RUN - 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	4.96%	3.80%	4.17%	7.80%	6.27%	6.30%	19.05	21.59	17.89	22.99
Weekly	11.24%	11.37%	11.52%	18.52%	13.80%	13.87%	17.67	23.28	15.39	26.73
Monthly	23.05%	25.10%	22.55%	37.92%	28.74%	28.88%	15.21	27.03	11.41	36.03
Quarterly	42.21%	49.19%	39.68%	63.65%	49.77%	50.02%	12.33	33.36	7.49	54.88
Annual	—	—	—	—	99.54%	100.05%	7.49	54.88	2.77	148.49
Option Time Horizon	—	—	—	—	32.54%	32.70%	14.65	28.08	10.58	38.88

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $20.28 | Strike (K): $21.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3700 (Bid $1.8400 / Ask $2.9000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 99.54% (CRR binomial tree, American, n=20 steps) | BS IV: 100.09% (European Black-Scholes) | Yahoo IV (Annual): 100.05% → 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 Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 6.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.72%	16	0.60%	0.60%
-14.72% to -11.00%	16	0.60%	1.21%
-11.00% to -7.29%	97	3.66%	4.87%
-7.29% to -3.57%	339	12.79%	17.65%
-3.57% to 0.15%	867	32.70%	50.36%
0.15% to 3.86%	861	32.48%	82.84%
3.86% to 7.58%	313	11.81%	94.64%
7.58% to 11.30%	96	3.62%	98.26%
11.30% to 15.02%	18	0.68%	98.94%
Greater than 15.02%	28	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.81%	5.10%	76.57%	68.27%
±2σ	-9.77%	10.06%	95.44%	95.45%
±3σ	-14.72%	15.02%	98.34%	99.73%

Descriptive Statistics

Mean	0.147%
Standard Error	0.096%
Median	0.080%
Mode	0.000%
Standard Deviation	4.956%
Sample Variance	24.563%
Kurtosis	6.81
Skewness	0.15
Range	72.865%
Minimum	-40.041%
Maximum	32.824%
Count	2651

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.593%	1340	50.55%	1.816%
Negative	-3.434%	1288	48.59%	-1.668%
Zero	0.000%	23	0.87%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.34%
20	1 Month	7.96%
60	1 Quarter	6.95%
250	1 Year	9.07%
750	3 Years	7.99%
1,250	5 Years	7.80%
2,500	10 Years	6.65%
5,000	20 Years	6.78%
12,500	50 Years	6.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.78. Further, an Excess Kurtosis of 15.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.81%	0	0.00%	0.00%
-4.81% to -1.95%	0	0.00%	0.00%
-1.95% to 0.90%	0	0.00%	0.00%
0.90% to 3.75%	509	19.19%	19.19%
3.75% to 6.60%	1079	40.69%	59.88%
6.60% to 9.46%	640	24.13%	84.01%
9.46% to 12.31%	252	9.50%	93.51%
12.31% to 15.16%	92	3.47%	96.98%
15.16% to 18.01%	38	1.43%	98.42%
Greater than 18.01%	42	1.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.80%	10.41%	81.90%	68.27%
±2σ	-1.00%	14.21%	96.38%	95.45%
±3σ	-4.81%	18.01%	98.42%	99.73%

Descriptive Statistics

Mean	6.603%
Standard Error	0.074%
Median	5.780%
Mode	4.564%
Standard Deviation	3.803%
Sample Variance	14.463%
Kurtosis	15.70
Skewness	2.78
Range	46.063%
Minimum	1.165%
Maximum	47.228%
Count	2652

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.603%	2652	100.00%	6.603%
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 0.19. Further, an Excess Kurtosis of 2.89 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.37%	15	0.57%	0.57%
-12.37% to -9.24%	28	1.06%	1.62%
-9.24% to -6.12%	96	3.62%	5.24%
-6.12% to -2.99%	367	13.84%	19.08%
-2.99% to 0.14%	871	32.84%	51.92%
0.14% to 3.27%	796	30.02%	81.94%
3.27% to 6.40%	317	11.95%	93.89%
6.40% to 9.53%	109	4.11%	98.00%
9.53% to 12.66%	34	1.28%	99.28%
Greater than 12.66%	19	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.03%	4.31%	74.32%	68.27%
±2σ	-8.20%	8.49%	94.65%	95.45%
±3σ	-12.37%	12.66%	98.72%	99.73%

