PRPL - 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	5.33%	4.99%	4.73%	8.02%	14.15%	14.17%	0.55	0.73	0.48	0.84
Weekly	11.18%	13.42%	11.38%	18.23%	31.15%	31.20%	0.47	0.87	0.34	1.19
Monthly	22.90%	34.59%	26.17%	38.71%	64.85%	64.95%	0.33	1.22	0.17	2.33
Quarterly	36.01%	64.62%	48.21%	59.48%	112.32%	112.50%	0.21	1.96	0.07	6.01
Annual	—	—	—	—	224.65%	225.00%	0.07	6.01	0.01	56.85
Option Time Horizon	—	—	—	—	86.41%	86.54%	0.27	1.51	0.11	3.58

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $0.64 | Strike (K): $2.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.0250 (Bid $0.0000 / Ask $0.0500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 224.65% (CRR binomial tree, American, n=20 steps) | BS IV: 224.95% (European Black-Scholes) | Yahoo IV (Annual): 225.00% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2023-04-27	$0.0010

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.98%	11	0.50%	0.50%
-15.98% to -11.98%	22	1.01%	1.51%
-11.98% to -7.98%	59	2.70%	4.21%
-7.98% to -3.98%	255	11.68%	15.90%
-3.98% to 0.02%	810	37.10%	53.00%
0.02% to 4.02%	698	31.97%	84.97%
4.02% to 8.02%	218	9.99%	94.96%
8.02% to 12.02%	61	2.79%	97.76%
12.02% to 16.02%	27	1.24%	98.99%
Greater than 16.02%	22	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.32%	5.35%	79.98%	68.27%
±2σ	-10.65%	10.68%	95.28%	95.45%
±3σ	-15.98%	16.02%	98.49%	99.73%

Descriptive Statistics

Mean	0.017%
Standard Error	0.114%
Median	0.000%
Mode	0.000%
Standard Deviation	5.333%
Sample Variance	28.436%
Kurtosis	8.39
Skewness	0.66
Range	72.013%
Minimum	-32.586%
Maximum	39.427%
Count	2183

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.775%	1026	47.00%	1.774%
Negative	-3.523%	1089	49.88%	-1.757%
Zero	0.000%	68	3.12%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.34%
20	1 Month	6.46%
60	1 Quarter	6.54%
250	1 Year	8.21%
750	3 Years	8.55%
1,250	5 Years	8.02%
2,500	10 Years	7.08%
5,000	20 Years	7.08%
12,500	50 Years	7.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.51. Further, an Excess Kurtosis of 13.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.87%	0	0.00%	0.00%
-7.87% to -4.12%	0	0.00%	0.00%
-4.12% to -0.39%	0	0.00%	0.00%
-0.39% to 3.35%	373	17.08%	17.08%
3.35% to 7.09%	952	43.59%	60.67%
7.09% to 10.83%	532	24.36%	85.03%
10.83% to 14.57%	182	8.33%	93.36%
14.57% to 18.31%	79	3.62%	96.98%
18.31% to 22.05%	34	1.56%	98.53%
Greater than 22.05%	32	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.11%	12.08%	79.53%	68.27%
±2σ	-2.88%	17.06%	96.38%	95.45%
±3σ	-7.86%	22.05%	98.53%	99.73%

Descriptive Statistics

Mean	7.093%
Standard Error	0.107%
Median	6.130%
Mode	0.500%
Standard Deviation	4.986%
Sample Variance	24.860%
Kurtosis	13.55
Skewness	2.51
Range	57.925%
Minimum	0.030%
Maximum	57.955%
Count	2184

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.093%	2184	100.00%	7.093%
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 0.27. Further, an Excess Kurtosis of 5.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.77%	13	0.60%	0.60%
-13.77% to -10.22%	28	1.28%	1.88%
-10.22% to -6.68%	65	2.98%	4.85%
-6.68% to -3.13%	259	11.86%	16.71%
-3.13% to 0.42%	807	36.95%	53.66%
0.42% to 3.97%	644	29.49%	83.15%
3.97% to 7.52%	259	11.86%	95.01%
7.52% to 11.06%	63	2.88%	97.89%
11.06% to 14.61%	23	1.05%	98.95%
Greater than 14.61%	23	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.31%	5.15%	76.83%	68.27%
±2σ	-9.04%	9.88%	94.64%	95.45%
±3σ	-13.77%	14.61%	98.35%	99.73%

