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%	3.30%	3.63%	3.65%	106.78	114.81	102.97	119.05
Weekly	5.39%	4.79%	5.40%	8.00%	7.98%	8.03%	102.22	119.92	94.38	129.89
Monthly	9.40%	8.38%	9.42%	16.35%	16.62%	16.72%	93.77	130.74	79.41	154.38
Quarterly	15.41%	14.44%	15.55%	27.46%	28.79%	28.97%	83.02	147.66	62.25	196.92
Annual	—	—	—	—	57.58%	57.93%	62.25	196.92	35.00	350.21
Option Time Horizon	—	—	—	—	21.73%	21.87%	89.09	137.60	71.69	171.00

Calculation Notes: Computed at 2026-03-23T16:32 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $110.72 | Strike (K): $112.00 (first OTM call ≥ spot) | Observed Mid-Price: $9.2500 (Bid $8.8000 / Ask $9.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 57.58% (CRR binomial tree, American, n=20 steps) | BS IV: 57.45% (European Black-Scholes) | Yahoo IV (Annual): 57.93% → 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 4.42 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	0.78%	0.78%
-7.58% to -5.66%	36	1.04%	1.83%
-5.66% to -3.73%	144	4.17%	6.00%
-3.73% to -1.80%	380	11.01%	17.01%
-1.80% to 0.12%	1089	31.57%	48.58%
0.12% to 2.05%	1209	35.04%	83.62%
2.05% to 3.98%	391	11.33%	94.96%
3.98% to 5.90%	106	3.07%	98.03%
5.90% to 7.83%	40	1.16%	99.19%
Greater than 7.83%	28	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.45%	2.69%	77.30%	68.27%
±2σ	-5.01%	5.26%	94.93%	95.45%
±3σ	-7.58%	7.83%	98.41%	99.73%

Descriptive Statistics

Mean	0.123%
Standard Error	0.044%
Median	0.177%
Mode	-1.606%
Standard Deviation	2.568%
Sample Variance	6.592%
Kurtosis	4.42
Skewness	0.12
Range	31.144%
Minimum	-15.656%
Maximum	15.488%
Count	3450

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.791%	1862	53.97%	0.967%
Negative	-1.836%	1584	45.91%	-0.843%
Zero	0.000%	4	0.12%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.76%
20	1 Month	4.57%
60	1 Quarter	4.33%
250	1 Year	3.35%
750	3 Years	2.93%
1,250	5 Years	3.30%
2,500	10 Years	3.24%
5,000	20 Years	3.40%
12,500	50 Years	3.40%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.36. Further, an Excess Kurtosis of 10.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.51%	0	0.00%	0.00%
-2.51% to -1.08%	0	0.00%	0.00%
-1.08% to 0.35%	0	0.00%	0.00%
0.35% to 1.79%	646	18.72%	18.72%
1.79% to 3.22%	1545	44.77%	63.49%
3.22% to 4.65%	699	20.25%	83.74%
4.65% to 6.08%	292	8.46%	92.21%
6.08% to 7.51%	142	4.11%	96.32%
7.51% to 8.95%	67	1.94%	98.26%
Greater than 8.95%	60	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.31%	5.13%	82.93%	68.27%
±2σ	-0.60%	7.04%	95.28%	95.45%
±3σ	-2.51%	8.95%	98.26%	99.73%

Descriptive Statistics

Mean	3.218%
Standard Error	0.032%
Median	2.679%
Mode	1.695%
Standard Deviation	1.909%
Sample Variance	3.643%
Kurtosis	10.39
Skewness	2.36
Range	21.778%
Minimum	0.625%
Maximum	22.403%
Count	3451

