PLUG - 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	6.11%	5.43%	5.30%	8.15%	6.63%	6.69%	1.75	2.00	1.64	2.14
Weekly	14.15%	17.27%	13.65%	19.69%	14.59%	14.73%	1.62	2.16	1.40	2.50
Monthly	29.13%	44.94%	28.18%	41.39%	30.37%	30.67%	1.38	2.53	1.02	3.43
Quarterly	80.36%	140.25%	47.95%	74.33%	52.60%	53.13%	1.11	3.16	0.65	5.35
Annual	—	—	—	—	105.20%	106.25%	0.65	5.35	0.23	15.33
Option Time Horizon	—	—	—	—	34.39%	34.73%	1.33	2.64	0.94	3.72

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $1.87 | Strike (K): $2.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.2100 (Bid $0.1800 / Ask $0.2400) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 105.20% (CRR binomial tree, American, n=20 steps) | BS IV: 106.44% (European Black-Scholes) | Yahoo IV (Annual): 106.25% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.53. Further, an Excess Kurtosis of 36.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.22%	23	0.35%	0.35%
-18.22% to -13.64%	40	0.60%	0.95%
-13.64% to -9.06%	149	2.25%	3.21%
-9.06% to -4.47%	766	11.58%	14.79%
-4.47% to 0.11%	2793	42.24%	57.03%
0.11% to 4.69%	1942	29.37%	86.40%
4.69% to 9.27%	578	8.74%	95.15%
9.27% to 13.86%	176	2.66%	97.81%
13.86% to 18.44%	72	1.09%	98.90%
Greater than 18.44%	73	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.00%	6.22%	81.78%	68.27%
±2σ	-12.11%	12.33%	95.86%	95.45%
±3σ	-18.22%	18.44%	98.55%	99.73%

Descriptive Statistics

Mean	0.109%
Standard Error	0.075%
Median	-0.312%
Mode	0.000%
Standard Deviation	6.110%
Sample Variance	37.331%
Kurtosis	36.53
Skewness	2.53
Range	169.931%
Minimum	-52.000%
Maximum	117.931%
Count	6612

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.597%	2846	43.04%	1.979%
Negative	-3.642%	3395	51.35%	-1.870%
Zero	0.000%	371	5.61%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.06%
20	1 Month	7.89%
60	1 Quarter	8.18%
250	1 Year	9.81%
750	3 Years	8.72%
1,250	5 Years	8.15%
2,500	10 Years	7.16%
5,000	20 Years	7.43%
12,500	50 Years	7.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.59. Further, an Excess Kurtosis of 49.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.86%	0	0.00%	0.00%
-8.86% to -4.78%	0	0.00%	0.00%
-4.78% to -0.71%	0	0.00%	0.00%
-0.71% to 3.36%	839	12.69%	12.69%
3.36% to 7.43%	3411	51.58%	64.27%
7.43% to 11.50%	1472	22.26%	86.53%
11.50% to 15.57%	502	7.59%	94.12%
15.57% to 19.64%	186	2.81%	96.93%
19.64% to 23.71%	84	1.27%	98.20%
Greater than 23.71%	119	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.00%	12.86%	88.17%	68.27%
±2σ	-3.43%	18.29%	96.16%	95.45%
±3σ	-8.85%	23.71%	98.20%	99.73%

Descriptive Statistics

Mean	7.429%
Standard Error	0.067%
Median	6.090%
Mode	5.263%
Standard Deviation	5.428%
Sample Variance	29.461%
Kurtosis	49.63
Skewness	4.59
Range	105.907%
Minimum	0.800%
Maximum	106.707%
Count	6613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.429%	6613	100.00%	7.429%
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 1.81. Further, an Excess Kurtosis of 34.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.27%	46	0.70%	0.70%
-15.27% to -11.29%	68	1.03%	1.72%
-11.29% to -7.32%	195	2.95%	4.67%
-7.32% to -3.34%	747	11.30%	15.97%
-3.34% to 0.64%	2282	34.51%	50.48%
0.64% to 4.62%	2231	33.74%	84.21%
4.62% to 8.60%	760	11.49%	95.71%
8.60% to 12.57%	178	2.69%	98.40%
12.57% to 16.55%	54	0.82%	99.21%
Greater than 16.55%	52	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.66%	5.95%	80.01%	68.27%
±2σ	-9.97%	11.25%	95.60%	95.45%
±3σ	-15.27%	16.55%	98.52%	99.73%