Descriptive Statistics

Mean	0.420%
Standard Error	0.101%
Median	0.171%
Mode	0.000%
Standard Deviation	4.731%
Sample Variance	22.382%
Kurtosis	5.11
Skewness	0.27
Range	62.586%
Minimum	-27.886%
Maximum	34.700%
Count	2184

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.534%	1145	52.43%	1.853%
Negative	-3.226%	970	44.41%	-1.433%
Zero	0.000%	69	3.16%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.88. Further, an Excess Kurtosis of 3.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.50%	2	0.41%	0.41%
-33.50% to -25.11%	4	0.82%	1.23%
-25.11% to -16.72%	17	3.48%	4.70%
-16.72% to -8.33%	56	11.45%	16.16%
-8.33% to 0.05%	187	38.24%	54.40%
0.05% to 8.44%	151	30.88%	85.28%
8.44% to 16.83%	41	8.38%	93.66%
16.83% to 25.22%	14	2.86%	96.52%
25.22% to 33.61%	10	2.04%	98.57%
Greater than 33.61%	7	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.13%	11.24%	78.73%	68.27%
±2σ	-22.31%	22.42%	93.87%	95.45%
±3σ	-33.50%	33.61%	98.16%	99.73%

Descriptive Statistics

Mean	0.054%
Standard Error	0.506%
Median	-0.169%
Mode	0.000%
Standard Deviation	11.184%
Sample Variance	125.074%
Kurtosis	3.89
Skewness	0.88
Range	97.899%
Minimum	-40.323%
Maximum	57.576%
Count	489

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.059%	225	46.01%	3.708%
Negative	-7.119%	251	51.33%	-3.654%
Zero	0.000%	13	2.66%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.31%
12	1 Quarter	11.45%
52	1 Year	17.07%
156	3 Years	18.92%
260	5 Years	18.23%
520	10 Years	15.09%
1,040	20 Years	15.09%
2,600	50 Years	15.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.82. Further, an Excess Kurtosis of 4.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.41%	0	0.00%	0.00%
-23.41% to -13.34%	0	0.00%	0.00%
-13.34% to -3.27%	0	0.00%	0.00%
-3.27% to 6.79%	84	17.14%	17.14%
6.79% to 16.86%	222	45.31%	62.45%
16.86% to 26.93%	107	21.84%	84.29%
26.93% to 36.99%	37	7.55%	91.84%
36.99% to 47.06%	22	4.49%	96.33%
47.06% to 57.13%	7	1.43%	97.76%
Greater than 57.13%	11	2.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.44%	30.28%	76.94%	68.27%
±2σ	-9.99%	43.71%	94.69%	95.45%
±3σ	-23.41%	57.13%	97.76%	99.73%

Descriptive Statistics

Mean	16.860%
Standard Error	0.606%
Median	14.156%
Mode	0.899%
Standard Deviation	13.423%
Sample Variance	180.166%
Kurtosis	4.88
Skewness	1.82
Range	88.920%
Minimum	0.071%
Maximum	88.991%
Count	490

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.860%	490	100.00%	16.860%
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 0.95. Further, an Excess Kurtosis of 5.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.61%	1	0.20%	0.20%
-32.61% to -24.08%	7	1.43%	1.63%
-24.08% to -15.54%	23	4.69%	6.33%
-15.54% to -7.00%	39	7.96%	14.29%
-7.00% to 1.53%	209	42.65%	56.94%
1.53% to 10.07%	139	28.37%	85.31%
10.07% to 18.61%	42	8.57%	93.88%
18.61% to 27.14%	15	3.06%	96.94%
27.14% to 35.68%	10	2.04%	98.98%
Greater than 35.68%	5	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.85%	12.91%	77.55%	68.27%
±2σ	-21.23%	24.30%	93.88%	95.45%
±3σ	-32.61%	35.68%	98.78%	99.73%

