EGAN - 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	6.63%	11.71%	7.19%	4.47%	5.14%	5.27%	8.93	9.90	8.48	10.42
Weekly	11.87%	21.60%	13.15%	10.10%	11.31%	11.59%	8.40	10.53	7.50	11.79
Monthly	25.17%	42.34%	26.25%	20.84%	23.54%	24.13%	7.43	11.89	5.87	15.05
Quarterly	39.60%	84.73%	45.67%	40.05%	40.76%	41.80%	6.25	14.13	4.16	21.24
Annual	—	—	—	—	81.53%	83.59%	4.16	21.24	1.84	48.00
Option Time Horizon	—	—	—	—	38.64%	39.62%	6.39	13.83	4.34	20.36

Calculation Notes: Computed at 2026-02-22T12:58 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $9.40 | Strike (K): $10.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.2500 (Bid $0.0000 / Ask $2.5000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 81.53% (CRR binomial tree, American, n=20 steps) | BS IV: 82.35% (European Black-Scholes) | Yahoo IV (Annual): 83.59% → 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 2.09. Further, an Excess Kurtosis of 19.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.74%	33	0.56%	0.56%
-19.74% to -14.77%	55	0.94%	1.50%
-14.77% to -9.79%	139	2.37%	3.88%
-9.79% to -4.82%	500	8.54%	12.42%
-4.82% to 0.15%	2633	44.99%	57.41%
0.15% to 5.13%	1826	31.20%	88.60%
5.13% to 10.10%	401	6.85%	95.46%
10.10% to 15.07%	131	2.24%	97.69%
15.07% to 20.05%	56	0.96%	98.65%
Greater than 20.05%	79	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.48%	6.78%	84.13%	68.27%
±2σ	-13.11%	13.42%	95.15%	95.45%
±3σ	-19.74%	20.05%	98.09%	99.73%

Descriptive Statistics

Mean	0.153%
Standard Error	0.087%
Median	0.000%
Mode	0.000%
Standard Deviation	6.632%
Sample Variance	43.987%
Kurtosis	19.63
Skewness	2.09
Range	127.778%
Minimum	-50.000%
Maximum	77.778%
Count	5853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.647%	2522	43.09%	2.002%
Negative	-3.909%	2769	47.31%	-1.849%
Zero	0.000%	562	9.60%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.36%
20	1 Month	5.41%
60	1 Quarter	5.41%
250	1 Year	5.76%
750	3 Years	4.68%
1,250	5 Years	4.47%
2,500	10 Years	5.35%
5,000	20 Years	8.03%
12,500	50 Years	8.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 8.13. Further, an Excess Kurtosis of 113.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.21%	0	0.00%	0.00%
-26.21% to -17.43%	0	0.00%	0.00%
-17.43% to -8.65%	0	0.00%	0.00%
-8.65% to 0.12%	0	0.00%	0.00%
0.12% to 8.90%	4054	69.25%	69.25%
8.90% to 17.68%	1227	20.96%	90.21%
17.68% to 26.46%	325	5.55%	95.76%
26.46% to 35.24%	117	2.00%	97.76%
35.24% to 44.02%	54	0.92%	98.68%
Greater than 44.02%	77	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.80%	20.61%	93.01%	68.27%
±2σ	-14.51%	32.32%	97.40%	95.45%
±3σ	-26.21%	44.02%	98.68%	99.73%

Descriptive Statistics

Mean	8.904%
Standard Error	0.153%
Median	5.769%
Mode	6.667%
Standard Deviation	11.706%
Sample Variance	137.037%
Kurtosis	113.17
Skewness	8.13
Range	233.179%
Minimum	0.154%
Maximum	233.333%
Count	5854

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.904%	5854	100.00%	8.904%
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 Left Skewed (Extreme Negative Tail Risk) with a Skewness factor of -1.65. Further, an Excess Kurtosis of 13.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.11%	85	1.45%	1.45%
-22.11% to -16.71%	59	1.01%	2.46%
-16.71% to -11.32%	158	2.70%	5.16%
-11.32% to -5.93%	375	6.41%	11.56%
-5.93% to -0.53%	1796	30.68%	42.24%
-0.53% to 4.86%	2662	45.47%	87.72%
4.86% to 10.25%	492	8.40%	96.12%
10.25% to 15.65%	148	2.53%	98.65%
15.65% to 21.04%	44	0.75%	99.40%
Greater than 21.04%	35	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.72%	6.66%	83.07%	68.27%
±2σ	-14.91%	13.85%	94.89%	95.45%
±3σ	-22.11%	21.04%	97.95%	99.73%

