SNOW - 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	3.82%	2.82%	3.06%	4.75%	4.21%	4.27%	165.38	179.93	158.56	187.67
Weekly	8.00%	7.56%	8.14%	11.30%	9.28%	9.39%	157.22	189.27	143.29	207.67
Monthly	13.64%	13.15%	12.81%	22.64%	19.31%	19.55%	142.20	209.25	117.23	253.83
Quarterly	25.06%	18.89%	24.55%	39.13%	33.45%	33.87%	123.46	241.03	88.36	336.78
Annual	—	—	—	—	66.90%	67.73%	88.36	336.78	45.26	657.51
Option Time Horizon	—	—	—	—	25.73%	26.05%	133.36	223.12	103.10	288.61

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $172.50 | Strike (K): $175.00 (first OTM call ≥ spot) | Observed Mid-Price: $16.9500 (Bid $16.4500 / Ask $17.4500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 66.90% (CRR binomial tree, American, n=20 steps) | BS IV: 66.79% (European Black-Scholes) | Yahoo IV (Annual): 67.73% → 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 0.70. Further, an Excess Kurtosis of 7.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.41%	7	0.51%	0.51%
-11.41% to -8.55%	17	1.25%	1.76%
-8.55% to -5.68%	58	4.26%	6.02%
-5.68% to -2.82%	152	11.15%	17.17%
-2.82% to 0.04%	432	31.69%	48.86%
0.04% to 2.91%	483	35.44%	84.30%
2.91% to 5.77%	146	10.71%	95.01%
5.77% to 8.63%	46	3.37%	98.39%
8.63% to 11.50%	8	0.59%	98.97%
Greater than 11.50%	14	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.77%	3.86%	77.70%	68.27%
±2σ	-7.59%	7.68%	95.38%	95.45%
±3σ	-11.41%	11.50%	98.46%	99.73%

Descriptive Statistics

Mean	0.044%
Standard Error	0.103%
Median	0.109%
Mode	-3.289%
Standard Deviation	3.818%
Sample Variance	14.579%
Kurtosis	7.29
Skewness	0.70
Range	50.845%
Minimum	-18.139%
Maximum	32.706%
Count	1363

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.571%	708	51.94%	1.335%
Negative	-2.693%	654	47.98%	-1.292%
Zero	0.000%	1	0.07%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.51%
20	1 Month	6.04%
60	1 Quarter	4.35%
250	1 Year	4.07%
750	3 Years	3.98%
1,250	5 Years	4.75%
2,500	10 Years	4.92%
5,000	20 Years	4.92%
12,500	50 Years	4.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.77. Further, an Excess Kurtosis of 17.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.81%	0	0.00%	0.00%
-3.81% to -1.69%	0	0.00%	0.00%
-1.69% to 0.42%	0	0.00%	0.00%
0.42% to 2.54%	271	19.87%	19.87%
2.54% to 4.65%	593	43.48%	63.34%
4.65% to 6.77%	261	19.13%	82.48%
6.77% to 8.89%	144	10.56%	93.04%
8.89% to 11.00%	48	3.52%	96.55%
11.00% to 13.12%	23	1.69%	98.24%
Greater than 13.12%	24	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.83%	7.47%	82.62%	68.27%
±2σ	-0.99%	10.30%	95.45%	95.45%
±3σ	-3.81%	13.12%	98.24%	99.73%

Descriptive Statistics

Mean	4.654%
Standard Error	0.076%
Median	3.882%
Mode	2.401%
Standard Deviation	2.821%
Sample Variance	7.955%
Kurtosis	17.68
Skewness	2.77
Range	37.016%
Minimum	1.014%
Maximum	38.030%
Count	1364

