LI - 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	4.35%	3.24%	3.26%	5.09%	2.92%	3.19%	16.55	17.54	16.07	18.06
Weekly	9.64%	9.56%	9.05%	12.44%	6.42%	7.02%	15.98	18.16	14.98	19.37
Monthly	22.69%	20.97%	19.93%	28.04%	13.37%	14.60%	14.90	19.47	13.04	22.26
Quarterly	38.39%	41.55%	40.51%	53.27%	23.15%	25.29%	13.51	21.47	10.72	27.07
Annual	—	—	—	—	46.30%	50.59%	10.72	27.07	6.75	43.00
Option Time Horizon	—	—	—	—	17.48%	19.09%	14.30	20.29	12.01	24.16

Calculation Notes: Computed at 2026-03-23T16:42 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $17.03 | Strike (K): $18.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.8400 (Bid $0.7500 / Ask $0.9300) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 46.30% (CRR binomial tree, American, n=20 steps) | BS IV: 46.68% (European Black-Scholes) | Yahoo IV (Annual): 50.59% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.74. Further, an Excess Kurtosis of 6.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.96%	10	0.71%	0.71%
-12.96% to -9.70%	10	0.71%	1.41%
-9.70% to -6.43%	42	2.96%	4.38%
-6.43% to -3.17%	176	12.42%	16.80%
-3.17% to 0.10%	520	36.70%	53.49%
0.10% to 3.36%	430	30.35%	83.84%
3.36% to 6.62%	137	9.67%	93.51%
6.62% to 9.89%	57	4.02%	97.53%
9.89% to 13.15%	21	1.48%	99.01%
Greater than 13.15%	14	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.26%	4.45%	79.11%	68.27%
±2σ	-8.61%	8.80%	94.78%	95.45%
±3σ	-12.96%	13.15%	98.31%	99.73%

Descriptive Statistics

Mean	0.095%
Standard Error	0.116%
Median	-0.201%
Mode	0.000%
Standard Deviation	4.352%
Sample Variance	18.936%
Kurtosis	6.04
Skewness	0.74
Range	52.512%
Minimum	-20.613%
Maximum	31.899%
Count	1417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.311%	672	47.42%	1.570%
Negative	-2.824%	740	52.22%	-1.475%
Zero	0.000%	5	0.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.42%
20	1 Month	3.73%
60	1 Quarter	3.36%
250	1 Year	3.40%
750	3 Years	4.16%
1,250	5 Years	5.09%
2,500	10 Years	5.51%
5,000	20 Years	5.51%
12,500	50 Years	5.51%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.67. Further, an Excess Kurtosis of 13.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.96%	0	0.00%	0.00%
-4.96% to -2.52%	0	0.00%	0.00%
-2.52% to -0.10%	0	0.00%	0.00%
-0.10% to 2.33%	257	18.12%	18.12%
2.33% to 4.76%	634	44.71%	62.83%
4.76% to 7.20%	299	21.09%	83.92%
7.20% to 9.62%	133	9.38%	93.30%
9.62% to 12.05%	51	3.60%	96.90%
12.05% to 14.48%	12	0.85%	97.74%
Greater than 14.48%	32	2.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.52%	8.00%	84.13%	68.27%
±2σ	-1.72%	11.25%	96.19%	95.45%
±3σ	-4.96%	14.48%	97.74%	99.73%

Descriptive Statistics

Mean	4.765%
Standard Error	0.086%
Median	3.874%
Mode	1.764%
Standard Deviation	3.240%
Sample Variance	10.495%
Kurtosis	13.12
Skewness	2.67
Range	34.863%
Minimum	0.660%
Maximum	35.523%
Count	1418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.765%	1418	100.00%	4.765%
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 0.73. Further, an Excess Kurtosis of 6.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.57%	6	0.42%	0.42%
-9.57% to -7.13%	16	1.13%	1.55%
-7.13% to -4.68%	53	3.74%	5.29%
-4.68% to -2.24%	160	11.28%	16.57%
-2.24% to 0.20%	492	34.70%	51.27%
0.20% to 2.64%	475	33.50%	84.77%
2.64% to 5.09%	136	9.59%	94.36%
5.09% to 7.53%	47	3.31%	97.67%
7.53% to 9.97%	18	1.27%	98.94%
Greater than 9.97%	15	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.06%	3.46%	78.35%	68.27%
±2σ	-6.31%	6.71%	94.92%	95.45%
±3σ	-9.57%	9.97%	98.52%	99.73%