Descriptive Statistics

Mean	1.532%
Standard Error	0.514%
Median	0.505%
Mode	0.000%
Standard Deviation	11.382%
Sample Variance	129.543%
Kurtosis	5.24
Skewness	0.95
Range	107.127%
Minimum	-35.577%
Maximum	71.550%
Count	490

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.224%	270	55.10%	4.532%
Negative	-7.066%	208	42.45%	-2.999%
Zero	0.000%	12	2.45%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 1.98 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.36%	0	0.00%	0.00%
-68.36% to -51.18%	1	0.82%	0.82%
-51.18% to -34.01%	6	4.92%	5.74%
-34.01% to -16.83%	18	14.75%	20.49%
-16.83% to 0.35%	45	36.89%	57.38%
0.35% to 17.53%	31	25.41%	82.79%
17.53% to 34.71%	11	9.02%	91.80%
34.71% to 51.88%	7	5.74%	97.54%
51.88% to 69.06%	1	0.82%	98.36%
Greater than 69.06%	2	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.55%	23.25%	74.59%	68.27%
±2σ	-45.46%	46.16%	95.90%	95.45%
±3σ	-68.36%	69.06%	98.36%	99.73%

Descriptive Statistics

Mean	0.351%
Standard Error	2.074%
Median	-0.167%
Mode	0.000%
Standard Deviation	22.904%
Sample Variance	524.590%
Kurtosis	1.98
Skewness	0.78
Range	140.527%
Minimum	-58.174%
Maximum	82.353%
Count	122

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.141%	58	47.54%	8.149%
Negative	-15.344%	62	50.82%	-7.798%
Zero	0.000%	2	1.64%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.85%
12	1 Year	33.10%
36	3 Years	39.85%
60	5 Years	38.71%
120	10 Years	31.23%
240	20 Years	30.80%
600	50 Years	30.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.95. Further, an Excess Kurtosis of 7.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.56%	0	0.00%	0.00%
-64.56% to -38.62%	0	0.00%	0.00%
-38.62% to -12.67%	0	0.00%	0.00%
-12.67% to 13.27%	28	22.76%	22.76%
13.27% to 39.21%	42	34.15%	56.91%
39.21% to 65.16%	31	25.20%	82.11%
65.16% to 91.10%	17	13.82%	95.93%
91.10% to 117.05%	2	1.63%	97.56%
117.05% to 142.99%	1	0.81%	98.37%
Greater than 142.99%	2	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.62%	73.81%	71.54%	68.27%
±2σ	-29.97%	108.40%	97.56%	95.45%
±3σ	-64.56%	142.99%	98.37%	99.73%

Descriptive Statistics

Mean	39.214%
Standard Error	3.119%
Median	34.375%
Mode	0.101%
Standard Deviation	34.592%
Sample Variance	1196.607%
Kurtosis	7.20
Skewness	1.95
Range	225.238%
Minimum	0.101%
Maximum	225.339%
Count	123

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.214%	123	100.00%	39.214%
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 1.71. Further, an Excess Kurtosis of 6.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -73.06%	0	0.00%	0.00%
-73.06% to -53.44%	0	0.00%	0.00%
-53.44% to -33.81%	3	2.44%	2.44%
-33.81% to -14.18%	18	14.63%	17.07%
-14.18% to 5.45%	56	45.53%	62.60%
5.45% to 25.07%	28	22.76%	85.37%
25.07% to 44.70%	10	8.13%	93.50%
44.70% to 64.33%	3	2.44%	95.93%
64.33% to 83.95%	3	2.44%	98.37%
Greater than 83.95%	2	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.73%	31.62%	80.49%	68.27%
±2σ	-46.90%	57.79%	95.12%	95.45%
±3σ	-73.06%	83.96%	98.37%	99.73%

