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	4.53%	2.53%	3.13%	5.38%	4.72%	4.72%	4.28	4.71	4.09	4.93
Weekly	9.29%	9.15%	9.48%	12.88%	10.40%	10.40%	4.05	4.98	3.65	5.53
Monthly	17.69%	18.65%	19.66%	28.20%	21.65%	21.65%	3.62	5.58	2.91	6.92
Quarterly	31.86%	37.40%	42.23%	44.74%	37.50%	37.50%	3.09	6.53	2.12	9.51
Annual	—	—	—	—	75.01%	75.00%	2.12	9.51	1.00	20.13
Option Time Horizon	—	—	—	—	28.31%	28.31%	3.38	5.96	2.55	7.91

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $4.49 | Strike (K): $5.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.3250 (Bid $0.2900 / Ask $0.3600) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 75.01% (CRR binomial tree, American, n=20 steps) | BS IV: 75.01% (European Black-Scholes) | Yahoo IV (Annual): 75.00% → 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 0.75. Further, an Excess Kurtosis of 31.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.55%	17	0.75%	0.75%
-13.55% to -10.16%	7	0.31%	1.05%
-10.16% to -6.76%	48	2.11%	3.16%
-6.76% to -3.37%	241	10.59%	13.75%
-3.37% to 0.03%	850	37.35%	51.10%
0.03% to 3.42%	789	34.67%	85.76%
3.42% to 6.82%	246	10.81%	96.57%
6.82% to 10.21%	55	2.42%	98.99%
10.21% to 13.61%	12	0.53%	99.52%
Greater than 13.61%	11	0.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.50%	4.56%	83.17%	68.27%
±2σ	-9.03%	9.08%	96.88%	95.45%
±3σ	-13.55%	13.61%	98.77%	99.73%

Descriptive Statistics

Mean	0.029%
Standard Error	0.095%
Median	-0.062%
Mode	0.000%
Standard Deviation	4.527%
Sample Variance	20.495%
Kurtosis	31.08
Skewness	0.75
Range	101.896%
Minimum	-43.080%
Maximum	58.816%
Count	2276

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.901%	1113	48.90%	1.419%
Negative	-2.770%	1142	50.18%	-1.390%
Zero	0.000%	21	0.92%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.44%
20	1 Month	4.39%
60	1 Quarter	4.50%
250	1 Year	4.70%
750	3 Years	4.64%
1,250	5 Years	5.38%
2,500	10 Years	5.23%
5,000	20 Years	5.23%
12,500	50 Years	5.23%

High-to-Low 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 10.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.75%	0	0.00%	0.00%
-2.75% to -0.85%	0	0.00%	0.00%
-0.85% to 1.05%	2	0.09%	0.09%
1.05% to 2.95%	467	20.51%	20.60%
2.95% to 4.85%	914	40.14%	60.74%
4.85% to 6.75%	522	22.92%	83.66%
6.75% to 8.65%	209	9.18%	92.84%
8.65% to 10.55%	89	3.91%	96.75%
10.55% to 12.45%	36	1.58%	98.33%
Greater than 12.45%	38	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.32%	7.39%	79.71%	68.27%
±2σ	-0.22%	9.92%	95.92%	95.45%
±3σ	-2.75%	12.45%	98.33%	99.73%

Descriptive Statistics

Mean	4.852%
Standard Error	0.053%
Median	4.302%
Mode	5.089%
Standard Deviation	2.534%
Sample Variance	6.423%
Kurtosis	10.30
Skewness	2.28
Range	27.524%
Minimum	0.841%
Maximum	28.365%
Count	2277

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.852%	2277	100.00%	4.852%
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 2.63 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.36%	11	0.48%	0.48%
-9.36% to -7.01%	26	1.14%	1.62%
-7.01% to -4.66%	93	4.08%	5.71%
-4.66% to -2.31%	309	13.57%	19.28%
-2.31% to 0.03%	714	31.36%	50.64%
0.03% to 2.38%	691	30.35%	80.98%
2.38% to 4.73%	307	13.48%	94.47%
4.73% to 7.07%	85	3.73%	98.20%
7.07% to 9.42%	27	1.19%	99.39%
Greater than 9.42%	14	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.10%	3.16%	73.30%	68.27%
±2σ	-6.23%	6.29%	95.08%	95.45%
±3σ	-9.36%	9.42%	98.90%	99.73%

