LC - 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	4.00%	3.06%	3.22%	5.30%	3.24%	3.34%	15.74	16.80	15.24	17.35
Weekly	9.15%	8.88%	9.03%	13.02%	7.14%	7.35%	15.14	17.46	14.10	18.75
Monthly	18.23%	18.89%	17.81%	29.34%	14.86%	15.31%	14.02	18.86	12.08	21.89
Quarterly	38.55%	40.26%	38.16%	51.56%	25.73%	26.51%	12.57	21.03	9.72	27.20
Annual	—	—	—	—	51.46%	53.03%	9.72	27.20	5.81	45.51
Option Time Horizon	—	—	—	—	19.79%	20.40%	13.34	19.82	10.94	24.16

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $16.26 | Strike (K): $17.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.0250 (Bid $0.9000 / Ask $1.1500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 51.46% (CRR binomial tree, American, n=20 steps) | BS IV: 52.10% (European Black-Scholes) | Yahoo IV (Annual): 53.03% → 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 0.87. Further, an Excess Kurtosis of 14.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.99%	10	0.36%	0.36%
-11.99% to -8.99%	24	0.85%	1.21%
-8.99% to -5.99%	94	3.34%	4.55%
-5.99% to -2.99%	331	11.77%	16.32%
-2.99% to 0.01%	1041	37.01%	53.32%
0.01% to 3.01%	846	30.07%	83.40%
3.01% to 6.01%	334	11.87%	95.27%
6.01% to 9.01%	75	2.67%	97.94%
9.01% to 12.01%	32	1.14%	99.08%
Greater than 12.01%	26	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.99%	4.01%	78.99%	68.27%
±2σ	-7.99%	8.01%	95.56%	95.45%
±3σ	-11.99%	12.01%	98.72%	99.73%

Descriptive Statistics

Mean	0.009%
Standard Error	0.075%
Median	-0.132%
Mode	0.000%
Standard Deviation	3.999%
Sample Variance	15.995%
Kurtosis	14.52
Skewness	0.87
Range	82.745%
Minimum	-34.930%
Maximum	47.815%
Count	2813

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.927%	1313	46.68%	1.366%
Negative	-2.653%	1439	51.16%	-1.357%
Zero	0.000%	61	2.17%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.08%
20	1 Month	5.80%
60	1 Quarter	4.52%
250	1 Year	4.77%
750	3 Years	4.55%
1,250	5 Years	5.30%
2,500	10 Years	5.28%
5,000	20 Years	5.25%
12,500	50 Years	5.25%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.57. Further, an Excess Kurtosis of 32.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.11%	0	0.00%	0.00%
-4.11% to -1.82%	0	0.00%	0.00%
-1.82% to 0.47%	0	0.00%	0.00%
0.47% to 2.77%	454	16.13%	16.13%
2.77% to 5.06%	1337	47.51%	63.65%
5.06% to 7.36%	596	21.18%	84.83%
7.36% to 9.65%	234	8.32%	93.14%
9.65% to 11.95%	96	3.41%	96.55%
11.95% to 14.24%	50	1.78%	98.33%
Greater than 14.24%	47	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.00%	8.12%	84.97%	68.27%
±2σ	-1.06%	11.18%	95.84%	95.45%
±3σ	-4.11%	14.24%	98.33%	99.73%

Descriptive Statistics

Mean	5.063%
Standard Error	0.058%
Median	4.310%
Mode	5.000%
Standard Deviation	3.059%
Sample Variance	9.355%
Kurtosis	32.43
Skewness	3.57
Range	53.661%
Minimum	1.080%
Maximum	54.741%
Count	2814

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.063%	2814	100.00%	5.063%
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 0.03. Further, an Excess Kurtosis of 2.86 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.48%	18	0.64%	0.64%
-9.48% to -7.07%	33	1.17%	1.81%
-7.07% to -4.66%	88	3.13%	4.94%
-4.66% to -2.25%	369	13.11%	18.05%
-2.25% to 0.16%	922	32.76%	50.82%
0.16% to 2.58%	872	30.99%	81.81%
2.58% to 4.99%	332	11.80%	93.60%
4.99% to 7.40%	127	4.51%	98.12%
7.40% to 9.81%	33	1.17%	99.29%
Greater than 9.81%	20	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.05%	3.38%	74.48%	68.27%
±2σ	-6.27%	6.60%	94.35%	95.45%
±3σ	-9.48%	9.81%	98.65%	99.73%