Descriptive Statistics

Mean	5.445%
Standard Error	2.360%
Median	0.200%
Mode	0.000%
Standard Deviation	26.170%
Sample Variance	684.859%
Kurtosis	6.13
Skewness	1.71
Range	188.070%
Minimum	-46.521%
Maximum	141.549%
Count	123

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.701%	67	54.47%	11.276%
Negative	-13.282%	54	43.90%	-5.831%
Zero	0.000%	2	1.63%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.56. Further, an Excess Kurtosis of 5.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.38%	0	0.00%	0.00%
-108.38% to -81.37%	0	0.00%	0.00%
-81.37% to -54.36%	2	4.76%	4.76%
-54.36% to -27.35%	4	9.52%	14.29%
-27.35% to -0.34%	14	33.33%	47.62%
-0.34% to 26.67%	18	42.86%	90.48%
26.67% to 53.68%	1	2.38%	92.86%
53.68% to 80.69%	2	4.76%	97.62%
80.69% to 107.70%	0	0.00%	97.62%
Greater than 107.70%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.35%	35.68%	78.57%	68.27%
±2σ	-72.37%	71.69%	95.24%	95.45%
±3σ	-108.38%	107.70%	97.62%	99.73%

Descriptive Statistics

Mean	-0.337%
Standard Error	5.557%
Median	-0.090%
Mode	-68.910%
Standard Deviation	36.014%
Sample Variance	1296.976%
Kurtosis	5.46
Skewness	1.56
Range	211.157%
Minimum	-68.910%
Maximum	142.247%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.842%	21	50.00%	10.921%
Negative	-22.516%	21	50.00%	-11.258%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	42.67%
12	3 Years	59.98%
20	5 Years	59.48%
40	10 Years	51.70%
80	20 Years	49.54%
200	50 Years	49.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 1.39 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -118.48%	0	0.00%	0.00%
-118.48% to -70.01%	0	0.00%	0.00%
-70.01% to -21.54%	0	0.00%	0.00%
-21.54% to 26.93%	11	25.58%	25.58%
26.93% to 75.40%	16	37.21%	62.79%
75.40% to 123.86%	9	20.93%	83.72%
123.86% to 172.33%	3	6.98%	90.70%
172.33% to 220.80%	2	4.65%	95.35%
220.80% to 269.27%	2	4.65%	100.00%
Greater than 269.27%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.77%	140.02%	65.12%	68.27%
±2σ	-53.85%	204.64%	93.02%	95.45%
±3σ	-118.48%	269.27%	100.00%	99.73%

Descriptive Statistics

Mean	75.396%
Standard Error	9.855%
Median	69.472%
Mode	1.712%
Standard Deviation	64.624%
Sample Variance	4176.318%
Kurtosis	1.39
Skewness	1.20
Range	259.374%
Minimum	1.712%
Maximum	261.086%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.396%	43	100.00%	75.396%
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 2.36. Further, an Excess Kurtosis of 7.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -130.36%	0	0.00%	0.00%
-130.36% to -94.21%	0	0.00%	0.00%
-94.21% to -58.05%	1	2.33%	2.33%
-58.05% to -21.90%	3	6.98%	9.30%
-21.90% to 14.26%	26	60.47%	69.77%
14.26% to 50.41%	7	16.28%	86.05%
50.41% to 86.56%	2	4.65%	90.70%
86.56% to 122.72%	2	4.65%	95.35%
122.72% to 158.87%	1	2.33%	97.67%
Greater than 158.87%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.95%	62.46%	81.40%	68.27%
±2σ	-82.16%	110.67%	95.35%	95.45%
±3σ	-130.36%	158.87%	97.67%	99.73%

Descriptive Statistics

Mean	14.256%
Standard Error	7.351%
Median	1.562%
Mode	-58.966%
Standard Deviation	48.206%
Sample Variance	2323.860%
Kurtosis	7.49
Skewness	2.36
Range	277.523%
Minimum	-58.966%
Maximum	218.557%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.577%	25	58.14%	20.684%
Negative	-15.357%	18	41.86%	-6.428%
Zero	0.000%	0	0.00%	0.000%

PRPL Deep Analytical Report