Descriptive Statistics

Mean	0.032%
Standard Error	0.066%
Median	0.000%
Mode	0.000%
Standard Deviation	3.129%
Sample Variance	9.791%
Kurtosis	2.63
Skewness	-0.01
Range	37.218%
Minimum	-18.707%
Maximum	18.511%
Count	2277

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.391%	1125	49.41%	1.181%
Negative	-2.340%	1118	49.10%	-1.149%
Zero	0.000%	34	1.49%	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 2.59 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.78%	5	1.06%	1.06%
-27.78% to -20.81%	6	1.27%	2.33%
-20.81% to -13.85%	10	2.12%	4.45%
-13.85% to -6.88%	67	14.19%	18.64%
-6.88% to 0.08%	156	33.05%	51.69%
0.08% to 7.05%	146	30.93%	82.63%
7.05% to 14.01%	55	11.65%	94.28%
14.01% to 20.98%	19	4.03%	98.31%
20.98% to 27.94%	2	0.42%	98.73%
Greater than 27.94%	6	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.20%	9.37%	76.06%	68.27%
±2σ	-18.49%	18.65%	94.28%	95.45%
±3σ	-27.78%	27.94%	97.67%	99.73%

Descriptive Statistics

Mean	0.082%
Standard Error	0.427%
Median	-0.419%
Mode	-8.364%
Standard Deviation	9.286%
Sample Variance	86.226%
Kurtosis	2.59
Skewness	0.19
Range	78.756%
Minimum	-34.757%
Maximum	43.999%
Count	472

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.067%	230	48.73%	3.444%
Negative	-6.583%	241	51.06%	-3.361%
Zero	0.000%	1	0.21%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.06%
12	1 Quarter	11.56%
52	1 Year	11.07%
156	3 Years	11.04%
260	5 Years	12.88%
520	10 Years	12.56%
1,040	20 Years	12.56%
2,600	50 Years	12.56%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.96. Further, an Excess Kurtosis of 12.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.91%	0	0.00%	0.00%
-13.91% to -7.05%	0	0.00%	0.00%
-7.05% to -0.19%	0	0.00%	0.00%
-0.19% to 6.67%	61	12.90%	12.90%
6.67% to 13.53%	245	51.80%	64.69%
13.53% to 20.39%	105	22.20%	86.89%
20.39% to 27.25%	34	7.19%	94.08%
27.25% to 34.10%	13	2.75%	96.83%
34.10% to 40.96%	6	1.27%	98.10%
Greater than 40.96%	9	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.38%	22.67%	87.95%	68.27%
±2σ	-4.77%	31.82%	95.35%	95.45%
±3σ	-13.91%	40.96%	98.10%	99.73%

Descriptive Statistics

Mean	13.526%
Standard Error	0.421%
Median	11.127%
Mode	13.491%
Standard Deviation	9.146%
Sample Variance	83.642%
Kurtosis	12.40
Skewness	2.96
Range	68.519%
Minimum	2.754%
Maximum	71.273%
Count	473

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.526%	473	100.00%	13.526%
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 1.08. Further, an Excess Kurtosis of 4.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.66%	1	0.21%	0.21%
-27.66% to -20.55%	5	1.06%	1.27%
-20.55% to -13.44%	13	2.75%	4.02%
-13.44% to -6.32%	67	14.16%	18.18%
-6.32% to 0.79%	168	35.52%	53.70%
0.79% to 7.90%	138	29.18%	82.88%
7.90% to 15.02%	60	12.68%	95.56%
15.02% to 22.13%	7	1.48%	97.04%
22.13% to 29.25%	5	1.06%	98.10%
Greater than 29.25%	9	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.70%	10.27%	78.22%	68.27%
±2σ	-18.18%	19.76%	95.35%	95.45%
±3σ	-27.66%	29.24%	97.89%	99.73%

