SNAP - 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	4.54%	2.54%	3.14%	5.43%	3.98%	4.05%	4.94	5.35	4.75	5.57
Weekly	9.31%	9.18%	9.51%	13.04%	8.75%	8.91%	4.71	5.61	4.31	6.12
Monthly	17.74%	18.72%	19.76%	28.36%	18.22%	18.55%	4.28	6.17	3.57	7.40
Quarterly	31.60%	37.48%	41.81%	44.58%	31.57%	32.13%	3.75	7.05	2.73	9.66
Annual	—	—	—	—	63.13%	64.26%	2.73	9.66	1.45	18.17
Option Time Horizon	—	—	—	—	24.28%	24.72%	4.03	6.55	3.16	8.35

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $5.14 | Strike (K): $6.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.2250 (Bid $0.2200 / Ask $0.2300) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 63.13% (CRR binomial tree, American, n=20 steps) | BS IV: 63.75% (European Black-Scholes) | Yahoo IV (Annual): 64.26% → 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 0.74. Further, an Excess Kurtosis of 30.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.59%	17	0.75%	0.75%
-13.59% to -10.19%	6	0.27%	1.02%
-10.19% to -6.78%	48	2.13%	3.15%
-6.78% to -3.37%	236	10.47%	13.61%
-3.37% to 0.04%	843	37.38%	51.00%
0.04% to 3.44%	785	34.81%	85.81%
3.44% to 6.85%	242	10.73%	96.54%
6.85% to 10.26%	55	2.44%	98.98%
10.26% to 13.66%	12	0.53%	99.51%
Greater than 13.66%	11	0.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.51%	4.58%	83.24%	68.27%
±2σ	-9.05%	9.12%	96.85%	95.45%
±3σ	-13.59%	13.66%	98.76%	99.73%

Descriptive Statistics

Mean	0.035%
Standard Error	0.096%
Median	-0.056%
Mode	0.000%
Standard Deviation	4.543%
Sample Variance	20.637%
Kurtosis	30.92
Skewness	0.74
Range	101.896%
Minimum	-43.080%
Maximum	58.816%
Count	2255

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.908%	1106	49.05%	1.426%
Negative	-2.781%	1128	50.02%	-1.391%
Zero	0.000%	21	0.93%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.12%
20	1 Month	5.41%
60	1 Quarter	4.06%
250	1 Year	4.72%
750	3 Years	4.68%
1,250	5 Years	5.43%
2,500	10 Years	5.24%
5,000	20 Years	5.24%
12,500	50 Years	5.24%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.27. Further, an Excess Kurtosis of 10.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.78%	0	0.00%	0.00%
-2.78% to -0.87%	0	0.00%	0.00%
-0.87% to 1.04%	2	0.09%	0.09%
1.04% to 2.95%	463	20.52%	20.61%
2.95% to 4.86%	906	40.16%	60.77%
4.86% to 6.76%	518	22.96%	83.73%
6.76% to 8.67%	205	9.09%	92.82%
8.67% to 10.58%	88	3.90%	96.72%
10.58% to 12.49%	36	1.60%	98.32%
Greater than 12.49%	38	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.31%	7.40%	79.65%	68.27%
±2σ	-0.23%	9.94%	95.88%	95.45%
±3σ	-2.78%	12.49%	98.32%	99.73%

Descriptive Statistics

Mean	4.855%
Standard Error	0.054%
Median	4.298%
Mode	5.089%
Standard Deviation	2.544%
Sample Variance	6.470%
Kurtosis	10.22
Skewness	2.27
Range	27.524%
Minimum	0.841%
Maximum	28.365%
Count	2256

