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%	5.42%	5.30%	8.11%	5.41%	5.49%	2.16	2.40	2.04	2.53
Weekly	14.14%	17.25%	13.63%	19.51%	11.91%	12.08%	2.02	2.56	1.79	2.89
Monthly	29.12%	44.87%	28.20%	41.45%	24.79%	25.15%	1.78	2.92	1.39	3.74
Quarterly	80.33%	140.12%	48.00%	75.20%	42.94%	43.55%	1.48	3.50	0.96	5.37
Annual	—	—	—	—	85.88%	87.11%	0.96	5.37	0.41	12.68
Option Time Horizon	—	—	—	—	32.42%	32.88%	1.65	3.15	1.19	4.35

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $2.28 | Strike (K): $2.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.2150 (Bid $0.2000 / Ask $0.2300) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 85.88% (CRR binomial tree, American, n=20 steps) | BS IV: 86.75% (European Black-Scholes) | Yahoo IV (Annual): 87.11% → 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 2.52. Further, an Excess Kurtosis of 36.37 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%	3.20%
-9.06% to -4.47%	771	11.62%	14.82%
-4.47% to 0.11%	2799	42.20%	57.02%
0.11% to 4.70%	1949	29.38%	86.40%
4.70% to 9.28%	579	8.73%	95.13%
9.28% to 13.86%	177	2.67%	97.80%
13.86% to 18.45%	72	1.09%	98.88%
Greater than 18.45%	74	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.00%	6.22%	81.74%	68.27%
±2σ	-12.11%	12.34%	95.85%	95.45%
±3σ	-18.22%	18.45%	98.54%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.075%
Median	-0.310%
Mode	0.000%
Standard Deviation	6.112%
Sample Variance	37.359%
Kurtosis	36.37
Skewness	2.52
Range	169.931%
Minimum	-52.000%
Maximum	117.931%
Count	6633

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.603%	2856	43.06%	1.982%
Negative	-3.643%	3404	51.32%	-1.870%
Zero	0.000%	373	5.62%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.32%
20	1 Month	8.73%
60	1 Quarter	8.28%
250	1 Year	9.84%
750	3 Years	8.77%
1,250	5 Years	8.11%
2,500	10 Years	7.20%
5,000	20 Years	7.44%
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 49.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.84%	0	0.00%	0.00%
-8.84% to -4.77%	0	0.00%	0.00%
-4.77% to -0.70%	0	0.00%	0.00%
-0.70% to 3.36%	842	12.69%	12.69%
3.36% to 7.43%	3423	51.60%	64.29%
7.43% to 11.50%	1476	22.25%	86.54%
11.50% to 15.57%	503	7.58%	94.12%
15.57% to 19.63%	186	2.80%	96.92%
19.63% to 23.70%	84	1.27%	98.19%
Greater than 23.70%	120	1.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.01%	12.85%	88.11%	68.27%
±2σ	-3.42%	18.28%	96.16%	95.45%
±3σ	-8.84%	23.70%	98.19%	99.73%

Descriptive Statistics

Mean	7.431%
Standard Error	0.067%
Median	6.098%
Mode	5.263%
Standard Deviation	5.423%
Sample Variance	29.407%
Kurtosis	49.65
Skewness	4.59
Range	105.907%
Minimum	0.800%
Maximum	106.707%
Count	6634

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.431%	6634	100.00%	7.431%
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 1.80. Further, an Excess Kurtosis of 34.79 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	0.69%	0.69%
-15.27% to -11.29%	68	1.03%	1.72%
-11.29% to -7.32%	194	2.92%	4.64%
-7.32% to -3.34%	754	11.37%	16.01%
-3.34% to 0.64%	2290	34.52%	50.53%
0.64% to 4.61%	2231	33.63%	84.16%
4.61% to 8.59%	767	11.56%	95.72%
8.59% to 12.56%	177	2.67%	98.39%
12.56% to 16.54%	55	0.83%	99.22%
Greater than 16.54%	52	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.67%	5.94%	79.95%	68.27%
±2σ	-9.97%	11.24%	95.60%	95.45%
±3σ	-15.27%	16.54%	98.52%	99.73%