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.218%	3451	100.00%	3.218%
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 3.03 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	0.43%	0.43%
-6.50% to -4.88%	43	1.25%	1.68%
-4.88% to -3.26%	112	3.25%	4.93%
-3.26% to -1.64%	451	13.07%	17.99%
-1.64% to -0.01%	1187	34.40%	52.39%
-0.01% to 1.61%	1041	30.17%	82.56%
1.61% to 3.23%	383	11.10%	93.65%
3.23% to 4.85%	134	3.88%	97.54%
4.85% to 6.48%	55	1.59%	99.13%
Greater than 6.48%	30	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.18%	2.15%	75.86%	68.27%
±2σ	-4.34%	4.31%	94.18%	95.45%
±3σ	-6.50%	6.48%	98.70%	99.73%

Descriptive Statistics

Mean	-0.013%
Standard Error	0.037%
Median	-0.123%
Mode	-0.398%
Standard Deviation	2.163%
Sample Variance	4.678%
Kurtosis	3.03
Skewness	0.33
Range	25.793%
Minimum	-12.222%
Maximum	13.571%
Count	3451

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.651%	1626	47.12%	0.778%
Negative	-1.498%	1822	52.80%	-0.791%
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 1.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.59%	3	0.42%	0.42%
-15.59% to -11.54%	13	1.82%	2.23%
-11.54% to -7.50%	32	4.47%	6.70%
-7.50% to -3.46%	82	11.45%	18.16%
-3.46% to 0.58%	220	30.73%	48.88%
0.58% to 4.62%	232	32.40%	81.28%
4.62% to 8.67%	92	12.85%	94.13%
8.67% to 12.71%	32	4.47%	98.60%
12.71% to 16.75%	8	1.12%	99.72%
Greater than 16.75%	2	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.81%	5.97%	74.30%	68.27%
±2σ	-10.20%	11.36%	93.44%	95.45%
±3σ	-15.59%	16.75%	99.30%	99.73%

Descriptive Statistics

Mean	0.582%
Standard Error	0.201%
Median	0.768%
Mode	-2.535%
Standard Deviation	5.389%
Sample Variance	29.046%
Kurtosis	1.57
Skewness	-0.14
Range	47.917%
Minimum	-23.919%
Maximum	23.998%
Count	716

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.091%	406	56.70%	2.320%
Negative	-4.015%	310	43.30%	-1.738%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.39%
12	1 Quarter	11.33%
52	1 Year	8.28%
156	3 Years	7.10%
260	5 Years	8.00%
520	10 Years	7.67%
1,040	20 Years	8.05%
2,600	50 Years	8.05%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.79. Further, an Excess Kurtosis of 4.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.98%	0	0.00%	0.00%
-5.98% to -2.38%	0	0.00%	0.00%
-2.38% to 1.21%	0	0.00%	0.00%
1.21% to 4.80%	142	19.80%	19.80%
4.80% to 8.39%	318	44.35%	64.16%
8.39% to 11.99%	130	18.13%	82.29%
11.99% to 15.58%	68	9.48%	91.77%
15.58% to 19.18%	29	4.04%	95.82%
19.18% to 22.77%	19	2.65%	98.47%
Greater than 22.77%	11	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.60%	13.19%	80.20%	68.27%
±2σ	-1.19%	17.98%	94.28%	95.45%
±3σ	-5.98%	22.77%	98.47%	99.73%

Descriptive Statistics

Mean	8.395%
Standard Error	0.179%
Median	7.031%
Mode	2.844%
Standard Deviation	4.791%
Sample Variance	22.957%
Kurtosis	4.26
Skewness	1.79
Range	33.770%
Minimum	1.812%
Maximum	35.582%
Count	717

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.395%	717	100.00%	8.395%
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 0.72. Further, an Excess Kurtosis of 2.58 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.38%	2	0.28%	0.28%
-16.38% to -12.33%	5	0.70%	0.98%
-12.33% to -8.28%	29	4.04%	5.02%
-8.28% to -4.23%	88	12.27%	17.29%
-4.23% to -0.18%	270	37.66%	54.95%
-0.18% to 3.87%	200	27.89%	82.85%
3.87% to 7.92%	74	10.32%	93.17%
7.92% to 11.97%	29	4.04%	97.21%
11.97% to 16.02%	14	1.95%	99.16%
Greater than 16.02%	6	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.58%	5.22%	75.59%	68.27%
±2σ	-10.98%	10.62%	93.58%	95.45%
±3σ	-16.38%	16.02%	98.88%	99.73%