Descriptive Statistics

Mean	-0.533%
Standard Error	0.094%
Median	0.000%
Mode	0.000%
Standard Deviation	7.191%
Sample Variance	51.717%
Kurtosis	13.14
Skewness	-1.65
Range	119.388%
Minimum	-69.388%
Maximum	50.000%
Count	5854

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.086%	2648	45.23%	1.848%
Negative	-5.095%	2736	46.74%	-2.381%
Zero	0.000%	470	8.03%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.46. Further, an Excess Kurtosis of 8.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.19%	4	0.29%	0.29%
-35.19% to -26.29%	11	0.81%	1.10%
-26.29% to -17.38%	46	3.38%	4.48%
-17.38% to -8.47%	137	10.06%	14.54%
-8.47% to 0.43%	595	43.69%	58.22%
0.43% to 9.34%	391	28.71%	86.93%
9.34% to 18.24%	97	7.12%	94.05%
18.24% to 27.15%	46	3.38%	97.43%
27.15% to 36.05%	15	1.10%	98.53%
Greater than 36.05%	20	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.44%	12.30%	80.18%	68.27%
±2σ	-23.32%	24.18%	94.64%	95.45%
±3σ	-35.19%	36.05%	98.24%	99.73%

Descriptive Statistics

Mean	0.431%
Standard Error	0.322%
Median	-0.048%
Mode	0.000%
Standard Deviation	11.874%
Sample Variance	140.988%
Kurtosis	8.77
Skewness	1.46
Range	139.308%
Minimum	-47.000%
Maximum	92.308%
Count	1362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.249%	592	43.47%	4.020%
Negative	-7.180%	681	50.00%	-3.590%
Zero	0.000%	89	6.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.39%
12	1 Quarter	11.09%
52	1 Year	12.76%
156	3 Years	10.51%
260	5 Years	10.10%
520	10 Years	12.14%
1,040	20 Years	16.36%
2,600	50 Years	18.69%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.02. Further, an Excess Kurtosis of 25.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.91%	0	0.00%	0.00%
-43.91% to -27.71%	0	0.00%	0.00%
-27.71% to -11.51%	0	0.00%	0.00%
-11.51% to 4.70%	57	4.18%	4.18%
4.70% to 20.90%	874	64.12%	68.31%
20.90% to 37.10%	266	19.52%	87.82%
37.10% to 53.30%	79	5.80%	93.62%
53.30% to 69.50%	42	3.08%	96.70%
69.50% to 85.71%	15	1.10%	97.80%
Greater than 85.71%	30	2.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.71%	42.50%	90.83%	68.27%
±2σ	-22.31%	64.10%	96.04%	95.45%
±3σ	-43.91%	85.71%	97.80%	99.73%

Descriptive Statistics

Mean	20.897%
Standard Error	0.585%
Median	14.286%
Mode	20.000%
Standard Deviation	21.603%
Sample Variance	466.709%
Kurtosis	25.93
Skewness	4.02
Range	232.407%
Minimum	0.926%
Maximum	233.333%
Count	1363

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.897%	1363	100.00%	20.897%
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 0.41. Further, an Excess Kurtosis of 6.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.00%	12	0.88%	0.88%
-40.00% to -30.14%	24	1.76%	2.64%
-30.14% to -20.28%	39	2.86%	5.50%
-20.28% to -10.41%	120	8.80%	14.31%
-10.41% to -0.55%	436	31.99%	46.29%
-0.55% to 9.31%	545	39.99%	86.28%
9.31% to 19.18%	119	8.73%	95.01%
19.18% to 29.04%	37	2.71%	97.73%
29.04% to 38.90%	17	1.25%	98.97%
Greater than 38.90%	14	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.70%	12.60%	80.04%	68.27%
±2σ	-26.85%	25.75%	94.50%	95.45%
±3σ	-40.00%	38.90%	98.09%	99.73%

