statistics

Mean	8.371%
Standard Error	0.179%
Median	6.958%
Mode	2.844%
Standard Deviation	4.789%
Sample Variance	22.937%
Kurtosis	4.32
Skewness	1.80
Range	33.770%
Minimum	1.812%
Maximum	35.582%
Count	713

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.371%	713	100.00%	8.371%
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 0.74. Further, an Excess Kurtosis of 2.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.30%	2	0.28%	0.28%
-16.30% to -12.27%	5	0.70%	0.98%
-12.27% to -8.24%	28	3.93%	4.91%
-8.24% to -4.20%	88	12.34%	17.25%
-4.20% to -0.17%	269	37.73%	54.98%
-0.17% to 3.86%	199	27.91%	82.89%
3.86% to 7.89%	74	10.38%	93.27%
7.89% to 11.93%	27	3.79%	97.05%
11.93% to 15.96%	15	2.10%	99.16%
Greater than 15.96%	6	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.55%	5.21%	75.74%	68.27%
±2σ	-10.92%	10.58%	93.55%	95.45%
±3σ	-16.30%	15.96%	98.88%	99.73%

Descriptive Statistics

Mean	-0.171%
Standard Error	0.201%
Median	-0.702%
Mode	-1.140%
Standard Deviation	5.377%
Sample Variance	28.917%
Kurtosis	2.66
Skewness	0.74
Range	49.047%
Minimum	-18.627%
Maximum	30.420%
Count	713

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.410%	306	42.92%	1.893%
Negative	-3.632%	405	56.80%	-2.063%
Zero	0.000%	2	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.11. Further, an Excess Kurtosis of 0.24 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.03%	1	0.61%	0.61%
-26.03% to -18.94%	2	1.22%	1.83%
-18.94% to -11.85%	6	3.66%	5.49%
-11.85% to -4.77%	28	17.07%	22.56%
-4.77% to 2.32%	45	27.44%	50.00%
2.32% to 9.41%	45	27.44%	77.44%
9.41% to 16.50%	23	14.02%	91.46%
16.50% to 23.58%	13	7.93%	99.39%
23.58% to 30.67%	1	0.61%	100.00%
Greater than 30.67%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.13%	11.77%	70.73%	68.27%
±2σ	-16.58%	21.22%	95.12%	95.45%
±3σ	-26.03%	30.67%	99.39%	99.73%

Descriptive Statistics

Mean	2.321%
Standard Error	0.738%
Median	2.181%
Mode	-28.131%
Standard Deviation	9.449%
Sample Variance	89.281%
Kurtosis	0.24
Skewness	-0.11
Range	52.504%
Minimum	-28.131%
Maximum	24.373%
Count	164

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.350%	98	59.76%	4.990%
Negative	-6.629%	66	40.24%	-2.668%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.33%
12	1 Year	15.73%
36	3 Years	14.92%
60	5 Years	16.31%
120	10 Years	15.81%
240	20 Years	16.67%
600	50 Years	16.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.34. Further, an Excess Kurtosis of 1.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.91%	0	0.00%	0.00%
-6.91% to -0.61%	0	0.00%	0.00%
-0.61% to 5.70%	0	0.00%	0.00%
5.70% to 12.00%	39	23.64%	23.64%
12.00% to 18.30%	62	37.58%	61.21%
18.30% to 24.61%	36	21.82%	83.03%
24.61% to 30.91%	14	8.48%	91.52%
30.91% to 37.22%	9	5.45%	96.97%
37.22% to 43.52%	1	0.61%	97.58%
Greater than 43.52%	4	2.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.90%	26.71%	74.55%	68.27%
±2σ	1.49%	35.11%	94.55%	95.45%
±3σ	-6.91%	43.52%	97.58%	99.73%

Descriptive Statistics

Mean	18.304%
Standard Error	0.654%
Median	15.914%
Mode	20.407%
Standard Deviation	8.405%
Sample Variance	70.643%
Kurtosis	1.79
Skewness	1.34
Range	41.629%
Minimum	6.923%
Maximum	48.552%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.304%	165	100.00%	18.304%
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 0.67. Further, an Excess Kurtosis of 1.46 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.79%	0	0.00%	0.00%
-29.79% to -22.68%	0	0.00%	0.00%
-22.68% to -15.56%	9	5.45%	5.45%
-15.56% to -8.45%	28	16.97%	22.42%
-8.45% to -1.34%	49	29.70%	52.12%
-1.34% to 5.77%	48	29.09%	81.21%
5.77% to 12.89%	20	12.12%	93.33%
12.89% to 20.00%	7	4.24%	97.58%
20.00% to 27.11%	2	1.21%	98.79%
Greater than 27.11%	2	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.82%	8.14%	72.12%	68.27%
±2σ	-20.30%	17.63%	96.36%	95.45%
±3σ	-29.79%	27.11%	98.79%	99.73%