Descriptive Statistics

Mean	0.201%
Standard Error	0.086%
Median	0.138%
Mode	0.000%
Standard Deviation	3.257%
Sample Variance	10.609%
Kurtosis	6.44
Skewness	0.73
Range	43.008%
Minimum	-18.777%
Maximum	24.231%
Count	1418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.332%	736	51.90%	1.210%
Negative	-2.111%	678	47.81%	-1.009%
Zero	0.000%	4	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.81. Further, an Excess Kurtosis of 3.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.46%	1	0.34%	0.34%
-28.46% to -21.23%	1	0.34%	0.68%
-21.23% to -14.00%	12	4.08%	4.76%
-14.00% to -6.77%	39	13.27%	18.03%
-6.77% to 0.46%	114	38.78%	56.80%
0.46% to 7.69%	69	23.47%	80.27%
7.69% to 14.92%	39	13.27%	93.54%
14.92% to 22.15%	13	4.42%	97.96%
22.15% to 29.38%	1	0.34%	98.30%
Greater than 29.38%	5	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.18%	10.10%	74.15%	68.27%
±2σ	-18.82%	19.74%	94.90%	95.45%
±3σ	-28.46%	29.38%	97.96%	99.73%

Descriptive Statistics

Mean	0.460%
Standard Error	0.562%
Median	-0.252%
Mode	7.143%
Standard Deviation	9.641%
Sample Variance	92.946%
Kurtosis	3.09
Skewness	0.81
Range	81.120%
Minimum	-31.518%
Maximum	49.602%
Count	294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.856%	139	47.28%	3.714%
Negative	-6.212%	154	52.38%	-3.254%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.61%
12	1 Quarter	8.32%
52	1 Year	8.42%
156	3 Years	10.38%
260	5 Years	12.44%
520	10 Years	13.36%
1,040	20 Years	13.36%
2,600	50 Years	13.36%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.64%	0	0.00%	0.00%
-14.64% to -7.46%	0	0.00%	0.00%
-7.46% to -0.29%	0	0.00%	0.00%
-0.29% to 6.88%	51	17.29%	17.29%
6.88% to 14.06%	135	45.76%	63.05%
14.06% to 21.23%	66	22.37%	85.42%
21.23% to 28.41%	25	8.47%	93.90%
28.41% to 35.58%	9	3.05%	96.95%
35.58% to 42.75%	4	1.36%	98.31%
Greater than 42.75%	5	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.49%	23.62%	88.14%	68.27%
±2σ	-5.07%	33.19%	96.27%	95.45%
±3σ	-14.64%	42.75%	98.31%	99.73%

Descriptive Statistics

Mean	14.058%
Standard Error	0.557%
Median	11.611%
Mode	6.765%
Standard Deviation	9.565%
Sample Variance	91.488%
Kurtosis	13.15
Skewness	2.95
Range	72.847%
Minimum	4.109%
Maximum	76.956%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.058%	295	100.00%	14.058%
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 0.60. Further, an Excess Kurtosis of 2.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.44%	2	0.68%	0.68%
-26.44% to -19.66%	1	0.34%	1.02%
-19.66% to -12.87%	8	2.71%	3.73%
-12.87% to -6.08%	52	17.63%	21.36%
-6.08% to 0.71%	91	30.85%	52.20%
0.71% to 7.50%	89	30.17%	82.37%
7.50% to 14.28%	36	12.20%	94.58%
14.28% to 21.07%	9	3.05%	97.63%
21.07% to 27.86%	3	1.02%	98.64%
Greater than 27.86%	4	1.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.34%	9.76%	74.58%	68.27%
±2σ	-17.39%	18.81%	95.25%	95.45%
±3σ	-26.44%	27.86%	97.97%	99.73%