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.855%	2256	100.00%	4.855%
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 0.00. Further, an Excess Kurtosis of 2.62 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.38%	11	0.49%	0.49%
-9.38% to -7.02%	26	1.15%	1.64%
-7.02% to -4.67%	93	4.12%	5.76%
-4.67% to -2.32%	301	13.34%	19.10%
-2.32% to 0.03%	710	31.47%	50.58%
0.03% to 2.38%	686	30.41%	80.98%
2.38% to 4.74%	304	13.48%	94.46%
4.74% to 7.09%	84	3.72%	98.18%
7.09% to 9.44%	27	1.20%	99.38%
Greater than 9.44%	14	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.10%	3.17%	73.32%	68.27%
±2σ	-6.24%	6.30%	95.04%	95.45%
±3σ	-9.38%	9.44%	98.89%	99.73%

Descriptive Statistics

Mean	0.032%
Standard Error	0.066%
Median	0.000%
Mode	0.000%
Standard Deviation	3.136%
Sample Variance	9.833%
Kurtosis	2.62
Skewness	0.00
Range	37.218%
Minimum	-18.707%
Maximum	18.511%
Count	2256

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.391%	1116	49.47%	1.183%
Negative	-2.349%	1106	49.02%	-1.152%
Zero	0.000%	34	1.51%	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 2.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.83%	5	1.07%	1.07%
-27.83% to -20.84%	6	1.28%	2.35%
-20.84% to -13.86%	10	2.14%	4.49%
-13.86% to -6.88%	66	14.10%	18.59%
-6.88% to 0.11%	154	32.91%	51.50%
0.11% to 7.09%	145	30.98%	82.48%
7.09% to 14.08%	55	11.75%	94.23%
14.08% to 21.06%	19	4.06%	98.29%
21.06% to 28.05%	2	0.43%	98.72%
Greater than 28.05%	6	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.20%	9.42%	75.85%	68.27%
±2σ	-18.52%	18.74%	94.23%	95.45%
±3σ	-27.83%	28.05%	97.65%	99.73%

Descriptive Statistics

Mean	0.110%
Standard Error	0.430%
Median	-0.337%
Mode	-8.364%
Standard Deviation	9.313%
Sample Variance	86.734%
Kurtosis	2.57
Skewness	0.18
Range	78.756%
Minimum	-34.757%
Maximum	43.999%
Count	468

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.087%	229	48.93%	3.468%
Negative	-6.603%	238	50.85%	-3.358%
Zero	0.000%	1	0.21%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	16.02%
12	1 Quarter	10.83%
52	1 Year	11.02%
156	3 Years	11.25%
260	5 Years	13.04%
520	10 Years	12.58%
1,040	20 Years	12.58%
2,600	50 Years	12.58%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.95. Further, an Excess Kurtosis of 12.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.98%	0	0.00%	0.00%
-13.98% to -7.10%	0	0.00%	0.00%
-7.10% to -0.22%	0	0.00%	0.00%
-0.22% to 6.67%	61	13.01%	13.01%
6.67% to 13.55%	242	51.60%	64.61%
13.55% to 20.43%	105	22.39%	86.99%
20.43% to 27.32%	33	7.04%	94.03%
27.32% to 34.20%	13	2.77%	96.80%
34.20% to 41.08%	6	1.28%	98.08%
Greater than 41.08%	9	1.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.37%	22.73%	88.06%	68.27%
±2σ	-4.81%	31.91%	95.31%	95.45%
±3σ	-13.98%	41.08%	98.08%	99.73%

Descriptive Statistics

Mean	13.550%
Standard Error	0.424%
Median	11.127%
Mode	13.491%
Standard Deviation	9.178%
Sample Variance	84.239%
Kurtosis	12.29
Skewness	2.95
Range	68.519%
Minimum	2.754%
Maximum	71.273%
Count	469

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.550%	469	100.00%	13.550%
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 1.09. Further, an Excess Kurtosis of 4.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.77%	1	0.21%	0.21%
-27.77% to -20.63%	4	0.85%	1.07%
-20.63% to -13.50%	14	2.99%	4.05%
-13.50% to -6.36%	68	14.50%	18.55%
-6.36% to 0.77%	165	35.18%	53.73%
0.77% to 7.91%	137	29.21%	82.94%
7.91% to 15.04%	59	12.58%	95.52%
15.04% to 22.18%	7	1.49%	97.01%
22.18% to 29.31%	5	1.07%	98.08%
Greater than 29.31%	9	1.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.74%	10.28%	78.04%	68.27%
±2σ	-18.25%	19.80%	95.31%	95.45%
±3σ	-27.77%	29.31%	97.87%	99.73%