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.654%	1364	100.00%	4.654%
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 0.17. Further, an Excess Kurtosis of 2.06 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.10%	7	0.51%	0.51%
-9.10% to -6.80%	14	1.03%	1.54%
-6.80% to -4.51%	51	3.74%	5.28%
-4.51% to -2.21%	180	13.20%	18.48%
-2.21% to 0.09%	467	34.24%	52.71%
0.09% to 2.39%	395	28.96%	81.67%
2.39% to 4.69%	166	12.17%	93.84%
4.69% to 6.99%	48	3.52%	97.36%
6.99% to 9.29%	22	1.61%	98.97%
Greater than 9.29%	14	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.97%	3.16%	75.00%	68.27%
±2σ	-6.04%	6.22%	94.28%	95.45%
±3σ	-9.10%	9.29%	98.46%	99.73%

Descriptive Statistics

Mean	0.091%
Standard Error	0.083%
Median	-0.061%
Mode	-2.513%
Standard Deviation	3.065%
Sample Variance	9.395%
Kurtosis	2.06
Skewness	0.17
Range	26.929%
Minimum	-14.519%
Maximum	12.410%
Count	1364

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.384%	664	48.68%	1.161%
Negative	-2.087%	699	51.25%	-1.070%
Zero	0.000%	1	0.07%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.40. Further, an Excess Kurtosis of 2.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.79%	1	0.35%	0.35%
-23.79% to -17.79%	4	1.41%	1.77%
-17.79% to -11.79%	10	3.53%	5.30%
-11.79% to -5.79%	37	13.07%	18.37%
-5.79% to 0.22%	88	31.10%	49.47%
0.22% to 6.22%	92	32.51%	81.98%
6.22% to 12.22%	36	12.72%	94.70%
12.22% to 18.22%	6	2.12%	96.82%
18.22% to 24.22%	7	2.47%	99.29%
Greater than 24.22%	2	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.78%	8.22%	74.91%	68.27%
±2σ	-15.79%	16.22%	94.70%	95.45%
±3σ	-23.79%	24.22%	98.94%	99.73%

Descriptive Statistics

Mean	0.216%
Standard Error	0.476%
Median	0.282%
Mode	-27.351%
Standard Deviation	8.001%
Sample Variance	64.020%
Kurtosis	2.24
Skewness	0.40
Range	61.872%
Minimum	-27.351%
Maximum	34.521%
Count	283

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.947%	145	51.24%	3.047%
Negative	-5.806%	138	48.76%	-2.831%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.93%
12	1 Quarter	9.39%
52	1 Year	9.88%
156	3 Years	9.65%
260	5 Years	11.30%
520	10 Years	11.64%
1,040	20 Years	11.64%
2,600	50 Years	11.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.74. Further, an Excess Kurtosis of 3.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.12%	0	0.00%	0.00%
-10.12% to -4.45%	0	0.00%	0.00%
-4.45% to 1.22%	0	0.00%	0.00%
1.22% to 6.89%	58	20.42%	20.42%
6.89% to 12.56%	119	41.90%	62.32%
12.56% to 18.23%	60	21.13%	83.45%
18.23% to 23.90%	26	9.15%	92.61%
23.90% to 29.57%	8	2.82%	95.42%
29.57% to 35.24%	7	2.46%	97.89%
Greater than 35.24%	6	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.00%	20.12%	80.63%	68.27%
±2σ	-2.56%	27.68%	94.37%	95.45%
±3σ	-10.12%	35.24%	97.89%	99.73%

Descriptive Statistics

Mean	12.561%
Standard Error	0.449%
Median	10.397%
Mode	7.489%
Standard Deviation	7.561%
Sample Variance	57.169%
Kurtosis	3.67
Skewness	1.74
Range	45.185%
Minimum	3.022%
Maximum	48.207%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.561%	284	100.00%	12.561%
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 0.64. Further, an Excess Kurtosis of 2.72 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.87%	1	0.35%	0.35%
-23.87% to -17.77%	3	1.06%	1.41%
-17.77% to -11.67%	11	3.87%	5.28%
-11.67% to -5.57%	36	12.68%	17.96%
-5.57% to 0.54%	103	36.27%	54.23%
0.54% to 6.64%	78	27.46%	81.69%
6.64% to 12.74%	31	10.92%	92.61%
12.74% to 18.84%	16	5.63%	98.24%
18.84% to 24.94%	1	0.35%	98.59%
Greater than 24.94%	4	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.60%	8.67%	76.41%	68.27%
±2σ	-15.74%	16.81%	94.01%	95.45%
±3σ	-23.87%	24.94%	98.24%	99.73%