Descriptive Statistics

Mean	0.636%
Standard Error	0.065%
Median	0.571%
Mode	0.000%
Standard Deviation	5.302%
Sample Variance	28.114%
Kurtosis	34.79
Skewness	1.80
Range	145.563%
Minimum	-47.785%
Maximum	97.778%
Count	6634

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.871%	3582	53.99%	2.090%
Negative	-3.592%	2686	40.49%	-1.454%
Zero	0.000%	366	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 18.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.84%	3	0.22%	0.22%
-41.84% to -31.23%	8	0.58%	0.80%
-31.23% to -20.63%	37	2.69%	3.49%
-20.63% to -10.03%	150	10.89%	14.38%
-10.03% to 0.58%	573	41.61%	55.99%
0.58% to 11.18%	415	30.14%	86.13%
11.18% to 21.79%	121	8.79%	94.92%
21.79% to 32.39%	42	3.05%	97.97%
32.39% to 42.99%	11	0.80%	98.77%
Greater than 42.99%	17	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.56%	14.72%	82.14%	68.27%
±2σ	-27.70%	28.86%	95.93%	95.45%
±3σ	-41.84%	43.00%	98.55%	99.73%

Descriptive Statistics

Mean	0.578%
Standard Error	0.381%
Median	-0.913%
Mode	0.000%
Standard Deviation	14.139%
Sample Variance	199.901%
Kurtosis	18.34
Skewness	2.47
Range	212.285%
Minimum	-64.103%
Maximum	148.182%
Count	1377

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.609%	619	44.95%	4.769%
Negative	-7.938%	727	52.80%	-4.191%
Zero	0.000%	31	2.25%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.25%
12	1 Quarter	17.60%
52	1 Year	24.28%
156	3 Years	21.12%
260	5 Years	19.51%
520	10 Years	17.19%
1,040	20 Years	17.25%
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 49.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.31%	0	0.00%	0.00%
-32.31% to -19.38%	0	0.00%	0.00%
-19.38% to -6.44%	0	0.00%	0.00%
-6.44% to 6.50%	91	6.60%	6.60%
6.50% to 19.43%	803	58.27%	64.88%
19.43% to 32.37%	333	24.17%	89.04%
32.37% to 45.30%	84	6.10%	95.14%
45.30% to 58.24%	34	2.47%	97.61%
58.24% to 71.17%	11	0.80%	98.40%
Greater than 71.17%	22	1.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.18%	36.68%	91.51%	68.27%
±2σ	-15.07%	53.93%	97.02%	95.45%
±3σ	-32.31%	71.17%	98.40%	99.73%

Descriptive Statistics

Mean	19.431%
Standard Error	0.465%
Median	15.075%
Mode	11.111%
Standard Deviation	17.248%
Sample Variance	297.481%
Kurtosis	49.76
Skewness	5.44
Range	229.793%
Minimum	3.540%
Maximum	233.333%
Count	1378

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.431%	1378	100.00%	19.431%
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 2.58. Further, an Excess Kurtosis of 28.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.21%	8	0.58%	0.58%
-39.21% to -28.98%	10	0.73%	1.31%
-28.98% to -18.76%	30	2.18%	3.48%
-18.76% to -8.54%	164	11.90%	15.38%
-8.54% to 1.69%	508	36.87%	52.25%
1.69% to 11.91%	479	34.76%	87.01%
11.91% to 22.14%	115	8.35%	95.36%
22.14% to 32.36%	40	2.90%	98.26%
32.36% to 42.58%	11	0.80%	99.06%
Greater than 42.58%	13	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.94%	15.32%	81.20%	68.27%
±2σ	-25.58%	28.95%	95.94%	95.45%
±3σ	-39.21%	42.58%	98.48%	99.73%