Descriptive Statistics

Mean	0.708%
Standard Error	0.527%
Median	0.531%
Mode	-10.000%
Standard Deviation	9.050%
Sample Variance	81.895%
Kurtosis	2.82
Skewness	0.60
Range	75.104%
Minimum	-31.979%
Maximum	43.125%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.664%	159	53.90%	3.592%
Negative	-6.254%	136	46.10%	-2.883%
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 1.26. Further, an Excess Kurtosis of 2.08 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.77%	0	0.00%	0.00%
-65.77% to -48.75%	0	0.00%	0.00%
-48.75% to -31.73%	2	2.94%	2.94%
-31.73% to -14.71%	11	16.18%	19.12%
-14.71% to 2.31%	30	44.12%	63.24%
2.31% to 19.33%	13	19.12%	82.35%
19.33% to 36.35%	7	10.29%	92.65%
36.35% to 53.37%	2	2.94%	95.59%
53.37% to 70.39%	2	2.94%	98.53%
Greater than 70.39%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.38%	25.00%	80.88%	68.27%
±2σ	-43.08%	47.70%	92.65%	95.45%
±3σ	-65.77%	70.39%	98.53%	99.73%

Descriptive Statistics

Mean	2.310%
Standard Error	2.752%
Median	-2.950%
Mode	-40.808%
Standard Deviation	22.694%
Sample Variance	515.024%
Kurtosis	2.08
Skewness	1.26
Range	119.241%
Minimum	-40.808%
Maximum	78.433%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.645%	28	41.18%	9.324%
Negative	-11.925%	40	58.82%	-7.015%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.68%
12	1 Year	18.08%
36	3 Years	24.53%
60	5 Years	28.04%
120	10 Years	30.18%
240	20 Years	30.18%
600	50 Years	30.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.97. Further, an Excess Kurtosis of 4.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.61%	0	0.00%	0.00%
-27.61% to -11.88%	0	0.00%	0.00%
-11.88% to 3.84%	0	0.00%	0.00%
3.84% to 19.57%	16	23.19%	23.19%
19.57% to 35.29%	26	37.68%	60.87%
35.29% to 51.02%	15	21.74%	82.61%
51.02% to 66.74%	7	10.14%	92.75%
66.74% to 82.47%	2	2.90%	95.65%
82.47% to 98.19%	1	1.45%	97.10%
Greater than 98.19%	2	2.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.33%	56.26%	85.51%	68.27%
±2σ	-6.64%	77.22%	95.65%	95.45%
±3σ	-27.61%	98.19%	97.10%	99.73%

Descriptive Statistics

Mean	35.292%
Standard Error	2.524%
Median	29.097%
Mode	12.727%
Standard Deviation	20.966%
Sample Variance	439.563%
Kurtosis	4.96
Skewness	1.97
Range	110.588%
Minimum	12.727%
Maximum	123.315%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.292%	69	100.00%	35.292%
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 0.33. Further, an Excess Kurtosis of 1.23 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -56.65%	0	0.00%	0.00%
-56.65% to -41.70%	0	0.00%	0.00%
-41.70% to -26.75%	6	8.70%	8.70%
-26.75% to -11.81%	10	14.49%	23.19%
-11.81% to 3.14%	17	24.64%	47.83%
3.14% to 18.08%	23	33.33%	81.16%
18.08% to 33.03%	10	14.49%	95.65%
33.03% to 47.98%	2	2.90%	98.55%
47.98% to 62.92%	0	0.00%	98.55%
Greater than 62.92%	1	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.79%	23.07%	75.36%	68.27%
±2σ	-36.72%	42.99%	94.20%	95.45%
±3σ	-56.65%	62.92%	98.55%	99.73%

