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	4.37%	3.25%	3.28%	5.17%	4.38%	4.48%	17.50	19.10	16.75	19.95
Weekly	9.69%	9.62%	9.09%	12.60%	9.65%	9.86%	16.60	20.13	15.07	22.17
Monthly	22.87%	20.94%	20.10%	28.33%	20.09%	20.52%	14.95	22.35	12.23	27.32
Quarterly	38.39%	41.55%	40.60%	53.27%	34.79%	35.55%	12.91	25.89	9.12	36.66
Annual	—	—	—	—	69.58%	71.09%	9.12	36.66	4.55	73.51
Option Time Horizon	—	—	—	—	22.74%	23.24%	14.56	22.95	11.60	28.81

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $18.28 | Strike (K): $17.50 (first OTM call ≥ spot) | Observed Mid-Price: $2.0950 (Bid $1.4900 / Ask $2.7000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 69.58% (CRR binomial tree, American, n=20 steps) | BS IV: 70.40% (European Black-Scholes) | Yahoo IV (Annual): 71.09% → 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 5.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.02%	10	0.72%	0.72%
-13.02% to -9.74%	10	0.72%	1.43%
-9.74% to -6.46%	42	3.01%	4.44%
-6.46% to -3.18%	174	12.46%	16.91%
-3.18% to 0.10%	511	36.60%	53.51%
0.10% to 3.38%	425	30.44%	83.95%
3.38% to 6.66%	135	9.67%	93.62%
6.66% to 9.94%	54	3.87%	97.49%
9.94% to 13.22%	22	1.58%	99.07%
Greater than 13.22%	13	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.27%	4.48%	79.01%	68.27%
±2σ	-8.64%	8.85%	94.84%	95.45%
±3σ	-13.02%	13.22%	98.35%	99.73%

Descriptive Statistics

Mean	0.102%
Standard Error	0.117%
Median	-0.198%
Mode	0.000%
Standard Deviation	4.373%
Sample Variance	19.123%
Kurtosis	5.99
Skewness	0.74
Range	52.512%
Minimum	-20.613%
Maximum	31.899%
Count	1396

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.327%	663	47.49%	1.580%
Negative	-2.835%	728	52.15%	-1.478%
Zero	0.000%	5	0.36%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.05%
20	1 Month	3.03%
60	1 Quarter	3.10%
250	1 Year	3.60%
750	3 Years	4.19%
1,250	5 Years	5.17%
2,500	10 Years	5.53%
5,000	20 Years	5.53%
12,500	50 Years	5.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.66. Further, an Excess Kurtosis of 13.03 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 -0.08%	0	0.00%	0.00%
-0.08% to 2.36%	257	18.40%	18.40%
2.36% to 4.80%	620	44.38%	62.78%
4.80% to 7.24%	294	21.05%	83.82%
7.24% to 9.67%	132	9.45%	93.27%
9.67% to 12.11%	50	3.58%	96.85%
12.11% to 14.55%	12	0.86%	97.71%
Greater than 14.55%	32	2.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.55%	8.05%	83.97%	68.27%
±2σ	-1.70%	11.30%	96.13%	95.45%
±3σ	-4.96%	14.55%	97.71%	99.73%

Descriptive Statistics

Mean	4.798%
Standard Error	0.087%
Median	3.919%
Mode	1.764%
Standard Deviation	3.251%
Sample Variance	10.566%
Kurtosis	13.03
Skewness	2.66
Range	34.863%
Minimum	0.660%
Maximum	35.523%
Count	1397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.798%	1397	100.00%	4.798%
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 0.71. Further, an Excess Kurtosis of 6.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.62%	6	0.43%	0.43%
-9.62% to -7.16%	15	1.07%	1.50%
-7.16% to -4.70%	54	3.87%	5.37%
-4.70% to -2.25%	160	11.45%	16.82%
-2.25% to 0.21%	484	34.65%	51.47%
0.21% to 2.67%	466	33.36%	84.82%
2.67% to 5.13%	134	9.59%	94.42%
5.13% to 7.59%	45	3.22%	97.64%
7.59% to 10.04%	18	1.29%	98.93%
Greater than 10.04%	15	1.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.06%	3.49%	78.02%	68.27%
±2σ	-6.34%	6.77%	94.85%	95.45%
±3σ	-9.62%	10.04%	98.50%	99.73%