Descriptive Statistics

Mean	0.163%
Standard Error	0.061%
Median	0.119%
Mode	0.000%
Standard Deviation	3.216%
Sample Variance	10.343%
Kurtosis	2.86
Skewness	0.03
Range	38.316%
Minimum	-20.265%
Maximum	18.051%
Count	2814

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.466%	1429	50.78%	1.252%
Negative	-2.325%	1318	46.84%	-1.089%
Zero	0.000%	67	2.38%	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 6.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.38%	2	0.34%	0.34%
-27.38% to -20.52%	4	0.68%	1.03%
-20.52% to -13.66%	23	3.94%	4.97%
-13.66% to -6.80%	80	13.70%	18.66%
-6.80% to 0.06%	189	32.36%	51.03%
0.06% to 6.92%	183	31.34%	82.36%
6.92% to 13.78%	75	12.84%	95.21%
13.78% to 20.64%	14	2.40%	97.60%
20.64% to 27.50%	9	1.54%	99.14%
Greater than 27.50%	5	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.09%	9.21%	76.54%	68.27%
±2σ	-18.23%	18.35%	95.38%	95.45%
±3σ	-27.38%	27.50%	98.80%	99.73%

Descriptive Statistics

Mean	0.060%
Standard Error	0.378%
Median	-0.065%
Mode	0.000%
Standard Deviation	9.147%
Sample Variance	83.663%
Kurtosis	6.03
Skewness	0.85
Range	99.118%
Minimum	-41.740%
Maximum	57.378%
Count	584

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.669%	286	48.97%	3.266%
Negative	-6.390%	293	50.17%	-3.206%
Zero	0.000%	5	0.86%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.40%
12	1 Quarter	11.22%
52	1 Year	11.52%
156	3 Years	11.09%
260	5 Years	13.02%
520	10 Years	12.55%
1,040	20 Years	12.44%
2,600	50 Years	12.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.54. Further, an Excess Kurtosis of 9.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.20%	0	0.00%	0.00%
-13.20% to -6.54%	0	0.00%	0.00%
-6.54% to 0.12%	0	0.00%	0.00%
0.12% to 6.78%	96	16.41%	16.41%
6.78% to 13.44%	287	49.06%	65.47%
13.44% to 20.10%	113	19.32%	84.79%
20.10% to 26.76%	46	7.86%	92.65%
26.76% to 33.42%	26	4.44%	97.09%
33.42% to 40.08%	7	1.20%	98.29%
Greater than 40.08%	10	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.56%	22.32%	85.98%	68.27%
±2σ	-4.32%	31.20%	95.73%	95.45%
±3σ	-13.20%	40.08%	98.29%	99.73%

Descriptive Statistics

Mean	13.437%
Standard Error	0.367%
Median	10.905%
Mode	6.213%
Standard Deviation	8.880%
Sample Variance	78.854%
Kurtosis	9.80
Skewness	2.54
Range	67.849%
Minimum	2.908%
Maximum	70.757%
Count	585

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.437%	585	100.00%	13.437%
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 4.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.24%	2	0.34%	0.34%
-26.24% to -19.47%	4	0.68%	1.03%
-19.47% to -12.70%	20	3.42%	4.44%
-12.70% to -5.93%	79	13.50%	17.95%
-5.93% to 0.84%	211	36.07%	54.02%
0.84% to 7.61%	164	28.03%	82.05%
7.61% to 14.38%	66	11.28%	93.33%
14.38% to 21.15%	26	4.44%	97.78%
21.15% to 27.92%	8	1.37%	99.15%
Greater than 27.92%	5	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.19%	9.87%	74.87%	68.27%
±2σ	-17.21%	18.89%	95.21%	95.45%
±3σ	-26.24%	27.92%	98.80%	99.73%