Descriptive Statistics

Mean	-0.551%
Standard Error	0.356%
Median	0.000%
Mode	0.000%
Standard Deviation	13.151%
Sample Variance	172.953%
Kurtosis	6.52
Skewness	0.41
Range	150.453%
Minimum	-58.000%
Maximum	92.453%
Count	1363

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.606%	627	46.00%	3.959%
Negative	-9.312%	660	48.42%	-4.509%
Zero	0.000%	76	5.58%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.13. Further, an Excess Kurtosis of 2.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -73.55%	0	0.00%	0.00%
-73.55% to -54.67%	2	0.63%	0.63%
-54.67% to -35.80%	12	3.79%	4.42%
-35.80% to -16.92%	44	13.88%	18.30%
-16.92% to 1.95%	129	40.69%	58.99%
1.95% to 20.83%	83	26.18%	85.17%
20.83% to 39.70%	21	6.62%	91.80%
39.70% to 58.58%	12	3.79%	95.58%
58.58% to 77.45%	9	2.84%	98.42%
Greater than 77.45%	5	1.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.22%	27.12%	76.66%	68.27%
±2σ	-48.38%	52.29%	93.38%	95.45%
±3σ	-73.55%	77.45%	98.42%	99.73%

Descriptive Statistics

Mean	1.951%
Standard Error	1.414%
Median	-0.333%
Mode	0.000%
Standard Deviation	25.167%
Sample Variance	633.379%
Kurtosis	2.68
Skewness	1.13
Range	170.780%
Minimum	-61.058%
Maximum	109.722%
Count	317

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.424%	147	46.37%	9.471%
Negative	-14.899%	160	50.47%	-7.520%
Zero	0.000%	10	3.15%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.71%
12	1 Year	28.12%
36	3 Years	21.98%
60	5 Years	20.84%
120	10 Years	25.49%
240	20 Years	32.30%
600	50 Years	38.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.03. Further, an Excess Kurtosis of 4.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -77.55%	0	0.00%	0.00%
-77.55% to -45.80%	0	0.00%	0.00%
-45.80% to -14.05%	0	0.00%	0.00%
-14.05% to 17.70%	56	17.61%	17.61%
17.70% to 49.45%	152	47.80%	65.41%
49.45% to 81.20%	58	18.24%	83.65%
81.20% to 112.96%	25	7.86%	91.51%
112.96% to 144.71%	15	4.72%	96.23%
144.71% to 176.46%	5	1.57%	97.80%
Greater than 176.46%	7	2.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.12%	91.79%	86.79%	68.27%
±2σ	-35.22%	134.12%	94.65%	95.45%
±3σ	-77.55%	176.46%	97.80%	99.73%

Descriptive Statistics

Mean	49.453%
Standard Error	2.374%
Median	34.604%
Mode	25.000%
Standard Deviation	42.335%
Sample Variance	1792.223%
Kurtosis	4.74
Skewness	2.03
Range	225.495%
Minimum	7.838%
Maximum	233.333%
Count	318

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.453%	318	100.00%	49.453%
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 1.40. Further, an Excess Kurtosis of 4.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.77%	0	0.00%	0.00%
-75.77% to -56.08%	0	0.00%	0.00%
-56.08% to -36.39%	14	4.40%	4.40%
-36.39% to -16.70%	39	12.26%	16.67%
-16.70% to 2.99%	133	41.82%	58.49%
2.99% to 22.68%	83	26.10%	84.59%
22.68% to 42.37%	25	7.86%	92.45%
42.37% to 62.07%	12	3.77%	96.23%
62.07% to 81.76%	9	2.83%	99.06%
Greater than 81.76%	3	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.26%	29.25%	77.36%	68.27%
±2σ	-49.52%	55.50%	94.65%	95.45%
±3σ	-75.77%	81.76%	99.06%	99.73%