Descriptive Statistics

Mean	0.213%
Standard Error	0.088%
Median	0.151%
Mode	0.000%
Standard Deviation	3.277%
Sample Variance	10.739%
Kurtosis	6.34
Skewness	0.71
Range	43.008%
Minimum	-18.777%
Maximum	24.231%
Count	1397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.344%	730	52.26%	1.225%
Negative	-2.132%	663	47.46%	-1.012%
Zero	0.000%	4	0.29%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.80. Further, an Excess Kurtosis of 3.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.59%	1	0.34%	0.34%
-28.59% to -21.32%	1	0.34%	0.69%
-21.32% to -14.05%	12	4.14%	4.83%
-14.05% to -6.78%	38	13.10%	17.93%
-6.78% to 0.49%	113	38.97%	56.90%
0.49% to 7.76%	67	23.10%	80.00%
7.76% to 15.03%	40	13.79%	93.79%
15.03% to 22.30%	12	4.14%	97.93%
22.30% to 29.57%	1	0.34%	98.28%
Greater than 29.57%	5	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.20%	10.18%	73.79%	68.27%
±2σ	-18.89%	19.88%	94.83%	95.45%
±3σ	-28.59%	29.57%	97.93%	99.73%

Descriptive Statistics

Mean	0.491%
Standard Error	0.569%
Median	-0.319%
Mode	7.143%
Standard Deviation	9.693%
Sample Variance	93.947%
Kurtosis	3.04
Skewness	0.80
Range	81.120%
Minimum	-31.518%
Maximum	49.602%
Count	290

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.943%	137	47.24%	3.752%
Negative	-6.223%	152	52.41%	-3.262%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.98%
12	1 Quarter	7.45%
52	1 Year	8.81%
156	3 Years	10.44%
260	5 Years	12.60%
520	10 Years	13.42%
1,040	20 Years	13.42%
2,600	50 Years	13.42%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.92. Further, an Excess Kurtosis of 12.95 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%	0	0.00%	0.00%
-14.72% to -7.51%	0	0.00%	0.00%
-7.51% to -0.30%	0	0.00%	0.00%
-0.30% to 6.91%	52	17.87%	17.87%
6.91% to 14.12%	131	45.02%	62.89%
14.12% to 21.34%	65	22.34%	85.22%
21.34% to 28.55%	25	8.59%	93.81%
28.55% to 35.76%	9	3.09%	96.91%
35.76% to 42.97%	4	1.37%	98.28%
Greater than 42.97%	5	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.51%	23.74%	87.63%	68.27%
±2σ	-5.11%	33.35%	96.22%	95.45%
±3σ	-14.72%	42.97%	98.28%	99.73%

Descriptive Statistics

Mean	14.123%
Standard Error	0.564%
Median	11.785%
Mode	6.765%
Standard Deviation	9.616%
Sample Variance	92.473%
Kurtosis	12.95
Skewness	2.92
Range	72.984%
Minimum	3.972%
Maximum	76.956%
Count	291

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.123%	291	100.00%	14.123%
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 2.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.57%	2	0.69%	0.69%
-26.57% to -19.75%	1	0.34%	1.03%
-19.75% to -12.93%	8	2.75%	3.78%
-12.93% to -6.11%	52	17.87%	21.65%
-6.11% to 0.71%	89	30.58%	52.23%
0.71% to 7.53%	87	29.90%	82.13%
7.53% to 14.35%	36	12.37%	94.50%
14.35% to 21.17%	9	3.09%	97.59%
21.17% to 27.99%	3	1.03%	98.63%
Greater than 27.99%	4	1.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.38%	9.80%	74.91%	68.27%
±2σ	-17.48%	18.90%	95.19%	95.45%
±3σ	-26.57%	27.99%	97.94%	99.73%

Descriptive Statistics

Mean	0.710%
Standard Error	0.533%
Median	0.531%
Mode	-10.000%
Standard Deviation	9.093%
Sample Variance	82.676%
Kurtosis	2.79
Skewness	0.60
Range	75.104%
Minimum	-31.979%
Maximum	43.125%
Count	291

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.638%	158	54.30%	3.604%
Negative	-6.332%	133	45.70%	-2.894%
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 1.24. Further, an Excess Kurtosis of 1.97 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -66.15%	0	0.00%	0.00%
-66.15% to -49.00%	0	0.00%	0.00%
-49.00% to -31.85%	2	2.99%	2.99%
-31.85% to -14.70%	11	16.42%	19.40%
-14.70% to 2.46%	29	43.28%	62.69%
2.46% to 19.61%	13	19.40%	82.09%
19.61% to 36.76%	7	10.45%	92.54%
36.76% to 53.91%	2	2.99%	95.52%
53.91% to 71.06%	2	2.99%	98.51%
Greater than 71.06%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.41%	25.33%	80.60%	68.27%
±2σ	-43.28%	48.20%	92.54%	95.45%
±3σ	-66.15%	71.06%	98.51%	99.73%