Descriptive Statistics

Mean	0.790%
Standard Error	0.436%
Median	-0.056%
Mode	-0.423%
Standard Deviation	9.485%
Sample Variance	89.956%
Kurtosis	4.45
Skewness	1.08
Range	84.289%
Minimum	-31.476%
Maximum	52.813%
Count	473

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.616%	234	49.47%	3.768%
Negative	-5.943%	237	50.11%	-2.978%
Zero	0.000%	2	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.30. Further, an Excess Kurtosis of 0.63 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.98%	0	0.00%	0.00%
-52.98% to -39.71%	1	0.93%	0.93%
-39.71% to -26.45%	4	3.70%	4.63%
-26.45% to -13.18%	20	18.52%	23.15%
-13.18% to 0.09%	28	25.93%	49.07%
0.09% to 13.36%	34	31.48%	80.56%
13.36% to 26.62%	14	12.96%	93.52%
26.62% to 39.89%	4	3.70%	97.22%
39.89% to 53.16%	3	2.78%	100.00%
Greater than 53.16%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.60%	17.78%	71.30%	68.27%
±2σ	-35.29%	35.47%	95.37%	95.45%
±3σ	-52.98%	53.16%	100.00%	99.73%

Descriptive Statistics

Mean	0.089%
Standard Error	1.702%
Median	0.148%
Mode	-50.422%
Standard Deviation	17.690%
Sample Variance	312.941%
Kurtosis	0.63
Skewness	0.30
Range	101.284%
Minimum	-50.422%
Maximum	50.862%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.528%	55	50.93%	6.889%
Negative	-13.857%	53	49.07%	-6.800%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.05%
12	1 Year	23.10%
36	3 Years	25.58%
60	5 Years	28.20%
120	10 Years	27.49%
240	20 Years	27.49%
600	50 Years	27.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.47. Further, an Excess Kurtosis of 9.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.55%	0	0.00%	0.00%
-22.55% to -8.56%	0	0.00%	0.00%
-8.56% to 5.43%	0	0.00%	0.00%
5.43% to 19.42%	24	22.02%	22.02%
19.42% to 33.41%	46	42.20%	64.22%
33.41% to 47.40%	20	18.35%	82.57%
47.40% to 61.38%	9	8.26%	90.83%
61.38% to 75.37%	7	6.42%	97.25%
75.37% to 89.36%	2	1.83%	99.08%
Greater than 89.36%	1	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.75%	52.06%	85.32%	68.27%
±2σ	-3.90%	70.71%	96.33%	95.45%
±3σ	-22.55%	89.36%	99.08%	99.73%

Descriptive Statistics

Mean	33.407%
Standard Error	1.787%
Median	28.499%
Mode	12.518%
Standard Deviation	18.652%
Sample Variance	347.885%
Kurtosis	9.65
Skewness	2.47
Range	128.040%
Minimum	12.518%
Maximum	140.558%
Count	109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.407%	109	100.00%	33.407%
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 1.34. Further, an Excess Kurtosis of 4.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.56%	0	0.00%	0.00%
-55.56% to -40.81%	0	0.00%	0.00%
-40.81% to -26.07%	4	3.67%	3.67%
-26.07% to -11.32%	17	15.60%	19.27%
-11.32% to 3.43%	40	36.70%	55.96%
3.43% to 18.17%	26	23.85%	79.82%
18.17% to 32.92%	16	14.68%	94.50%
32.92% to 47.67%	4	3.67%	98.17%
47.67% to 62.41%	1	0.92%	99.08%
Greater than 62.41%	1	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.23%	23.09%	73.39%	68.27%
±2σ	-35.90%	42.75%	96.33%	95.45%
±3σ	-55.56%	62.41%	99.08%	99.73%