Descriptive Statistics

Mean	-0.179%
Standard Error	0.202%
Median	-0.702%
Mode	-1.140%
Standard Deviation	5.399%
Sample Variance	29.145%
Kurtosis	2.58
Skewness	0.72
Range	49.047%
Minimum	-18.627%
Maximum	30.420%
Count	717

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.422%	308	42.96%	1.900%
Negative	-3.662%	407	56.76%	-2.079%
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 0.27 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.84%	1	0.61%	0.61%
-25.84% to -18.80%	2	1.21%	1.82%
-18.80% to -11.75%	7	4.24%	6.06%
-11.75% to -4.70%	27	16.36%	22.42%
-4.70% to 2.35%	47	28.48%	50.91%
2.35% to 9.39%	44	26.67%	77.58%
9.39% to 16.44%	23	13.94%	91.52%
16.44% to 23.49%	12	7.27%	98.79%
23.49% to 30.53%	2	1.21%	100.00%
Greater than 30.53%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.05%	11.74%	70.91%	68.27%
±2σ	-16.45%	21.14%	95.15%	95.45%
±3σ	-25.84%	30.53%	99.39%	99.73%

Descriptive Statistics

Mean	2.346%
Standard Error	0.731%
Median	2.337%
Mode	-7.692%
Standard Deviation	9.396%
Sample Variance	88.288%
Kurtosis	0.27
Skewness	-0.11
Range	52.504%
Minimum	-28.131%
Maximum	24.373%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.297%	99	60.00%	4.978%
Negative	-6.581%	66	40.00%	-2.632%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.15%
12	1 Year	15.81%
36	3 Years	15.10%
60	5 Years	16.35%
120	10 Years	15.85%
240	20 Years	16.69%
600	50 Years	16.69%

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 1.81 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.83%	0	0.00%	0.00%
-6.83% to -0.54%	0	0.00%	0.00%
-0.54% to 5.75%	0	0.00%	0.00%
5.75% to 12.03%	41	24.70%	24.70%
12.03% to 18.32%	60	36.14%	60.84%
18.32% to 24.60%	37	22.29%	83.13%
24.60% to 30.89%	14	8.43%	91.57%
30.89% to 37.17%	9	5.42%	96.99%
37.17% to 43.46%	1	0.60%	97.59%
Greater than 43.46%	4	2.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.94%	26.70%	74.70%	68.27%
±2σ	1.55%	35.08%	93.98%	95.45%
±3σ	-6.83%	43.46%	97.59%	99.73%

Descriptive Statistics

Mean	18.317%
Standard Error	0.651%
Median	15.924%
Mode	20.407%
Standard Deviation	8.381%
Sample Variance	70.244%
Kurtosis	1.81
Skewness	1.34
Range	41.629%
Minimum	6.923%
Maximum	48.552%
Count	166

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.317%	166	100.00%	18.317%
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 0.68. Further, an Excess Kurtosis of 1.53 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.66%	0	0.00%	0.00%
-29.66% to -22.59%	0	0.00%	0.00%
-22.59% to -15.52%	10	6.02%	6.02%
-15.52% to -8.45%	27	16.27%	22.29%
-8.45% to -1.39%	50	30.12%	52.41%
-1.39% to 5.68%	48	28.92%	81.33%
5.68% to 12.75%	21	12.65%	93.98%
12.75% to 19.82%	6	3.61%	97.59%
19.82% to 26.89%	2	1.20%	98.80%
Greater than 26.89%	2	1.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.81%	8.04%	71.69%	68.27%
±2σ	-20.23%	17.46%	95.78%	95.45%
±3σ	-29.66%	26.89%	98.80%	99.73%