Descriptive Statistics

Mean	1.688%
Standard Error	0.367%
Median	1.245%
Mode	0.000%
Standard Deviation	13.632%
Sample Variance	185.820%
Kurtosis	28.93
Skewness	2.58
Range	228.938%
Minimum	-57.509%
Maximum	171.429%
Count	1378

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.586%	746	54.14%	5.189%
Negative	-8.122%	594	43.11%	-3.501%
Zero	0.000%	38	2.76%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.61. Further, an Excess Kurtosis of 14.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.34%	0	0.00%	0.00%
-85.34% to -63.50%	0	0.00%	0.00%
-63.50% to -41.66%	6	1.89%	1.89%
-41.66% to -19.82%	43	13.56%	15.46%
-19.82% to 2.02%	144	45.43%	60.88%
2.02% to 23.86%	79	24.92%	85.80%
23.86% to 45.70%	26	8.20%	94.01%
45.70% to 67.54%	8	2.52%	96.53%
67.54% to 89.39%	5	1.58%	98.11%
Greater than 89.39%	6	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.10%	31.14%	82.65%	68.27%
±2σ	-56.22%	60.26%	94.95%	95.45%
±3σ	-85.34%	89.39%	98.11%	99.73%

Descriptive Statistics

Mean	2.022%
Standard Error	1.636%
Median	-1.810%
Mode	0.000%
Standard Deviation	29.121%
Sample Variance	848.006%
Kurtosis	14.44
Skewness	2.61
Range	295.327%
Minimum	-63.469%
Maximum	231.858%
Count	317

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.213%	139	43.85%	10.179%
Negative	-14.945%	173	54.57%	-8.156%
Zero	0.000%	5	1.58%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	33.69%
12	1 Year	52.42%
36	3 Years	45.08%
60	5 Years	41.45%
120	10 Years	38.92%
240	20 Years	38.96%
600	50 Years	39.71%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.72. Further, an Excess Kurtosis of 37.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.53%	0	0.00%	0.00%
-84.53% to -50.88%	0	0.00%	0.00%
-50.88% to -17.23%	0	0.00%	0.00%
-17.23% to 16.42%	21	6.60%	6.60%
16.42% to 50.07%	195	61.32%	67.92%
50.07% to 83.72%	63	19.81%	87.74%
83.72% to 117.37%	24	7.55%	95.28%
117.37% to 151.02%	6	1.89%	97.17%
151.02% to 184.67%	3	0.94%	98.11%
Greater than 184.67%	6	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.20%	94.94%	91.19%	68.27%
±2σ	-39.67%	139.81%	96.54%	95.45%
±3σ	-84.54%	184.67%	98.11%	99.73%

Descriptive Statistics

Mean	50.069%
Standard Error	2.516%
Median	39.276%
Mode	15.789%
Standard Deviation	44.868%
Sample Variance	2013.128%
Kurtosis	37.31
Skewness	4.72
Range	498.090%
Minimum	9.677%
Maximum	507.767%
Count	318

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.069%	318	100.00%	50.069%
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 10.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.19%	0	0.00%	0.00%
-79.19% to -58.05%	1	0.31%	0.31%
-58.05% to -36.90%	11	3.46%	3.77%
-36.90% to -15.75%	43	13.52%	17.30%
-15.75% to 5.39%	124	38.99%	56.29%
5.39% to 26.54%	93	29.25%	85.53%
26.54% to 47.69%	27	8.49%	94.03%
47.69% to 68.84%	11	3.46%	97.48%
68.84% to 89.98%	4	1.26%	98.74%
Greater than 89.98%	4	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.80%	33.59%	80.50%	68.27%
±2σ	-51.00%	61.79%	96.23%	95.45%
±3σ	-79.19%	89.98%	98.74%	99.73%