Descriptive Statistics

Mean	0.641%
Standard Error	0.065%
Median	0.579%
Mode	0.000%
Standard Deviation	5.304%
Sample Variance	28.129%
Kurtosis	34.86
Skewness	1.81
Range	145.563%
Minimum	-47.785%
Maximum	97.778%
Count	6613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.869%	3575	54.06%	2.092%
Negative	-3.590%	2673	40.42%	-1.451%
Zero	0.000%	365	5.52%	0.000%

Close-to-Close 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 18.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.88%	3	0.22%	0.22%
-41.88% to -31.27%	8	0.58%	0.80%
-31.27% to -20.66%	37	2.69%	3.50%
-20.66% to -10.05%	150	10.92%	14.42%
-10.05% to 0.56%	571	41.59%	56.01%
0.56% to 11.18%	414	30.15%	86.16%
11.18% to 21.79%	120	8.74%	94.90%
21.79% to 32.40%	42	3.06%	97.96%
32.40% to 43.01%	11	0.80%	98.76%
Greater than 43.01%	17	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.58%	14.71%	82.16%	68.27%
±2σ	-27.73%	28.86%	95.92%	95.45%
±3σ	-41.88%	43.01%	98.54%	99.73%

Descriptive Statistics

Mean	0.564%
Standard Error	0.382%
Median	-0.915%
Mode	0.000%
Standard Deviation	14.149%
Sample Variance	200.182%
Kurtosis	18.35
Skewness	2.47
Range	212.285%
Minimum	-64.103%
Maximum	148.182%
Count	1373

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.620%	616	44.87%	4.765%
Negative	-7.944%	726	52.88%	-4.201%
Zero	0.000%	31	2.26%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.18%
12	1 Quarter	17.26%
52	1 Year	24.30%
156	3 Years	21.12%
260	5 Years	19.69%
520	10 Years	17.14%
1,040	20 Years	17.23%
2,600	50 Years	17.41%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.44. Further, an Excess Kurtosis of 49.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.36%	0	0.00%	0.00%
-32.36% to -19.41%	0	0.00%	0.00%
-19.41% to -6.46%	0	0.00%	0.00%
-6.46% to 6.49%	90	6.55%	6.55%
6.49% to 19.44%	801	58.30%	64.85%
19.44% to 32.39%	332	24.16%	89.01%
32.39% to 45.34%	84	6.11%	95.12%
45.34% to 58.29%	34	2.47%	97.60%
58.29% to 71.24%	11	0.80%	98.40%
Greater than 71.24%	22	1.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.17%	36.71%	91.48%	68.27%
±2σ	-15.10%	53.98%	97.02%	95.45%
±3σ	-32.36%	71.24%	98.40%	99.73%

Descriptive Statistics

Mean	19.440%
Standard Error	0.466%
Median	15.074%
Mode	11.111%
Standard Deviation	17.268%
Sample Variance	298.191%
Kurtosis	49.65
Skewness	5.44
Range	229.793%
Minimum	3.540%
Maximum	233.333%
Count	1374

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.440%	1374	100.00%	19.440%
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 2.57. Further, an Excess Kurtosis of 28.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.25%	8	0.58%	0.58%
-39.25% to -29.02%	10	0.73%	1.31%
-29.02% to -18.78%	30	2.18%	3.49%
-18.78% to -8.54%	164	11.94%	15.43%
-8.54% to 1.70%	505	36.75%	52.18%
1.70% to 11.93%	478	34.79%	86.97%
11.93% to 22.17%	115	8.37%	95.34%
22.17% to 32.41%	40	2.91%	98.25%
32.41% to 42.65%	11	0.80%	99.05%
Greater than 42.65%	13	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.95%	15.35%	81.15%	68.27%
±2σ	-25.60%	29.00%	96.00%	95.45%
±3σ	-39.25%	42.65%	98.47%	99.73%

