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	3.81%	2.81%	3.07%	4.72%	3.16%	3.18%	168.64	179.64	163.40	185.40
Weekly	8.01%	7.54%	8.15%	11.27%	6.95%	7.00%	162.37	186.59	151.46	200.02
Monthly	13.57%	13.10%	12.79%	22.48%	14.47%	14.56%	150.61	201.16	130.31	232.48
Quarterly	25.05%	18.82%	24.54%	39.17%	25.06%	25.23%	135.47	223.63	105.43	287.34
Annual	—	—	—	—	50.13%	50.45%	105.43	287.34	63.87	474.35
Option Time Horizon	—	—	—	—	18.92%	19.04%	144.05	210.31	119.22	254.12

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $174.05 | Strike (K): $175.00 (first OTM call ≥ spot) | Observed Mid-Price: $13.0250 (Bid $12.5000 / Ask $13.5500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 50.13% (CRR binomial tree, American, n=20 steps) | BS IV: 49.80% (European Black-Scholes) | Yahoo IV (Annual): 50.45% → 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 0.69. Further, an Excess Kurtosis of 7.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.39%	8	0.58%	0.58%
-11.39% to -8.53%	17	1.23%	1.81%
-8.53% to -5.67%	58	4.19%	6.00%
-5.67% to -2.81%	154	11.13%	17.12%
-2.81% to 0.04%	437	31.58%	48.70%
0.04% to 2.90%	493	35.62%	84.32%
2.90% to 5.76%	148	10.69%	95.01%
5.76% to 8.62%	46	3.32%	98.34%
8.62% to 11.48%	9	0.65%	98.99%
Greater than 11.48%	14	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.77%	3.85%	77.60%	68.27%
±2σ	-7.58%	7.67%	95.30%	95.45%
±3σ	-11.39%	11.48%	98.41%	99.73%

Descriptive Statistics

Mean	0.044%
Standard Error	0.102%
Median	0.117%
Mode	-3.289%
Standard Deviation	3.811%
Sample Variance	14.520%
Kurtosis	7.24
Skewness	0.69
Range	50.845%
Minimum	-18.139%
Maximum	32.706%
Count	1384

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.565%	721	52.09%	1.336%
Negative	-2.701%	662	47.83%	-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	3.81%
20	1 Month	4.98%
60	1 Quarter	4.84%
250	1 Year	4.05%
750	3 Years	3.98%
1,250	5 Years	4.72%
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 2.76. 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 -3.77%	0	0.00%	0.00%
-3.77% to -1.66%	0	0.00%	0.00%
-1.66% to 0.45%	0	0.00%	0.00%
0.45% to 2.55%	276	19.93%	19.93%
2.55% to 4.66%	598	43.18%	63.10%
4.66% to 6.77%	269	19.42%	82.53%
6.77% to 8.88%	143	10.32%	92.85%
8.88% to 10.98%	52	3.75%	96.61%
10.98% to 13.09%	23	1.66%	98.27%
Greater than 13.09%	24	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.85%	7.47%	82.67%	68.27%
±2σ	-0.96%	10.28%	95.45%	95.45%
±3σ	-3.77%	13.09%	98.27%	99.73%

Descriptive Statistics

Mean	4.661%
Standard Error	0.076%
Median	3.900%
Mode	2.401%
Standard Deviation	2.810%
Sample Variance	7.896%
Kurtosis	17.67
Skewness	2.76
Range	37.016%
Minimum	1.014%
Maximum	38.030%
Count	1385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.661%	1385	100.00%	4.661%
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 0.18. Further, an Excess Kurtosis of 2.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.12%	7	0.51%	0.51%
-9.12% to -6.82%	14	1.01%	1.52%
-6.82% to -4.51%	53	3.83%	5.34%
-4.51% to -2.21%	183	13.21%	18.56%
-2.21% to 0.09%	474	34.22%	52.78%
0.09% to 2.39%	399	28.81%	81.59%
2.39% to 4.69%	170	12.27%	93.86%
4.69% to 6.99%	48	3.47%	97.33%
6.99% to 9.29%	23	1.66%	98.99%
Greater than 9.29%	14	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.98%	3.15%	74.73%	68.27%
±2σ	-6.05%	6.22%	94.30%	95.45%
±3σ	-9.12%	9.29%	98.48%	99.73%

Descriptive Statistics

Mean	0.086%
Standard Error	0.082%
Median	-0.061%
Mode	-2.513%
Standard Deviation	3.067%
Sample Variance	9.406%
Kurtosis	2.02
Skewness	0.18
Range	26.929%
Minimum	-14.519%
Maximum	12.410%
Count	1385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.388%	673	48.59%	1.160%
Negative	-2.094%	711	51.34%	-1.075%
Zero	0.000%	1	0.07%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.38. Further, an Excess Kurtosis of 2.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.81%	1	0.35%	0.35%
-23.81% to -17.80%	4	1.39%	1.74%
-17.80% to -11.79%	11	3.83%	5.57%
-11.79% to -5.79%	37	12.89%	18.47%
-5.79% to 0.22%	89	31.01%	49.48%
0.22% to 6.23%	92	32.06%	81.53%
6.23% to 12.24%	38	13.24%	94.77%
12.24% to 18.25%	6	2.09%	96.86%
18.25% to 24.25%	7	2.44%	99.30%
Greater than 24.25%	2	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.79%	8.23%	75.26%	68.27%
±2σ	-15.80%	16.24%	94.77%	95.45%
±3σ	-23.81%	24.25%	98.95%	99.73%