Descriptive Statistics

Mean	0.840%
Standard Error	0.373%
Median	0.253%
Mode	0.000%
Standard Deviation	9.027%
Sample Variance	81.494%
Kurtosis	4.72
Skewness	0.69
Range	97.129%
Minimum	-37.389%
Maximum	59.740%
Count	585

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.168%	296	50.60%	3.627%
Negative	-5.761%	283	48.38%	-2.787%
Zero	0.000%	6	1.03%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 1.00. Further, an Excess Kurtosis of 2.13 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.66%	0	0.00%	0.00%
-54.66% to -40.99%	0	0.00%	0.00%
-40.99% to -27.32%	5	3.73%	3.73%
-27.32% to -13.65%	23	17.16%	20.90%
-13.65% to 0.03%	51	38.06%	58.96%
0.03% to 13.70%	26	19.40%	78.36%
13.70% to 27.37%	21	15.67%	94.03%
27.37% to 41.04%	4	2.99%	97.01%
41.04% to 54.72%	2	1.49%	98.51%
Greater than 54.72%	2	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.21%	18.25%	73.13%	68.27%
±2σ	-36.44%	36.48%	95.52%	95.45%
±3σ	-54.66%	54.71%	98.51%	99.73%

Descriptive Statistics

Mean	0.025%
Standard Error	1.575%
Median	-3.048%
Mode	-39.747%
Standard Deviation	18.230%
Sample Variance	332.331%
Kurtosis	2.13
Skewness	1.00
Range	110.625%
Minimum	-39.747%
Maximum	70.878%
Count	134

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.718%	55	41.05%	6.862%
Negative	-11.597%	79	58.95%	-6.837%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.83%
12	1 Year	25.30%
36	3 Years	25.76%
60	5 Years	29.34%
120	10 Years	27.43%
240	20 Years	27.16%
600	50 Years	27.16%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.86. Further, an Excess Kurtosis of 12.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.69%	0	0.00%	0.00%
-24.69% to -10.52%	0	0.00%	0.00%
-10.52% to 3.65%	0	0.00%	0.00%
3.65% to 17.82%	20	14.81%	14.81%
17.82% to 31.99%	56	41.48%	56.30%
31.99% to 46.16%	40	29.63%	85.93%
46.16% to 60.32%	12	8.89%	94.81%
60.32% to 74.49%	4	2.96%	97.78%
74.49% to 88.66%	1	0.74%	98.52%
Greater than 88.66%	2	1.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.10%	50.88%	85.19%	68.27%
±2σ	-5.79%	69.77%	95.56%	95.45%
±3σ	-24.69%	88.66%	98.52%	99.73%

Descriptive Statistics

Mean	31.987%
Standard Error	1.626%
Median	28.662%
Mode	7.319%
Standard Deviation	18.891%
Sample Variance	356.874%
Kurtosis	12.51
Skewness	2.86
Range	131.418%
Minimum	7.319%
Maximum	138.737%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.987%	135	100.00%	31.987%
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 0.44. Further, an Excess Kurtosis of 0.84 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.30%	0	0.00%	0.00%
-50.30% to -36.94%	2	1.48%	1.48%
-36.94% to -23.58%	4	2.96%	4.44%
-23.58% to -10.22%	24	17.78%	22.22%
-10.22% to 3.15%	40	29.63%	51.85%
3.15% to 16.51%	39	28.89%	80.74%
16.51% to 29.87%	13	9.63%	90.37%
29.87% to 43.23%	10	7.41%	97.78%
43.23% to 56.59%	2	1.48%	99.26%
Greater than 56.59%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.67%	20.96%	72.59%	68.27%
±2σ	-32.48%	38.77%	94.07%	95.45%
±3σ	-50.30%	56.59%	99.26%	99.73%