Descriptive Statistics

Mean	0.536%
Standard Error	0.483%
Median	-0.185%
Mode	2.370%
Standard Deviation	8.136%
Sample Variance	66.198%
Kurtosis	2.72
Skewness	0.64
Range	64.214%
Minimum	-25.592%
Maximum	38.622%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.582%	139	48.94%	3.221%
Negative	-5.297%	144	50.70%	-2.686%
Zero	0.000%	1	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.15. Further, an Excess Kurtosis of 2.59 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.64%	0	0.00%	0.00%
-40.64% to -30.41%	0	0.00%	0.00%
-30.41% to -20.18%	2	3.08%	3.08%
-20.18% to -9.95%	14	21.54%	24.62%
-9.95% to 0.28%	24	36.92%	61.54%
0.28% to 10.51%	15	23.08%	84.62%
10.51% to 20.74%	5	7.69%	92.31%
20.74% to 30.97%	4	6.15%	98.46%
30.97% to 41.20%	0	0.00%	98.46%
Greater than 41.20%	1	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.36%	13.92%	75.38%	68.27%
±2σ	-27.00%	27.56%	93.85%	95.45%
±3σ	-40.64%	41.20%	98.46%	99.73%

Descriptive Statistics

Mean	0.278%
Standard Error	1.692%
Median	-1.317%
Mode	-25.542%
Standard Deviation	13.640%
Sample Variance	186.054%
Kurtosis	2.59
Skewness	1.15
Range	77.780%
Minimum	-25.542%
Maximum	52.238%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.972%	25	38.46%	4.989%
Negative	-7.656%	40	61.54%	-4.711%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	21.22%
12	1 Year	20.37%
36	3 Years	20.61%
60	5 Years	22.64%
120	10 Years	23.54%
240	20 Years	23.54%
600	50 Years	23.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.08. Further, an Excess Kurtosis of 1.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.84%	0	0.00%	0.00%
-11.84% to -1.98%	0	0.00%	0.00%
-1.98% to 7.88%	0	0.00%	0.00%
7.88% to 17.75%	15	22.73%	22.73%
17.75% to 27.61%	26	39.39%	62.12%
27.61% to 37.47%	14	21.21%	83.33%
37.47% to 47.34%	4	6.06%	89.39%
47.34% to 57.20%	4	6.06%	95.45%
57.20% to 67.06%	3	4.55%	100.00%
Greater than 67.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.46%	40.76%	71.21%	68.27%
±2σ	1.31%	53.91%	95.45%	95.45%
±3σ	-11.84%	67.06%	100.00%	99.73%

Descriptive Statistics

Mean	27.610%
Standard Error	1.619%
Median	23.995%
Mode	8.858%
Standard Deviation	13.150%
Sample Variance	172.913%
Kurtosis	1.18
Skewness	1.08
Range	58.163%
Minimum	8.858%
Maximum	67.021%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.610%	66	100.00%	27.610%
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 -0.01. 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 -36.80%	0	0.00%	0.00%
-36.80% to -27.19%	1	1.52%	1.52%
-27.19% to -17.58%	5	7.58%	9.09%
-17.58% to -7.97%	8	12.12%	21.21%
-7.97% to 1.64%	20	30.30%	51.52%
1.64% to 11.25%	16	24.24%	75.76%
11.25% to 20.86%	12	18.18%	93.94%
20.86% to 30.47%	2	3.03%	96.97%
30.47% to 40.08%	2	3.03%	100.00%
Greater than 40.08%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.17%	14.45%	72.73%	68.27%
±2σ	-23.98%	27.27%	95.45%	95.45%
±3σ	-36.80%	40.08%	100.00%	99.73%