Descriptive Statistics

Mean	5.395%
Standard Error	1.581%
Median	2.545%
Mode	0.000%
Standard Deviation	28.196%
Sample Variance	795.024%
Kurtosis	10.05
Skewness	2.01
Range	254.771%
Minimum	-70.933%
Maximum	183.838%
Count	318

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.394%	178	55.98%	11.975%
Negative	-15.274%	137	43.08%	-6.580%
Zero	0.000%	3	0.94%	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 -231.09%	0	0.00%	0.00%
-231.09% to -170.84%	0	0.00%	0.00%
-170.84% to -110.59%	0	0.00%	0.00%
-110.59% to -50.34%	7	6.60%	6.60%
-50.34% to 9.91%	69	65.09%	71.70%
9.91% to 70.16%	20	18.87%	90.57%
70.16% to 130.41%	6	5.66%	96.23%
130.41% to 190.66%	1	0.94%	97.17%
190.66% to 250.91%	0	0.00%	97.17%
Greater than 250.91%	3	2.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-70.42%	90.24%	95.28%	68.27%
±2σ	-150.75%	170.57%	96.23%	95.45%
±3σ	-231.09%	250.90%	97.17%	99.73%

Descriptive Statistics

Mean	9.909%
Standard Error	7.803%
Median	-5.597%
Mode	-64.444%
Standard Deviation	80.332%
Sample Variance	6453.201%
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	58.636%	44	41.51%	24.339%
Negative	-24.672%	62	58.49%	-14.431%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	113.64%
12	3 Years	85.06%
20	5 Years	75.20%
40	10 Years	80.14%
80	20 Years	81.34%
200	50 Years	83.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.41. Further, an Excess Kurtosis of 23.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -299.51%	0	0.00%	0.00%
-299.51% to -194.42%	0	0.00%	0.00%
-194.42% to -89.33%	0	0.00%	0.00%
-89.33% to 15.76%	0	0.00%	0.00%
15.76% to 120.86%	72	67.29%	67.29%
120.86% to 225.95%	24	22.43%	89.72%
225.95% to 331.04%	7	6.54%	96.26%
331.04% to 436.13%	1	0.93%	97.20%
436.13% to 541.22%	1	0.93%	98.13%
Greater than 541.22%	2	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.27%	260.98%	93.46%	68.27%
±2σ	-159.39%	401.10%	97.20%	95.45%
±3σ	-299.51%	541.22%	98.13%	99.73%

Descriptive Statistics

Mean	120.855%
Standard Error	13.546%
Median	81.275%
Mode	20.909%
Standard Deviation	140.121%
Sample Variance	19633.924%
Kurtosis	23.98
Skewness	4.41
Range	967.980%
Minimum	20.909%
Maximum	988.889%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	120.855%	107	100.00%	120.855%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.98. 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 -128.79%	0	0.00%	0.00%
-128.79% to -92.79%	0	0.00%	0.00%
-92.79% to -56.78%	4	3.74%	3.74%
-56.78% to -20.78%	15	14.02%	17.76%
-20.78% to 15.22%	48	44.86%	62.62%
15.22% to 51.22%	22	20.56%	83.18%
51.22% to 87.23%	8	7.48%	90.65%
87.23% to 123.23%	6	5.61%	96.26%
123.23% to 159.23%	3	2.80%	99.07%
Greater than 159.23%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.78%	63.22%	75.70%	68.27%
±2σ	-80.78%	111.23%	93.46%	95.45%
±3σ	-128.79%	159.23%	99.07%	99.73%

Descriptive Statistics

Mean	15.221%
Standard Error	4.641%
Median	6.989%
Mode	0.000%
Standard Deviation	48.003%
Sample Variance	2304.273%
Kurtosis	1.69
Skewness	0.98
Range	269.633%
Minimum	-82.133%
Maximum	187.500%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	42.351%	63	58.88%	24.936%
Negative	-24.750%	42	39.25%	-9.715%
Zero	0.000%	2	1.87%	0.000%

PLUG Deep Analytical Report