Descriptive Statistics

Mean	0.771%
Standard Error	0.439%
Median	-0.056%
Mode	-0.423%
Standard Deviation	9.513%
Sample Variance	90.495%
Kurtosis	4.43
Skewness	1.09
Range	84.289%
Minimum	-31.476%
Maximum	52.813%
Count	469

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.618%	232	49.47%	3.768%
Negative	-5.982%	235	50.11%	-2.997%
Zero	0.000%	2	0.43%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 0.62 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.00%	0	0.00%	0.00%
-53.00% to -39.70%	1	0.93%	0.93%
-39.70% to -26.40%	4	3.74%	4.67%
-26.40% to -13.10%	19	17.76%	22.43%
-13.10% to 0.21%	29	27.10%	49.53%
0.21% to 13.51%	33	30.84%	80.37%
13.51% to 26.81%	14	13.08%	93.46%
26.81% to 40.12%	4	3.74%	97.20%
40.12% to 53.42%	3	2.80%	100.00%
Greater than 53.42%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.53%	17.94%	71.03%	68.27%
±2σ	-35.27%	35.68%	95.33%	95.45%
±3σ	-53.00%	53.42%	100.00%	99.73%

Descriptive Statistics

Mean	0.207%
Standard Error	1.715%
Median	0.207%
Mode	-50.422%
Standard Deviation	17.737%
Sample Variance	314.613%
Kurtosis	0.62
Skewness	0.29
Range	101.284%
Minimum	-50.422%
Maximum	50.862%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.528%	55	51.40%	6.954%
Negative	-13.883%	52	48.60%	-6.747%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.53%
12	1 Year	22.95%
36	3 Years	25.74%
60	5 Years	28.36%
120	10 Years	27.54%
240	20 Years	27.54%
600	50 Years	27.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.45. Further, an Excess Kurtosis of 9.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.67%	0	0.00%	0.00%
-22.67% to -8.63%	0	0.00%	0.00%
-8.63% to 5.41%	0	0.00%	0.00%
5.41% to 19.45%	24	22.22%	22.22%
19.45% to 33.49%	45	41.67%	63.89%
33.49% to 47.53%	20	18.52%	82.41%
47.53% to 61.57%	9	8.33%	90.74%
61.57% to 75.61%	7	6.48%	97.22%
75.61% to 89.65%	2	1.85%	99.07%
Greater than 89.65%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.77%	52.21%	85.19%	68.27%
±2σ	-3.95%	70.93%	96.30%	95.45%
±3σ	-22.67%	89.65%	99.07%	99.73%

Descriptive Statistics

Mean	33.486%
Standard Error	1.801%
Median	28.505%
Mode	12.518%
Standard Deviation	18.720%
Sample Variance	350.452%
Kurtosis	9.55
Skewness	2.45
Range	128.040%
Minimum	12.518%
Maximum	140.558%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.486%	108	100.00%	33.486%
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 1.35. Further, an Excess Kurtosis of 4.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.92%	0	0.00%	0.00%
-55.92% to -41.10%	0	0.00%	0.00%
-41.10% to -26.28%	4	3.70%	3.70%
-26.28% to -11.45%	15	13.89%	17.59%
-11.45% to 3.37%	42	38.89%	56.48%
3.37% to 18.19%	25	23.15%	79.63%
18.19% to 33.01%	15	13.89%	93.52%
33.01% to 47.84%	5	4.63%	98.15%
47.84% to 62.66%	1	0.93%	99.07%
Greater than 62.66%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.40%	23.13%	73.15%	68.27%
±2σ	-36.16%	42.89%	96.30%	95.45%
±3σ	-55.92%	62.66%	99.07%	99.73%