Descriptive Statistics

Mean	3.145%
Standard Error	1.533%
Median	2.387%
Mode	-40.727%
Standard Deviation	17.814%
Sample Variance	317.354%
Kurtosis	0.84
Skewness	0.44
Range	107.744%
Minimum	-40.727%
Maximum	67.017%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.244%	75	55.56%	8.469%
Negative	-12.181%	59	43.70%	-5.324%
Zero	0.000%	1	0.74%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.35. Further, an Excess Kurtosis of 2.10 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.35%	0	0.00%	0.00%
-113.35% to -84.44%	0	0.00%	0.00%
-84.44% to -55.54%	1	2.22%	2.22%
-55.54% to -26.63%	7	15.56%	17.78%
-26.63% to 2.28%	22	48.89%	66.67%
2.28% to 31.19%	7	15.56%	82.22%
31.19% to 60.10%	4	8.89%	91.11%
60.10% to 89.01%	3	6.67%	97.78%
89.01% to 117.92%	0	0.00%	97.78%
Greater than 117.92%	1	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.26%	40.83%	73.33%	68.27%
±2σ	-74.81%	79.37%	95.56%	95.45%
±3σ	-113.35%	117.92%	97.78%	99.73%

Descriptive Statistics

Mean	2.281%
Standard Error	5.746%
Median	-7.032%
Mode	-59.182%
Standard Deviation	38.545%
Sample Variance	1485.693%
Kurtosis	2.10
Skewness	1.35
Range	191.516%
Minimum	-59.182%
Maximum	132.334%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	44.457%	15	33.33%	14.819%
Negative	-18.807%	30	66.67%	-12.538%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	41.26%
12	3 Years	48.99%
20	5 Years	51.56%
40	10 Years	50.89%
80	20 Years	49.93%
200	50 Years	49.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.74. Further, an Excess Kurtosis of 3.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.07%	0	0.00%	0.00%
-54.07% to -23.87%	0	0.00%	0.00%
-23.87% to 6.32%	0	0.00%	0.00%
6.32% to 36.51%	7	15.22%	15.22%
36.51% to 66.71%	22	47.83%	63.04%
66.71% to 96.90%	8	17.39%	80.43%
96.90% to 127.09%	5	10.87%	91.30%
127.09% to 157.29%	2	4.35%	95.65%
157.29% to 187.48%	1	2.17%	97.83%
Greater than 187.48%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	26.45%	106.97%	78.26%	68.27%
±2σ	-13.81%	147.22%	95.65%	95.45%
±3σ	-54.07%	187.48%	97.83%	99.73%

Descriptive Statistics

Mean	66.707%
Standard Error	5.936%
Median	53.938%
Mode	18.127%
Standard Deviation	40.258%
Sample Variance	1620.711%
Kurtosis	3.65
Skewness	1.74
Range	199.947%
Minimum	18.127%
Maximum	218.074%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	66.707%	46	100.00%	66.707%
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 1.14. Further, an Excess Kurtosis of 3.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.53%	0	0.00%	0.00%
-103.53% to -74.91%	0	0.00%	0.00%
-74.91% to -46.29%	1	2.17%	2.17%
-46.29% to -17.67%	8	17.39%	19.57%
-17.67% to 10.95%	17	36.96%	56.52%
10.95% to 39.57%	13	28.26%	84.78%
39.57% to 68.19%	4	8.70%	93.48%
68.19% to 96.81%	2	4.35%	97.83%
96.81% to 125.43%	0	0.00%	97.83%
Greater than 125.43%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.21%	49.11%	69.57%	68.27%
±2σ	-65.37%	87.27%	95.65%	95.45%
±3σ	-103.53%	125.43%	97.83%	99.73%

Descriptive Statistics

Mean	10.951%
Standard Error	5.626%
Median	7.909%
Mode	-56.406%
Standard Deviation	38.161%
Sample Variance	1456.230%
Kurtosis	3.10
Skewness	1.14
Range	207.899%
Minimum	-56.406%
Maximum	151.493%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.085%	31	67.39%	19.601%
Negative	-26.525%	15	32.61%	-8.650%
Zero	0.000%	0	0.00%	0.000%

LC Deep Analytical Report