Descriptive Statistics

Mean	0.143%
Standard Error	0.081%
Median	0.000%
Mode	0.000%
Standard Deviation	4.172%
Sample Variance	17.407%
Kurtosis	2.89
Skewness	0.19
Range	50.141%
Minimum	-24.713%
Maximum	25.428%
Count	2652

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.232%	1307	49.28%	1.593%
Negative	-2.932%	1311	49.43%	-1.449%
Zero	0.000%	34	1.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. Further, an Excess Kurtosis of 2.93 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.98%	5	0.91%	0.91%
-32.98% to -24.54%	4	0.73%	1.64%
-24.54% to -16.11%	16	2.91%	4.55%
-16.11% to -7.68%	76	13.82%	18.36%
-7.68% to 0.76%	180	32.73%	51.09%
0.76% to 9.19%	172	31.27%	82.36%
9.19% to 17.62%	71	12.91%	95.27%
17.62% to 26.06%	10	1.82%	97.09%
26.06% to 34.49%	10	1.82%	98.91%
Greater than 34.49%	6	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.49%	12.00%	76.91%	68.27%
±2σ	-21.73%	23.25%	94.91%	95.45%
±3σ	-32.98%	34.49%	98.00%	99.73%

Descriptive Statistics

Mean	0.757%
Standard Error	0.479%
Median	0.462%
Mode	0.000%
Standard Deviation	11.245%
Sample Variance	126.455%
Kurtosis	2.93
Skewness	0.35
Range	100.498%
Minimum	-43.478%
Maximum	57.020%
Count	550

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.630%	284	51.64%	4.456%
Negative	-7.765%	262	47.64%	-3.699%
Zero	0.000%	4	0.73%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.11%
12	1 Quarter	14.34%
52	1 Year	21.40%
156	3 Years	19.09%
260	5 Years	18.52%
520	10 Years	15.62%
1,040	20 Years	15.89%
2,600	50 Years	15.89%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.67%	0	0.00%	0.00%
-16.67% to -8.14%	0	0.00%	0.00%
-8.14% to 0.38%	0	0.00%	0.00%
0.38% to 8.91%	93	16.88%	16.88%
8.91% to 17.44%	257	46.64%	63.52%
17.44% to 25.96%	121	21.96%	85.48%
25.96% to 34.49%	47	8.53%	94.01%
34.49% to 43.02%	17	3.09%	97.10%
43.02% to 51.54%	5	0.91%	98.00%
Greater than 51.54%	11	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.07%	28.80%	84.21%	68.27%
±2σ	-5.30%	40.17%	95.64%	95.45%
±3σ	-16.67%	51.54%	98.00%	99.73%

Descriptive Statistics

Mean	17.436%
Standard Error	0.484%
Median	14.561%
Mode	7.212%
Standard Deviation	11.369%
Sample Variance	129.255%
Kurtosis	15.38
Skewness	2.95
Range	110.653%
Minimum	2.513%
Maximum	113.166%
Count	551

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.436%	551	100.00%	17.436%
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 1.54. Further, an Excess Kurtosis of 8.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.95%	1	0.18%	0.18%
-33.95% to -25.30%	4	0.73%	0.91%
-25.30% to -16.66%	16	2.90%	3.81%
-16.66% to -8.02%	75	13.61%	17.42%
-8.02% to 0.62%	209	37.93%	55.35%
0.62% to 9.27%	157	28.49%	83.85%
9.27% to 17.91%	62	11.25%	95.10%
17.91% to 26.55%	15	2.72%	97.82%
26.55% to 35.19%	5	0.91%	98.73%
Greater than 35.19%	7	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.90%	12.15%	77.50%	68.27%
±2σ	-22.42%	23.67%	95.10%	95.45%
±3σ	-33.95%	35.19%	98.55%	99.73%