Descriptive Statistics

Mean	1.697%
Standard Error	0.368%
Median	1.256%
Mode	0.000%
Standard Deviation	13.650%
Sample Variance	186.320%
Kurtosis	28.84
Skewness	2.57
Range	228.938%
Minimum	-57.509%
Maximum	171.429%
Count	1374

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.609%	744	54.15%	5.203%
Negative	-8.138%	592	43.09%	-3.506%
Zero	0.000%	38	2.77%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.62. Further, an Excess Kurtosis of 14.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.42%	0	0.00%	0.00%
-85.42% to -63.58%	0	0.00%	0.00%
-63.58% to -41.73%	6	1.90%	1.90%
-41.73% to -19.89%	43	13.61%	15.51%
-19.89% to 1.96%	144	45.57%	61.08%
1.96% to 23.80%	79	25.00%	86.08%
23.80% to 45.64%	25	7.91%	93.99%
45.64% to 67.49%	8	2.53%	96.52%
67.49% to 89.33%	5	1.58%	98.10%
Greater than 89.33%	6	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.17%	31.08%	82.59%	68.27%
±2σ	-56.30%	60.21%	94.94%	95.45%
±3σ	-85.42%	89.33%	98.10%	99.73%

Descriptive Statistics

Mean	1.955%
Standard Error	1.638%
Median	-1.870%
Mode	0.000%
Standard Deviation	29.126%
Sample Variance	848.321%
Kurtosis	14.50
Skewness	2.62
Range	295.327%
Minimum	-63.469%
Maximum	231.858%
Count	316

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.185%	138	43.67%	10.125%
Negative	-14.923%	173	54.75%	-8.170%
Zero	0.000%	5	1.58%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.15%
12	1 Year	51.33%
36	3 Years	44.64%
60	5 Years	41.39%
120	10 Years	38.67%
240	20 Years	38.82%
600	50 Years	39.68%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.71. Further, an Excess Kurtosis of 37.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.75%	0	0.00%	0.00%
-84.75% to -51.05%	0	0.00%	0.00%
-51.05% to -17.34%	0	0.00%	0.00%
-17.34% to 16.37%	21	6.62%	6.62%
16.37% to 50.08%	194	61.20%	67.82%
50.08% to 83.78%	63	19.87%	87.70%
83.78% to 117.49%	24	7.57%	95.27%
117.49% to 151.20%	6	1.89%	97.16%
151.20% to 184.90%	3	0.95%	98.11%
Greater than 184.90%	6	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.13%	95.02%	91.17%	68.27%
±2σ	-39.81%	139.96%	96.53%	95.45%
±3σ	-84.75%	184.90%	98.11%	99.73%

Descriptive Statistics

Mean	50.075%
Standard Error	2.524%
Median	39.216%
Mode	15.789%
Standard Deviation	44.943%
Sample Variance	2019.886%
Kurtosis	37.16
Skewness	4.71
Range	498.090%
Minimum	9.677%
Maximum	507.767%
Count	317

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.075%	317	100.00%	50.075%
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 2.01. Further, an Excess Kurtosis of 10.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.08%	0	0.00%	0.00%
-79.08% to -57.94%	1	0.32%	0.32%
-57.94% to -36.80%	11	3.47%	3.79%
-36.80% to -15.67%	42	13.25%	17.03%
-15.67% to 5.47%	124	39.12%	56.15%
5.47% to 26.61%	93	29.34%	85.49%
26.61% to 47.75%	27	8.52%	94.01%
47.75% to 68.89%	11	3.47%	97.48%
68.89% to 90.03%	4	1.26%	98.74%
Greater than 90.03%	4	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.71%	33.66%	81.07%	68.27%
±2σ	-50.90%	61.84%	96.21%	95.45%
±3σ	-79.08%	90.03%	98.74%	99.73%