Descriptive Statistics

Mean	3.137%
Standard Error	2.399%
Median	3.720%
Mode	-39.539%
Standard Deviation	19.928%
Sample Variance	397.130%
Kurtosis	1.23
Skewness	0.33
Range	110.714%
Minimum	-39.539%
Maximum	71.175%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.136%	42	60.87%	9.213%
Negative	-15.527%	27	39.13%	-6.076%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.74. Further, an Excess Kurtosis of -0.20 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.59%	0	0.00%	0.00%
-108.59% to -79.80%	0	0.00%	0.00%
-79.80% to -51.00%	1	4.35%	4.35%
-51.00% to -22.21%	2	8.70%	13.04%
-22.21% to 6.58%	12	52.17%	65.22%
6.58% to 35.38%	3	13.04%	78.26%
35.38% to 64.17%	2	8.70%	86.96%
64.17% to 92.97%	3	13.04%	100.00%
92.97% to 121.76%	0	0.00%	100.00%
Greater than 121.76%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.81%	44.98%	69.57%	68.27%
±2σ	-70.20%	83.37%	100.00%	95.45%
±3σ	-108.59%	121.76%	100.00%	99.73%

Descriptive Statistics

Mean	6.584%
Standard Error	8.005%
Median	-5.058%
Mode	-58.526%
Standard Deviation	38.392%
Sample Variance	1473.977%
Kurtosis	-0.20
Skewness	0.74
Range	141.345%
Minimum	-58.526%
Maximum	82.819%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.651%	10	43.48%	17.674%
Negative	-19.621%	13	56.52%	-11.090%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	25.35%
12	3 Years	45.86%
20	5 Years	53.27%
40	10 Years	56.49%
80	20 Years	56.49%
200	50 Years	56.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.91. Further, an Excess Kurtosis of 1.12 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.41%	0	0.00%	0.00%
-53.41% to -22.25%	0	0.00%	0.00%
-22.25% to 8.91%	0	0.00%	0.00%
8.91% to 40.08%	8	33.33%	33.33%
40.08% to 71.24%	5	20.83%	54.17%
71.24% to 102.41%	7	29.17%	83.33%
102.41% to 133.57%	3	12.50%	95.83%
133.57% to 164.73%	0	0.00%	95.83%
164.73% to 195.90%	1	4.17%	100.00%
Greater than 195.90%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	29.69%	112.79%	70.83%	68.27%
±2σ	-11.86%	154.35%	95.83%	95.45%
±3σ	-53.41%	195.90%	100.00%	99.73%

Descriptive Statistics

Mean	71.242%
Standard Error	8.482%
Median	70.034%
Mode	15.894%
Standard Deviation	41.552%
Sample Variance	1726.535%
Kurtosis	1.12
Skewness	0.91
Range	171.509%
Minimum	15.894%
Maximum	187.403%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	71.242%	24	100.00%	71.242%
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 1.77. Further, an Excess Kurtosis of 5.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -114.19%	0	0.00%	0.00%
-114.19% to -83.80%	0	0.00%	0.00%
-83.80% to -53.42%	0	0.00%	0.00%
-53.42% to -23.04%	5	20.83%	20.83%
-23.04% to 7.34%	7	29.17%	50.00%
7.34% to 37.72%	10	41.67%	91.67%
37.72% to 68.11%	1	4.17%	95.83%
68.11% to 98.49%	0	0.00%	95.83%
98.49% to 128.87%	0	0.00%	95.83%
Greater than 128.87%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.17%	47.85%	79.17%	68.27%
±2σ	-73.68%	88.36%	95.83%	95.45%
±3σ	-114.19%	128.87%	95.83%	99.73%

Descriptive Statistics

Mean	7.342%
Standard Error	8.269%
Median	7.122%
Mode	-43.458%
Standard Deviation	40.509%
Sample Variance	1641.014%
Kurtosis	5.39
Skewness	1.77
Range	190.888%
Minimum	-43.458%
Maximum	147.430%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.627%	13	54.17%	17.673%
Negative	-22.540%	11	45.83%	-10.331%
Zero	0.000%	0	0.00%	0.000%

LI Deep Analytical Report