Descriptive Statistics

Mean	2.457%
Standard Error	2.794%
Median	-2.687%
Mode	-40.808%
Standard Deviation	22.869%
Sample Variance	523.010%
Kurtosis	1.97
Skewness	1.24
Range	119.241%
Minimum	-40.808%
Maximum	78.433%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.793%	28	41.79%	9.525%
Negative	-12.144%	39	58.21%	-7.069%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.85%
12	1 Year	18.73%
36	3 Years	24.70%
60	5 Years	28.33%
120	10 Years	30.44%
240	20 Years	30.44%
600	50 Years	30.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.98. Further, an Excess Kurtosis of 4.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.19%	0	0.00%	0.00%
-27.19% to -11.49%	0	0.00%	0.00%
-11.49% to 4.22%	0	0.00%	0.00%
4.22% to 19.92%	15	22.06%	22.06%
19.92% to 35.62%	27	39.71%	61.76%
35.62% to 51.33%	14	20.59%	82.35%
51.33% to 67.03%	7	10.29%	92.65%
67.03% to 82.73%	2	2.94%	95.59%
82.73% to 98.44%	1	1.47%	97.06%
Greater than 98.44%	2	2.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.68%	56.56%	86.76%	68.27%
±2σ	-6.25%	77.50%	95.59%	95.45%
±3σ	-27.19%	98.44%	97.06%	99.73%

Descriptive Statistics

Mean	35.623%
Standard Error	2.539%
Median	30.061%
Mode	12.787%
Standard Deviation	20.938%
Sample Variance	438.413%
Kurtosis	4.98
Skewness	1.98
Range	110.528%
Minimum	12.787%
Maximum	123.315%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.623%	68	100.00%	35.623%
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 1.15 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -57.20%	0	0.00%	0.00%
-57.20% to -42.13%	0	0.00%	0.00%
-42.13% to -27.05%	6	8.82%	8.82%
-27.05% to -11.97%	8	11.76%	20.59%
-11.97% to 3.10%	18	26.47%	47.06%
3.10% to 18.18%	23	33.82%	80.88%
18.18% to 33.26%	10	14.71%	95.59%
33.26% to 48.34%	2	2.94%	98.53%
48.34% to 63.41%	0	0.00%	98.53%
Greater than 63.41%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.00%	23.21%	75.00%	68.27%
±2σ	-37.10%	43.31%	94.12%	95.45%
±3σ	-57.20%	63.41%	98.53%	99.73%

Descriptive Statistics

Mean	3.105%
Standard Error	2.438%
Median	3.772%
Mode	-39.539%
Standard Deviation	20.103%
Sample Variance	404.128%
Kurtosis	1.15
Skewness	0.33
Range	110.714%
Minimum	-39.539%
Maximum	71.175%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.462%	41	60.29%	9.323%
Negative	-15.659%	27	39.71%	-6.218%
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 0.71. Further, an Excess Kurtosis of -0.23 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.24%	0	0.00%	0.00%
-108.24% to -79.45%	0	0.00%	0.00%
-79.45% to -50.66%	1	4.35%	4.35%
-50.66% to -21.87%	2	8.70%	13.04%
-21.87% to 6.92%	11	47.83%	60.87%
6.92% to 35.71%	4	17.39%	78.26%
35.71% to 64.50%	2	8.70%	86.96%
64.50% to 93.29%	3	13.04%	100.00%
93.29% to 122.08%	0	0.00%	100.00%
Greater than 122.08%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.47%	45.31%	69.57%	68.27%
±2σ	-69.85%	83.69%	100.00%	95.45%
±3σ	-108.24%	122.08%	100.00%	99.73%

Descriptive Statistics

Mean	6.920%
Standard Error	8.004%
Median	-5.058%
Mode	-58.526%
Standard Deviation	38.386%
Sample Variance	1473.490%
Kurtosis	-0.23
Skewness	0.71
Range	141.345%
Minimum	-58.526%
Maximum	82.819%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.423%	10	43.48%	18.010%
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 1.78. Further, an Excess Kurtosis of 5.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -114.75%	0	0.00%	0.00%
-114.75% to -84.30%	0	0.00%	0.00%
-84.30% to -53.85%	0	0.00%	0.00%
-53.85% to -23.40%	5	20.83%	20.83%
-23.40% to 7.05%	7	29.17%	50.00%
7.05% to 37.51%	10	41.67%	91.67%
37.51% to 67.96%	1	4.17%	95.83%
67.96% to 98.41%	0	0.00%	95.83%
98.41% to 128.86%	0	0.00%	95.83%
Greater than 128.86%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.55%	47.66%	79.17%	68.27%
±2σ	-74.15%	88.26%	95.83%	95.45%
±3σ	-114.75%	128.86%	95.83%	99.73%

Descriptive Statistics

Mean	7.055%
Standard Error	8.288%
Median	7.122%
Mode	-43.458%
Standard Deviation	40.603%
Sample Variance	1648.633%
Kurtosis	5.37
Skewness	1.78
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	-23.166%	11	45.83%	-10.618%
Zero	0.000%	0	0.00%	0.000%

LI Deep Analytical Report