Descriptive Statistics

Mean	0.222%
Standard Error	0.473%
Median	0.282%
Mode	-27.351%
Standard Deviation	8.010%
Sample Variance	64.153%
Kurtosis	2.18
Skewness	0.38
Range	61.872%
Minimum	-27.351%
Maximum	34.521%
Count	287

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.971%	147	51.22%	3.058%
Negative	-5.816%	140	48.78%	-2.837%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.96%
12	1 Quarter	11.37%
52	1 Year	9.95%
156	3 Years	9.74%
260	5 Years	11.27%
520	10 Years	11.67%
1,040	20 Years	11.67%
2,600	50 Years	11.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.71. Further, an Excess Kurtosis of 3.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.03%	0	0.00%	0.00%
-10.03% to -4.37%	0	0.00%	0.00%
-4.37% to 1.28%	0	0.00%	0.00%
1.28% to 6.94%	61	21.18%	21.18%
6.94% to 12.60%	117	40.62%	61.81%
12.60% to 18.25%	61	21.18%	82.99%
18.25% to 23.91%	28	9.72%	92.71%
23.91% to 29.57%	8	2.78%	95.49%
29.57% to 35.22%	7	2.43%	97.92%
Greater than 35.22%	6	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.05%	20.14%	80.90%	68.27%
±2σ	-2.49%	27.68%	94.44%	95.45%
±3σ	-10.03%	35.22%	97.92%	99.73%

Descriptive Statistics

Mean	12.597%
Standard Error	0.444%
Median	10.418%
Mode	7.489%
Standard Deviation	7.542%
Sample Variance	56.889%
Kurtosis	3.61
Skewness	1.71
Range	45.185%
Minimum	3.022%
Maximum	48.207%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.597%	288	100.00%	12.597%
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 2.63 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.94%	1	0.35%	0.35%
-23.94% to -17.83%	3	1.04%	1.39%
-17.83% to -11.71%	10	3.47%	4.86%
-11.71% to -5.60%	39	13.54%	18.40%
-5.60% to 0.52%	103	35.76%	54.17%
0.52% to 6.63%	79	27.43%	81.60%
6.63% to 12.75%	31	10.76%	92.36%
12.75% to 18.86%	17	5.90%	98.26%
18.86% to 24.98%	1	0.35%	98.61%
Greater than 24.98%	4	1.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.63%	8.67%	76.39%	68.27%
±2σ	-15.79%	16.83%	94.10%	95.45%
±3σ	-23.94%	24.98%	98.26%	99.73%

Descriptive Statistics

Mean	0.519%
Standard Error	0.480%
Median	-0.185%
Mode	2.370%
Standard Deviation	8.154%
Sample Variance	66.481%
Kurtosis	2.63
Skewness	0.64
Range	64.214%
Minimum	-25.592%
Maximum	38.622%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.596%	141	48.96%	3.229%
Negative	-5.345%	146	50.69%	-2.710%
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 1.14. Further, an Excess Kurtosis of 2.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.42%	0	0.00%	0.00%
-40.42% to -30.24%	0	0.00%	0.00%
-30.24% to -20.06%	2	3.03%	3.03%
-20.06% to -9.89%	14	21.21%	24.24%
-9.89% to 0.29%	24	36.36%	60.61%
0.29% to 10.47%	16	24.24%	84.85%
10.47% to 20.64%	4	6.06%	90.91%
20.64% to 30.82%	5	7.58%	98.48%
30.82% to 41.00%	0	0.00%	98.48%
Greater than 41.00%	1	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.28%	13.86%	75.76%	68.27%
±2σ	-26.85%	27.43%	93.94%	95.45%
±3σ	-40.42%	41.00%	98.48%	99.73%

Descriptive Statistics

Mean	0.291%
Standard Error	1.670%
Median	-1.058%
Mode	-25.542%
Standard Deviation	13.569%
Sample Variance	184.105%
Kurtosis	2.61
Skewness	1.14
Range	77.780%
Minimum	-25.542%
Maximum	52.238%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.600%	26	39.39%	4.964%
Negative	-7.709%	40	60.61%	-4.672%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.59%
12	1 Year	20.03%
36	3 Years	20.59%
60	5 Years	22.48%
120	10 Years	23.45%
240	20 Years	23.45%
600	50 Years	23.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.10. Further, an Excess Kurtosis of 1.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.83%	0	0.00%	0.00%
-11.83% to -2.00%	0	0.00%	0.00%
-2.00% to 7.82%	0	0.00%	0.00%
7.82% to 17.65%	15	22.39%	22.39%
17.65% to 27.48%	26	38.81%	61.19%
27.48% to 37.31%	15	22.39%	83.58%
37.31% to 47.14%	4	5.97%	89.55%
47.14% to 56.96%	4	5.97%	95.52%
56.96% to 66.79%	2	2.99%	98.51%
Greater than 66.79%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.38%	40.58%	71.64%	68.27%
±2σ	1.27%	53.69%	95.52%	95.45%
±3σ	-11.83%	66.79%	98.51%	99.73%