Descriptive Statistics

Mean	0.624%
Standard Error	0.491%
Median	-0.182%
Mode	0.000%
Standard Deviation	11.523%
Sample Variance	132.786%
Kurtosis	8.65
Skewness	1.54
Range	123.802%
Minimum	-36.131%
Maximum	87.671%
Count	551

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.943%	264	47.91%	4.285%
Negative	-7.154%	282	51.18%	-3.661%
Zero	0.000%	5	0.91%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.85. Further, an Excess Kurtosis of 1.21 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -66.30%	0	0.00%	0.00%
-66.30% to -49.01%	0	0.00%	0.00%
-49.01% to -31.73%	4	3.17%	3.17%
-31.73% to -14.44%	29	23.02%	26.19%
-14.44% to 2.84%	33	26.19%	52.38%
2.84% to 20.13%	37	29.37%	81.75%
20.13% to 37.41%	12	9.52%	91.27%
37.41% to 54.70%	8	6.35%	97.62%
54.70% to 71.98%	1	0.79%	98.41%
Greater than 71.98%	2	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.20%	25.89%	76.19%	68.27%
±2σ	-43.25%	48.94%	95.24%	95.45%
±3σ	-66.30%	71.98%	98.41%	99.73%

Descriptive Statistics

Mean	2.844%
Standard Error	2.053%
Median	0.440%
Mode	-47.777%
Standard Deviation	23.047%
Sample Variance	531.143%
Kurtosis	1.21
Skewness	0.85
Range	133.832%
Minimum	-47.777%
Maximum	86.055%
Count	126

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.410%	63	50.00%	10.205%
Negative	-14.721%	63	50.00%	-7.360%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.16%
12	1 Year	42.21%
36	3 Years	39.40%
60	5 Years	37.92%
120	10 Years	34.34%
240	20 Years	35.18%
600	50 Years	35.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.04. Further, an Excess Kurtosis of 6.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.78%	0	0.00%	0.00%
-31.78% to -12.96%	0	0.00%	0.00%
-12.96% to 5.87%	0	0.00%	0.00%
5.87% to 24.69%	30	23.62%	23.62%
24.69% to 43.51%	44	34.65%	58.27%
43.51% to 62.34%	30	23.62%	81.89%
62.34% to 81.16%	14	11.02%	92.91%
81.16% to 99.99%	5	3.94%	96.85%
99.99% to 118.81%	1	0.79%	97.64%
Greater than 118.81%	3	2.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.42%	68.61%	80.31%	68.27%
±2σ	-6.68%	93.71%	96.06%	95.45%
±3σ	-31.78%	118.81%	97.64%	99.73%

Descriptive Statistics

Mean	43.514%
Standard Error	2.227%
Median	39.121%
Mode	11.488%
Standard Deviation	25.099%
Sample Variance	629.950%
Kurtosis	6.68
Skewness	2.04
Range	164.581%
Minimum	11.488%
Maximum	176.069%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.514%	127	100.00%	43.514%
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 0.69. Further, an Excess Kurtosis of 1.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.24%	0	0.00%	0.00%
-65.24% to -48.33%	0	0.00%	0.00%
-48.33% to -31.42%	7	5.51%	5.51%
-31.42% to -14.51%	23	18.11%	23.62%
-14.51% to 2.41%	40	31.50%	55.12%
2.41% to 19.32%	28	22.05%	77.17%
19.32% to 36.23%	22	17.32%	94.49%
36.23% to 53.14%	4	3.15%	97.64%
53.14% to 70.06%	1	0.79%	98.43%
Greater than 70.06%	2	1.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.14%	24.96%	69.29%	68.27%
±2σ	-42.69%	47.51%	95.28%	95.45%
±3σ	-65.24%	70.06%	98.43%	99.73%