Descriptive Statistics

Mean	3.428%
Standard Error	1.883%
Median	0.505%
Mode	-35.718%
Standard Deviation	19.662%
Sample Variance	386.578%
Kurtosis	4.56
Skewness	1.34
Range	136.001%
Minimum	-35.718%
Maximum	100.283%
Count	109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.519%	55	50.46%	8.840%
Negative	-11.131%	53	48.62%	-5.412%
Zero	0.000%	1	0.92%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.46. Further, an Excess Kurtosis of 0.17 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -94.89%	0	0.00%	0.00%
-94.89% to -71.00%	0	0.00%	0.00%
-71.00% to -47.10%	2	5.56%	5.56%
-47.10% to -23.20%	6	16.67%	22.22%
-23.20% to 0.69%	13	36.11%	58.33%
0.69% to 24.59%	8	22.22%	80.56%
24.59% to 48.49%	3	8.33%	88.89%
48.49% to 72.38%	3	8.33%	97.22%
72.38% to 96.28%	1	2.78%	100.00%
Greater than 96.28%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.17%	32.55%	72.22%	68.27%
±2σ	-63.03%	64.42%	91.67%	95.45%
±3σ	-94.89%	96.28%	100.00%	99.73%

Descriptive Statistics

Mean	0.693%
Standard Error	5.310%
Median	-6.220%
Mode	-65.285%
Standard Deviation	31.862%
Sample Variance	1015.160%
Kurtosis	0.17
Skewness	0.46
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	-21.654%	20	55.56%	-12.030%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.76%
12	3 Years	40.57%
20	5 Years	44.74%
40	10 Years	48.82%
80	20 Years	48.82%
200	50 Years	48.82%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.31%	0	0.00%	0.00%
-44.31% to -16.26%	0	0.00%	0.00%
-16.26% to 11.79%	0	0.00%	0.00%
11.79% to 39.84%	8	21.62%	21.62%
39.84% to 67.88%	15	40.54%	62.16%
67.88% to 95.93%	9	24.32%	86.49%
95.93% to 123.98%	2	5.41%	91.89%
123.98% to 152.03%	2	5.41%	97.30%
152.03% to 180.08%	0	0.00%	97.30%
Greater than 180.08%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	30.49%	105.28%	86.49%	68.27%
±2σ	-6.91%	142.68%	97.30%	95.45%
±3σ	-44.31%	180.08%	97.30%	99.73%

Descriptive Statistics

Mean	67.884%
Standard Error	6.148%
Median	58.693%
Mode	27.702%
Standard Deviation	37.398%
Sample Variance	1398.645%
Kurtosis	7.57
Skewness	2.37
Range	195.531%
Minimum	27.702%
Maximum	223.233%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	67.884%	37	100.00%	67.884%
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 2.20. Further, an Excess Kurtosis of 7.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -116.11%	0	0.00%	0.00%
-116.11% to -84.44%	0	0.00%	0.00%
-84.44% to -52.77%	0	0.00%	0.00%
-52.77% to -21.10%	7	18.92%	18.92%
-21.10% to 10.57%	13	35.14%	54.05%
10.57% to 42.24%	12	32.43%	86.49%
42.24% to 73.92%	3	8.11%	94.59%
73.92% to 105.59%	1	2.70%	97.30%
105.59% to 137.26%	0	0.00%	97.30%
Greater than 137.26%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.65%	52.80%	75.68%	68.27%
±2σ	-73.88%	95.03%	97.30%	95.45%
±3σ	-116.11%	137.26%	97.30%	99.73%

Descriptive Statistics

Mean	10.574%
Standard Error	6.942%
Median	6.910%
Mode	-44.428%
Standard Deviation	42.228%
Sample Variance	1783.212%
Kurtosis	7.47
Skewness	2.20
Range	230.460%
Minimum	-44.428%
Maximum	186.032%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.819%	21	56.76%	19.195%
Negative	-19.936%	16	43.24%	-8.621%
Zero	0.000%	0	0.00%	0.000%

SNAP Deep Analytical Report