Descriptive Statistics

Mean	3.368%
Standard Error	1.902%
Median	0.252%
Mode	-35.718%
Standard Deviation	19.763%
Sample Variance	390.563%
Kurtosis	4.51
Skewness	1.35
Range	136.001%
Minimum	-35.718%
Maximum	100.283%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.661%	54	50.00%	8.830%
Negative	-11.131%	53	49.07%	-5.462%
Zero	0.000%	1	0.93%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.47. Further, an Excess Kurtosis of 0.22 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -93.86%	0	0.00%	0.00%
-93.86% to -70.16%	0	0.00%	0.00%
-70.16% to -46.46%	2	5.56%	5.56%
-46.46% to -22.75%	6	16.67%	22.22%
-22.75% to 0.95%	13	36.11%	58.33%
0.95% to 24.65%	8	22.22%	80.56%
24.65% to 48.35%	3	8.33%	88.89%
48.35% to 72.06%	3	8.33%	97.22%
72.06% to 95.76%	1	2.78%	100.00%
Greater than 95.76%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.66%	32.55%	75.00%	68.27%
±2σ	-62.26%	64.16%	91.67%	95.45%
±3σ	-93.86%	95.76%	100.00%	99.73%

Descriptive Statistics

Mean	0.948%
Standard Error	5.267%
Median	-6.220%
Mode	-65.285%
Standard Deviation	31.604%
Sample Variance	998.807%
Kurtosis	0.22
Skewness	0.47
Range	140.976%
Minimum	-65.285%
Maximum	75.691%
Count	36

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.627%	16	44.44%	12.723%
Negative	-21.195%	20	55.56%	-11.775%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	30.92%
12	3 Years	40.29%
20	5 Years	44.58%
40	10 Years	48.72%
80	20 Years	48.72%
200	50 Years	48.72%

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 7.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.78%	0	0.00%	0.00%
-44.78% to -16.66%	0	0.00%	0.00%
-16.66% to 11.45%	0	0.00%	0.00%
11.45% to 39.56%	8	21.62%	21.62%
39.56% to 67.67%	15	40.54%	62.16%
67.67% to 95.79%	9	24.32%	86.49%
95.79% to 123.90%	2	5.41%	91.89%
123.90% to 152.01%	2	5.41%	97.30%
152.01% to 180.13%	0	0.00%	97.30%
Greater than 180.13%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	30.19%	105.16%	86.49%	68.27%
±2σ	-7.29%	142.64%	97.30%	95.45%
±3σ	-44.78%	180.13%	97.30%	99.73%

Descriptive Statistics

Mean	67.675%
Standard Error	6.162%
Median	58.693%
Mode	27.702%
Standard Deviation	37.484%
Sample Variance	1405.052%
Kurtosis	7.53
Skewness	2.36
Range	195.531%
Minimum	27.702%
Maximum	223.233%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	67.675%	37	100.00%	67.675%
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 2.28. Further, an Excess Kurtosis of 7.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.37%	0	0.00%	0.00%
-115.37% to -84.01%	0	0.00%	0.00%
-84.01% to -52.65%	0	0.00%	0.00%
-52.65% to -21.30%	7	18.92%	18.92%
-21.30% to 10.06%	13	35.14%	54.05%
10.06% to 41.42%	13	35.14%	89.19%
41.42% to 72.78%	2	5.41%	94.59%
72.78% to 104.14%	1	2.70%	97.30%
104.14% to 135.50%	0	0.00%	97.30%
Greater than 135.50%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.75%	51.87%	78.38%	68.27%
±2σ	-73.56%	93.68%	97.30%	95.45%
±3σ	-115.37%	135.50%	97.30%	99.73%

Descriptive Statistics

Mean	10.062%
Standard Error	6.874%
Median	6.910%
Mode	-44.428%
Standard Deviation	41.811%
Sample Variance	1748.118%
Kurtosis	7.99
Skewness	2.28
Range	230.460%
Minimum	-44.428%
Maximum	186.032%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.918%	21	56.76%	18.683%
Negative	-19.936%	16	43.24%	-8.621%
Zero	0.000%	0	0.00%	0.000%

SNAP Deep Analytical Report