Descriptive Statistics

Mean	-1.385%
Standard Error	0.731%
Median	-1.820%
Mode	-21.946%
Standard Deviation	9.424%
Sample Variance	88.818%
Kurtosis	1.53
Skewness	0.68
Range	58.548%
Minimum	-21.946%
Maximum	36.602%
Count	166

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.048%	71	42.77%	3.015%
Negative	-7.769%	94	56.63%	-4.399%
Zero	0.000%	1	0.60%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.19. Further, an Excess Kurtosis of 0.76 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.41%	0	0.00%	0.00%
-39.41% to -27.86%	1	1.82%	1.82%
-27.86% to -16.30%	3	5.45%	7.27%
-16.30% to -4.75%	9	16.36%	23.64%
-4.75% to 6.81%	14	25.45%	49.09%
6.81% to 18.36%	19	34.55%	83.64%
18.36% to 29.92%	6	10.91%	94.55%
29.92% to 41.47%	2	3.64%	98.18%
41.47% to 53.03%	1	1.82%	100.00%
Greater than 53.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.60%	22.21%	72.73%	68.27%
±2σ	-24.01%	37.62%	96.36%	95.45%
±3σ	-39.41%	53.03%	100.00%	99.73%

Descriptive Statistics

Mean	6.807%
Standard Error	2.077%
Median	7.316%
Mode	-36.358%
Standard Deviation	15.407%
Sample Variance	237.379%
Kurtosis	0.76
Skewness	-0.19
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	-11.260%	16	29.09%	-3.276%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	22.42%
12	3 Years	26.72%
20	5 Years	27.46%
40	10 Years	27.07%
80	20 Years	29.45%
200	50 Years	29.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.83. Further, an Excess Kurtosis of -0.07 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.13%	0	0.00%	0.00%
-9.13% to 1.70%	0	0.00%	0.00%
1.70% to 12.52%	0	0.00%	0.00%
12.52% to 23.35%	13	23.21%	23.21%
23.35% to 34.18%	21	37.50%	60.71%
34.18% to 45.00%	10	17.86%	78.57%
45.00% to 55.83%	6	10.71%	89.29%
55.83% to 66.66%	4	7.14%	96.43%
66.66% to 77.48%	2	3.57%	100.00%
Greater than 77.48%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.74%	48.61%	67.86%	68.27%
±2σ	5.30%	63.05%	96.43%	95.45%
±3σ	-9.13%	77.48%	100.00%	99.73%

Descriptive Statistics

Mean	34.177%
Standard Error	1.929%
Median	30.138%
Mode	13.190%
Standard Deviation	14.436%
Sample Variance	208.387%
Kurtosis	-0.07
Skewness	0.83
Range	57.911%
Minimum	13.190%
Maximum	71.101%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.177%	56	100.00%	34.177%
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 1.43. Further, an Excess Kurtosis of 3.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.98%	0	0.00%	0.00%
-50.98% to -39.31%	0	0.00%	0.00%
-39.31% to -27.65%	1	1.79%	1.79%
-27.65% to -15.99%	7	12.50%	14.29%
-15.99% to -4.32%	24	42.86%	57.14%
-4.32% to 7.34%	15	26.79%	83.93%
7.34% to 19.00%	4	7.14%	91.07%
19.00% to 30.67%	3	5.36%	96.43%
30.67% to 42.33%	1	1.79%	98.21%
Greater than 42.33%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.88%	11.23%	78.57%	68.27%
±2σ	-35.43%	26.78%	92.86%	95.45%
±3σ	-50.98%	42.33%	98.21%	99.73%

Descriptive Statistics

Mean	-4.324%
Standard Error	2.078%
Median	-6.930%
Mode	-35.718%
Standard Deviation	15.551%
Sample Variance	241.820%
Kurtosis	3.83
Skewness	1.43
Range	93.335%
Minimum	-35.718%
Maximum	57.617%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.293%	15	26.79%	4.096%
Negative	-11.500%	41	73.21%	-8.420%
Zero	0.000%	0	0.00%	0.000%

NOW Deep Analytical Report