Descriptive Statistics

Mean	2.992%
Standard Error	1.472%
Median	-0.280%
Mode	0.000%
Standard Deviation	26.255%
Sample Variance	689.346%
Kurtosis	4.68
Skewness	1.40
Range	195.679%
Minimum	-50.000%
Maximum	145.679%
Count	318

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.030%	150	47.17%	10.392%
Negative	-14.525%	162	50.94%	-7.399%
Zero	0.000%	6	1.89%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.09. Further, an Excess Kurtosis of 1.74 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.08%	0	0.00%	0.00%
-115.08% to -85.38%	0	0.00%	0.00%
-85.38% to -55.67%	3	2.83%	2.83%
-55.67% to -25.97%	20	18.87%	21.70%
-25.97% to 3.73%	40	37.74%	59.43%
3.73% to 33.44%	24	22.64%	82.08%
33.44% to 63.14%	9	8.49%	90.57%
63.14% to 92.84%	6	5.66%	96.23%
92.84% to 122.54%	2	1.89%	98.11%
Greater than 122.54%	2	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.87%	43.34%	73.58%	68.27%
±2σ	-75.48%	82.94%	96.23%	95.45%
±3σ	-115.08%	122.54%	98.11%	99.73%

Descriptive Statistics

Mean	3.732%
Standard Error	3.847%
Median	-1.567%
Mode	0.000%
Standard Deviation	39.604%
Sample Variance	1568.493%
Kurtosis	1.74
Skewness	1.09
Range	218.336%
Minimum	-70.968%
Maximum	147.368%
Count	106

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.451%	48	45.28%	16.506%
Negative	-24.618%	55	51.89%	-12.774%
Zero	0.000%	3	2.83%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	65.42%
12	3 Years	45.32%
20	5 Years	40.05%
40	10 Years	51.81%
80	20 Years	57.05%
200	50 Years	66.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.11. Further, an Excess Kurtosis of 5.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -151.01%	0	0.00%	0.00%
-151.01% to -87.46%	0	0.00%	0.00%
-87.46% to -23.92%	0	0.00%	0.00%
-23.92% to 39.63%	18	16.82%	16.82%
39.63% to 103.17%	50	46.73%	63.55%
103.17% to 166.72%	22	20.56%	84.11%
166.72% to 230.26%	7	6.54%	90.65%
230.26% to 293.81%	6	5.61%	96.26%
293.81% to 357.35%	1	0.93%	97.20%
Greater than 357.35%	3	2.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.45%	187.90%	86.92%	68.27%
±2σ	-66.28%	272.62%	95.33%	95.45%
±3σ	-151.01%	357.35%	97.20%	99.73%

Descriptive Statistics

Mean	103.172%
Standard Error	8.191%
Median	71.622%
Mode	15.184%
Standard Deviation	84.726%
Sample Variance	7178.508%
Kurtosis	5.53
Skewness	2.11
Range	485.831%
Minimum	15.184%
Maximum	501.015%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	103.172%	107	100.00%	103.172%
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 1.85. Further, an Excess Kurtosis of 6.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -126.93%	0	0.00%	0.00%
-126.93% to -92.67%	0	0.00%	0.00%
-92.67% to -58.42%	0	0.00%	0.00%
-58.42% to -24.17%	19	17.76%	17.76%
-24.17% to 10.09%	45	42.06%	59.81%
10.09% to 44.34%	22	20.56%	80.37%
44.34% to 78.60%	16	14.95%	95.33%
78.60% to 112.85%	0	0.00%	95.33%
112.85% to 147.10%	4	3.74%	99.07%
Greater than 147.10%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.58%	55.76%	78.50%	68.27%
±2σ	-81.26%	101.43%	95.33%	95.45%
±3σ	-126.93%	147.10%	99.07%	99.73%

Descriptive Statistics

Mean	10.088%
Standard Error	4.415%
Median	0.855%
Mode	0.000%
Standard Deviation	45.672%
Sample Variance	2085.975%
Kurtosis	6.32
Skewness	1.85
Range	302.136%
Minimum	-57.692%
Maximum	244.444%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.094%	57	53.27%	20.826%
Negative	-23.936%	48	44.86%	-10.738%
Zero	0.000%	2	1.87%	0.000%

EGAN Deep Analytical Report