Descriptive Statistics

Mean	5.473%
Standard Error	1.583%
Median	2.548%
Mode	0.000%
Standard Deviation	28.185%
Sample Variance	794.389%
Kurtosis	10.09
Skewness	2.01
Range	254.771%
Minimum	-70.933%
Maximum	183.838%
Count	317

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.366%	178	56.15%	11.997%
Negative	-15.207%	136	42.90%	-6.524%
Zero	0.000%	3	0.95%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.12. Further, an Excess Kurtosis of 19.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -231.35%	0	0.00%	0.00%
-231.35% to -171.08%	0	0.00%	0.00%
-171.08% to -110.81%	0	0.00%	0.00%
-110.81% to -50.54%	7	6.60%	6.60%
-50.54% to 9.73%	69	65.09%	71.70%
9.73% to 70.00%	20	18.87%	90.57%
70.00% to 130.27%	6	5.66%	96.23%
130.27% to 190.54%	1	0.94%	97.17%
190.54% to 250.81%	0	0.00%	97.17%
Greater than 250.81%	3	2.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-70.63%	90.09%	95.28%	68.27%
±2σ	-150.99%	170.45%	96.23%	95.45%
±3σ	-231.35%	250.81%	97.17%	99.73%

Descriptive Statistics

Mean	9.729%
Standard Error	7.805%
Median	-6.482%
Mode	-64.444%
Standard Deviation	80.359%
Sample Variance	6457.589%
Kurtosis	19.83
Skewness	4.12
Range	550.382%
Minimum	-64.444%
Maximum	485.938%
Count	106

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	59.830%	43	40.57%	24.271%
Negative	-24.467%	63	59.43%	-14.542%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	109.28%
12	3 Years	83.61%
20	5 Years	74.33%
40	10 Years	79.70%
80	20 Years	81.13%
200	50 Years	82.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.40. Further, an Excess Kurtosis of 23.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -300.12%	0	0.00%	0.00%
-300.12% to -194.93%	0	0.00%	0.00%
-194.93% to -89.73%	0	0.00%	0.00%
-89.73% to 15.45%	0	0.00%	0.00%
15.45% to 120.64%	72	67.29%	67.29%
120.64% to 225.83%	24	22.43%	89.72%
225.83% to 331.02%	7	6.54%	96.26%
331.02% to 436.21%	1	0.93%	97.20%
436.21% to 541.40%	1	0.93%	98.13%
Greater than 541.40%	2	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.61%	260.90%	93.46%	68.27%
±2σ	-159.86%	401.15%	97.20%	95.45%
±3σ	-300.11%	541.40%	98.13%	99.73%

Descriptive Statistics

Mean	120.644%
Standard Error	13.559%
Median	81.275%
Mode	20.909%
Standard Deviation	140.253%
Sample Variance	19670.841%
Kurtosis	23.91
Skewness	4.40
Range	967.980%
Minimum	20.909%
Maximum	988.889%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	120.644%	107	100.00%	120.644%
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 0.97. Further, an Excess Kurtosis of 1.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -128.46%	0	0.00%	0.00%
-128.46% to -92.49%	0	0.00%	0.00%
-92.49% to -56.52%	4	3.74%	3.74%
-56.52% to -20.56%	15	14.02%	17.76%
-20.56% to 15.41%	48	44.86%	62.62%
15.41% to 51.38%	23	21.50%	84.11%
51.38% to 87.34%	7	6.54%	90.65%
87.34% to 123.31%	6	5.61%	96.26%
123.31% to 159.27%	3	2.80%	99.07%
Greater than 159.27%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.55%	63.36%	75.70%	68.27%
±2σ	-80.50%	111.32%	93.46%	95.45%
±3σ	-128.46%	159.27%	99.07%	99.73%

Descriptive Statistics

Mean	15.409%
Standard Error	4.636%
Median	7.279%
Mode	0.000%
Standard Deviation	47.955%
Sample Variance	2299.689%
Kurtosis	1.69
Skewness	0.97
Range	269.633%
Minimum	-82.133%
Maximum	187.500%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.898%	64	59.81%	25.060%
Negative	-25.188%	41	38.32%	-9.652%
Zero	0.000%	2	1.87%	0.000%

PLUG Deep Analytical Report