Descriptive Statistics

Mean	27.480%
Standard Error	1.601%
Median	23.970%
Mode	8.858%
Standard Deviation	13.104%
Sample Variance	171.718%
Kurtosis	1.22
Skewness	1.10
Range	58.163%
Minimum	8.858%
Maximum	67.021%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.480%	67	100.00%	27.480%
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 0.02. Further, an Excess Kurtosis of 0.53 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 -27.21%	1	1.49%	1.49%
-27.21% to -17.61%	5	7.46%	8.96%
-17.61% to -8.02%	8	11.94%	20.90%
-8.02% to 1.57%	21	31.34%	52.24%
1.57% to 11.17%	16	23.88%	76.12%
11.17% to 20.76%	12	17.91%	94.03%
20.76% to 30.36%	2	2.99%	97.01%
30.36% to 39.95%	2	2.99%	100.00%
Greater than 39.95%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.22%	14.37%	71.64%	68.27%
±2σ	-24.01%	27.16%	95.52%	95.45%
±3σ	-36.80%	39.95%	100.00%	99.73%

Descriptive Statistics

Mean	1.574%
Standard Error	1.563%
Median	1.451%
Mode	-33.650%
Standard Deviation	12.793%
Sample Variance	163.661%
Kurtosis	0.53
Skewness	0.02
Range	67.405%
Minimum	-33.650%
Maximum	33.755%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.212%	37	55.22%	5.639%
Negative	-9.081%	30	44.78%	-4.066%
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 0.65. 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 -73.95%	0	0.00%	0.00%
-73.95% to -55.17%	0	0.00%	0.00%
-55.17% to -36.39%	1	4.55%	4.55%
-36.39% to -17.60%	4	18.18%	22.73%
-17.60% to 1.18%	8	36.36%	59.09%
1.18% to 19.96%	3	13.64%	72.73%
19.96% to 38.75%	4	18.18%	90.91%
38.75% to 57.53%	1	4.55%	95.45%
57.53% to 76.31%	1	4.55%	100.00%
Greater than 76.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.87%	26.23%	72.73%	68.27%
±2σ	-48.91%	51.27%	95.45%	95.45%
±3σ	-73.95%	76.32%	100.00%	99.73%

Descriptive Statistics

Mean	1.180%
Standard Error	5.340%
Median	-7.530%
Mode	-37.862%
Standard Deviation	25.045%
Sample Variance	627.232%
Kurtosis	-0.31
Skewness	0.65
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	-16.452%	13	59.09%	-9.722%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.83%
12	3 Years	37.29%
20	5 Years	39.17%
40	10 Years	41.19%
80	20 Years	41.19%
200	50 Years	41.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.93. Further, an Excess Kurtosis of 0.71 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.60%	0	0.00%	0.00%
-4.60% to 9.51%	0	0.00%	0.00%
9.51% to 23.62%	0	0.00%	0.00%
23.62% to 37.73%	5	21.74%	21.74%
37.73% to 51.85%	9	39.13%	60.87%
51.85% to 65.96%	4	17.39%	78.26%
65.96% to 80.07%	3	13.04%	91.30%
80.07% to 94.18%	1	4.35%	95.65%
94.18% to 108.29%	1	4.35%	100.00%
Greater than 108.29%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	33.03%	70.66%	73.91%	68.27%
±2σ	14.22%	89.48%	95.65%	95.45%
±3σ	-4.60%	108.29%	100.00%	99.73%

Descriptive Statistics

Mean	51.846%
Standard Error	3.923%
Median	46.532%
Mode	26.687%
Standard Deviation	18.815%
Sample Variance	354.000%
Kurtosis	0.71
Skewness	0.93
Range	73.867%
Minimum	26.687%
Maximum	100.554%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	51.846%	23	100.00%	51.846%
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 0.13 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 -32.11%	1	4.35%	4.35%
-32.11% to -13.71%	5	21.74%	26.09%
-13.71% to 4.70%	4	17.39%	43.48%
4.70% to 23.10%	9	39.13%	82.61%
23.10% to 41.51%	2	8.70%	91.30%
41.51% to 59.91%	1	4.35%	95.65%
59.91% to 78.31%	1	4.35%	100.00%
Greater than 78.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.84%	29.24%	69.57%	68.27%
±2σ	-44.38%	53.77%	95.65%	95.45%
±3σ	-68.92%	78.31%	100.00%	99.73%

Descriptive Statistics

Mean	4.698%
Standard Error	5.116%
Median	7.098%
Mode	-36.103%
Standard Deviation	24.538%
Sample Variance	602.098%
Kurtosis	0.13
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	22.073%	13	56.52%	12.476%
Negative	-17.890%	10	43.48%	-7.778%
Zero	0.000%	0	0.00%	0.000%

SNOW Deep Analytical Report