Descriptive Statistics

Mean	2.406%
Standard Error	2.001%
Median	0.658%
Mode	-46.252%
Standard Deviation	22.550%
Sample Variance	508.487%
Kurtosis	1.57
Skewness	0.69
Range	138.925%
Minimum	-46.252%
Maximum	92.673%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.003%	66	51.97%	9.876%
Negative	-15.551%	61	48.03%	-7.469%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.36. Further, an Excess Kurtosis of 2.97 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -117.26%	0	0.00%	0.00%
-117.26% to -85.60%	0	0.00%	0.00%
-85.60% to -53.94%	1	2.38%	2.38%
-53.94% to -22.28%	9	21.43%	23.81%
-22.28% to 9.38%	15	35.71%	59.52%
9.38% to 41.04%	7	16.67%	76.19%
41.04% to 72.70%	8	19.05%	95.24%
72.70% to 104.36%	1	2.38%	97.62%
104.36% to 136.02%	0	0.00%	97.62%
Greater than 136.02%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.83%	51.59%	78.57%	68.27%
±2σ	-75.05%	93.81%	95.24%	95.45%
±3σ	-117.26%	136.02%	97.62%	99.73%

Descriptive Statistics

Mean	9.381%
Standard Error	6.514%
Median	4.136%
Mode	-55.045%
Standard Deviation	42.214%
Sample Variance	1782.048%
Kurtosis	2.97
Skewness	1.36
Range	216.556%
Minimum	-55.045%
Maximum	161.511%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.049%	23	54.76%	20.289%
Negative	-25.450%	18	42.86%	-10.907%
Zero	0.000%	1	2.38%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	73.61%
12	3 Years	68.61%
20	5 Years	63.65%
40	10 Years	63.75%
80	20 Years	64.67%
200	50 Years	64.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.22. Further, an Excess Kurtosis of 1.71 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.91%	0	0.00%	0.00%
-59.91% to -23.02%	0	0.00%	0.00%
-23.02% to 13.88%	0	0.00%	0.00%
13.88% to 50.77%	10	23.26%	23.26%
50.77% to 87.66%	16	37.21%	60.47%
87.66% to 124.55%	8	18.60%	79.07%
124.55% to 161.44%	5	11.63%	90.70%
161.44% to 198.33%	2	4.65%	95.35%
198.33% to 235.22%	1	2.33%	97.67%
Greater than 235.22%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	38.47%	136.84%	72.09%	68.27%
±2σ	-10.72%	186.03%	95.35%	95.45%
±3σ	-59.90%	235.22%	97.67%	99.73%

Descriptive Statistics

Mean	87.656%
Standard Error	7.501%
Median	83.970%
Mode	19.661%
Standard Deviation	49.187%
Sample Variance	2419.329%
Kurtosis	1.71
Skewness	1.22
Range	227.724%
Minimum	19.661%
Maximum	247.385%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	87.656%	43	100.00%	87.656%
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 0.86. Further, an Excess Kurtosis of 0.95 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -112.80%	0	0.00%	0.00%
-112.80% to -83.04%	0	0.00%	0.00%
-83.04% to -53.28%	1	2.33%	2.33%
-53.28% to -23.51%	10	23.26%	25.58%
-23.51% to 6.25%	13	30.23%	55.81%
6.25% to 36.01%	11	25.58%	81.40%
36.01% to 65.77%	5	11.63%	93.02%
65.77% to 95.53%	1	2.33%	95.35%
95.53% to 125.30%	1	2.33%	97.67%
Greater than 125.30%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.44%	45.93%	74.42%	68.27%
±2σ	-73.12%	85.61%	95.35%	95.45%
±3σ	-112.80%	125.30%	97.67%	99.73%

Descriptive Statistics

Mean	6.248%
Standard Error	6.052%
Median	-1.701%
Mode	-63.505%
Standard Deviation	39.683%
Sample Variance	1574.769%
Kurtosis	0.95
Skewness	0.86
Range	189.459%
Minimum	-63.505%
Maximum	125.954%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.769%	19	44.19%	18.456%
Negative	-21.872%	24	55.81%	-12.208%
Zero	0.000%	0	0.00%	0.000%

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