Descriptive Statistics

Mean	1.641%
Standard Error	1.577%
Median	1.501%
Mode	-33.650%
Standard Deviation	12.813%
Sample Variance	164.176%
Kurtosis	0.54
Skewness	-0.01
Range	67.405%
Minimum	-33.650%
Maximum	33.755%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.137%	37	56.06%	5.683%
Negative	-9.200%	29	43.94%	-4.042%
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 0.66. Further, an Excess Kurtosis of -0.31 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.04%	0	0.00%	0.00%
-74.04% to -55.24%	0	0.00%	0.00%
-55.24% to -36.45%	1	4.55%	4.55%
-36.45% to -17.65%	4	18.18%	22.73%
-17.65% to 1.15%	8	36.36%	59.09%
1.15% to 19.94%	3	13.64%	72.73%
19.94% to 38.74%	4	18.18%	90.91%
38.74% to 57.53%	1	4.55%	95.45%
57.53% to 76.33%	1	4.55%	100.00%
Greater than 76.33%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.92%	26.21%	72.73%	68.27%
±2σ	-48.98%	51.27%	95.45%	95.45%
±3σ	-74.04%	76.33%	100.00%	99.73%

Descriptive Statistics

Mean	1.145%
Standard Error	5.343%
Median	-7.914%
Mode	-37.862%
Standard Deviation	25.061%
Sample Variance	628.056%
Kurtosis	-0.31
Skewness	0.66
Range	95.944%
Minimum	-37.862%
Maximum	58.082%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.647%	9	40.91%	10.901%
Negative	-16.511%	13	59.09%	-9.757%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.65%
12	3 Years	37.23%
20	5 Years	39.13%
40	10 Years	41.15%
80	20 Years	41.15%
200	50 Years	41.15%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.91. Further, an Excess Kurtosis of 0.69 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.86%	0	0.00%	0.00%
-4.86% to 9.30%	0	0.00%	0.00%
9.30% to 23.46%	0	0.00%	0.00%
23.46% to 37.63%	4	17.39%	17.39%
37.63% to 51.79%	10	43.48%	60.87%
51.79% to 65.96%	4	17.39%	78.26%
65.96% to 80.12%	3	13.04%	91.30%
80.12% to 94.29%	1	4.35%	95.65%
94.29% to 108.45%	1	4.35%	100.00%
Greater than 108.45%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	32.91%	70.68%	73.91%	68.27%
±2σ	14.02%	89.57%	95.65%	95.45%
±3σ	-4.86%	108.45%	100.00%	99.73%

Descriptive Statistics

Mean	51.794%
Standard Error	3.938%
Median	46.532%
Mode	26.275%
Standard Deviation	18.886%
Sample Variance	356.695%
Kurtosis	0.69
Skewness	0.91
Range	74.279%
Minimum	26.275%
Maximum	100.554%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	51.794%	23	100.00%	51.794%
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 0.43. Further, an Excess Kurtosis of 0.12 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.92%	0	0.00%	0.00%
-68.92% to -50.51%	0	0.00%	0.00%
-50.51% to -32.09%	1	4.35%	4.35%
-32.09% to -13.68%	5	21.74%	26.09%
-13.68% to 4.74%	4	17.39%	43.48%
4.74% to 23.16%	9	39.13%	82.61%
23.16% to 41.57%	2	8.70%	91.30%
41.57% to 59.99%	1	4.35%	95.65%
59.99% to 78.40%	1	4.35%	100.00%
Greater than 78.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.81%	29.29%	69.57%	68.27%
±2σ	-44.37%	53.85%	95.65%	95.45%
±3σ	-68.92%	78.40%	100.00%	99.73%

Descriptive Statistics

Mean	4.740%
Standard Error	5.120%
Median	7.098%
Mode	-36.103%
Standard Deviation	24.554%
Sample Variance	602.898%
Kurtosis	0.12
Skewness	0.43
Range	100.475%
Minimum	-36.103%
Maximum	64.372%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.148%	13	56.52%	12.518%
Negative	-17.890%	10	43.48%	-7.778%
Zero	0.000%	0	0.00%	0.000%

SNOW Deep Analytical Report