Descriptive Statistics

Mean	-1.339%
Standard Error	0.738%
Median	-1.798%
Mode	-21.946%
Standard Deviation	9.483%
Sample Variance	89.925%
Kurtosis	1.46
Skewness	0.67
Range	58.548%
Minimum	-21.946%
Maximum	36.602%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.104%	71	43.03%	3.057%
Negative	-7.800%	93	56.36%	-4.396%
Zero	0.000%	1	0.61%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.18. Further, an Excess Kurtosis of 0.67 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.85%	0	0.00%	0.00%
-39.85% to -28.21%	1	1.82%	1.82%
-28.21% to -16.57%	3	5.45%	7.27%
-16.57% to -4.94%	9	16.36%	23.64%
-4.94% to 6.70%	14	25.45%	49.09%
6.70% to 18.33%	19	34.55%	83.64%
18.33% to 29.97%	6	10.91%	94.55%
29.97% to 41.60%	2	3.64%	98.18%
41.60% to 53.24%	1	1.82%	100.00%
Greater than 53.24%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.82%	22.21%	70.91%	68.27%
±2σ	-24.33%	37.72%	96.36%	95.45%
±3σ	-39.85%	53.24%	100.00%	99.73%

Descriptive Statistics

Mean	6.696%
Standard Error	2.092%
Median	7.316%
Mode	-36.358%
Standard Deviation	15.514%
Sample Variance	240.685%
Kurtosis	0.67
Skewness	-0.18
Range	84.121%
Minimum	-36.358%
Maximum	47.763%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.219%	39	70.91%	10.083%
Negative	-11.643%	16	29.09%	-3.387%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	21.37%
12	3 Years	26.37%
20	5 Years	27.25%
40	10 Years	26.96%
80	20 Years	29.37%
200	50 Years	29.37%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.84. Further, an Excess Kurtosis of -0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.36%	0	0.00%	0.00%
-9.36% to 1.50%	0	0.00%	0.00%
1.50% to 12.36%	0	0.00%	0.00%
12.36% to 23.22%	11	19.64%	19.64%
23.22% to 34.09%	23	41.07%	60.71%
34.09% to 44.95%	10	17.86%	78.57%
44.95% to 55.81%	6	10.71%	89.29%
55.81% to 66.67%	4	7.14%	96.43%
66.67% to 77.53%	2	3.57%	100.00%
Greater than 77.53%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.60%	48.57%	67.86%	68.27%
±2σ	5.12%	63.05%	96.43%	95.45%
±3σ	-9.36%	77.53%	100.00%	99.73%

Descriptive Statistics

Mean	34.086%
Standard Error	1.935%
Median	30.138%
Mode	13.190%
Standard Deviation	14.483%
Sample Variance	209.765%
Kurtosis	-0.08
Skewness	0.84
Range	57.911%
Minimum	13.190%
Maximum	71.101%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.086%	56	100.00%	34.086%
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 1.39. Further, an Excess Kurtosis of 3.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.22%	0	0.00%	0.00%
-51.22% to -39.46%	0	0.00%	0.00%
-39.46% to -27.71%	1	1.79%	1.79%
-27.71% to -15.95%	7	12.50%	14.29%
-15.95% to -4.19%	24	42.86%	57.14%
-4.19% to 7.56%	14	25.00%	82.14%
7.56% to 19.32%	5	8.93%	91.07%
19.32% to 31.08%	3	5.36%	96.43%
31.08% to 42.83%	1	1.79%	98.21%
Greater than 42.83%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.87%	11.48%	76.79%	68.27%
±2σ	-35.54%	27.16%	94.64%	95.45%
±3σ	-51.22%	42.83%	98.21%	99.73%

Descriptive Statistics

Mean	-4.193%
Standard Error	2.095%
Median	-6.930%
Mode	-35.718%
Standard Deviation	15.675%
Sample Variance	245.691%
Kurtosis	3.59
Skewness	1.39
Range	93.335%
Minimum	-35.718%
Maximum	57.617%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.781%	15	26.79%	4.227%
Negative	-11.500%	41	73.21%	-8.420%
Zero	0.000%	0	0.00%	0.000%

NOW Deep Analytical Report