LCID - 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	5.52%	5.28%	4.57%	7.10%	5.66%	5.75%	9.02	10.11	8.53	10.70
Weekly	11.84%	12.81%	11.01%	16.91%	12.47%	12.65%	8.43	10.82	7.44	12.25
Monthly	27.05%	35.99%	22.61%	36.96%	25.95%	26.33%	7.37	12.38	5.68	16.05
Quarterly	40.60%	57.49%	34.37%	57.67%	44.94%	45.61%	6.09	14.97	3.89	23.46
Annual	—	—	—	—	89.89%	91.21%	3.89	23.46	1.58	57.65
Option Time Horizon	—	—	—	—	34.57%	35.08%	6.76	13.49	4.78	19.07

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $9.55 | Strike (K): $10.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.1600 (Bid $1.0800 / Ask $1.2400) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 89.89% (CRR binomial tree, American, n=20 steps) | BS IV: 90.62% (European Black-Scholes) | Yahoo IV (Annual): 91.21% → 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 1.21. 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 -16.58%	6	0.44%	0.44%
-16.58% to -12.44%	9	0.66%	1.10%
-12.44% to -8.30%	37	2.72%	3.82%
-8.30% to -4.16%	167	12.27%	16.09%
-4.16% to -0.02%	501	36.81%	52.90%
-0.02% to 4.11%	421	30.93%	83.84%
4.11% to 8.25%	146	10.73%	94.56%
8.25% to 12.39%	47	3.45%	98.02%
12.39% to 16.53%	13	0.96%	98.97%
Greater than 16.53%	14	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.54%	5.49%	79.35%	68.27%
±2σ	-11.06%	11.01%	96.25%	95.45%
±3σ	-16.58%	16.53%	98.53%	99.73%

Descriptive Statistics

Mean	-0.024%
Standard Error	0.150%
Median	-0.308%
Mode	0.000%
Standard Deviation	5.518%
Sample Variance	30.450%
Kurtosis	9.80
Skewness	1.21
Range	81.626%
Minimum	-38.626%
Maximum	43.000%
Count	1361

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.121%	609	44.75%	1.844%
Negative	-3.531%	720	52.90%	-1.868%
Zero	0.000%	32	2.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.79%
20	1 Month	6.24%
60	1 Quarter	5.95%
250	1 Year	6.38%
750	3 Years	6.58%
1,250	5 Years	7.10%
2,500	10 Years	7.08%
5,000	20 Years	7.08%
12,500	50 Years	7.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.13. Further, an Excess Kurtosis of 80.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.90%	0	0.00%	0.00%
-8.90% to -4.94%	0	0.00%	0.00%
-4.94% to -0.98%	0	0.00%	0.00%
-0.98% to 2.98%	128	9.40%	9.40%
2.98% to 6.95%	720	52.86%	62.26%
6.95% to 10.91%	351	25.77%	88.03%
10.91% to 14.87%	99	7.27%	95.30%
14.87% to 18.84%	33	2.42%	97.72%
18.84% to 22.80%	13	0.95%	98.68%
Greater than 22.80%	18	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.66%	12.23%	85.61%	68.27%
±2σ	-3.62%	17.52%	97.36%	95.45%
±3σ	-8.90%	22.80%	98.68%	99.73%

Descriptive Statistics

Mean	6.948%
Standard Error	0.143%
Median	5.925%
Mode	4.369%
Standard Deviation	5.284%
Sample Variance	27.925%
Kurtosis	80.97
Skewness	6.13
Range	99.688%
Minimum	0.200%
Maximum	99.888%
Count	1362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.948%	1362	100.00%	6.948%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.57. Further, an Excess Kurtosis of 4.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.36%	11	0.81%	0.81%
-13.36% to -9.94%	18	1.32%	2.13%
-9.94% to -6.51%	45	3.30%	5.43%
-6.51% to -3.09%	170	12.48%	17.91%
-3.09% to 0.34%	420	30.84%	48.75%
0.34% to 3.77%	457	33.55%	82.31%
3.77% to 7.19%	154	11.31%	93.61%
7.19% to 10.62%	73	5.36%	98.97%
10.62% to 14.04%	9	0.66%	99.63%
Greater than 14.04%	5	0.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.23%	4.91%	74.82%	68.27%
±2σ	-8.80%	9.48%	95.30%	95.45%
±3σ	-13.36%	14.04%	98.83%	99.73%

Descriptive Statistics

Mean	0.340%
Standard Error	0.124%
Median	0.404%
Mode	0.000%
Standard Deviation	4.568%
Sample Variance	20.863%
Kurtosis	4.37
Skewness	-0.57
Range	54.329%
Minimum	-30.148%
Maximum	24.181%
Count	1362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.326%	741	54.41%	1.810%
Negative	-3.415%	586	43.02%	-1.469%
Zero	0.000%	35	2.57%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.70. Further, an Excess Kurtosis of 2.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.66%	1	0.35%	0.35%
-35.66% to -26.78%	1	0.35%	0.71%
-26.78% to -17.90%	9	3.18%	3.89%
-17.90% to -9.02%	41	14.49%	18.37%
-9.02% to -0.14%	101	35.69%	54.06%
-0.14% to 8.74%	88	31.10%	85.16%
8.74% to 17.62%	18	6.36%	91.52%
17.62% to 26.51%	13	4.59%	96.11%
26.51% to 35.39%	7	2.47%	98.59%
Greater than 35.39%	4	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.98%	11.70%	77.74%	68.27%
±2σ	-23.82%	23.55%	94.35%	95.45%
±3σ	-35.66%	35.39%	98.23%	99.73%

Descriptive Statistics

Mean	-0.138%
Standard Error	0.704%
Median	-0.710%
Mode	-11.111%
Standard Deviation	11.842%
Sample Variance	140.228%
Kurtosis	2.26
Skewness	0.70
Range	90.107%
Minimum	-46.610%
Maximum	43.497%
Count	283

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.202%	127	44.88%	4.129%
Negative	-7.791%	155	54.77%	-4.267%
Zero	0.000%	1	0.35%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.99%
12	1 Quarter	13.87%
52	1 Year	14.85%
156	3 Years	15.50%
260	5 Years	16.91%
520	10 Years	17.07%
1,040	20 Years	17.07%
2,600	50 Years	17.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.72. Further, an Excess Kurtosis of 14.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.87%	0	0.00%	0.00%
-19.87% to -10.26%	0	0.00%	0.00%
-10.26% to -0.66%	0	0.00%	0.00%
-0.66% to 8.95%	41	14.44%	14.44%
8.95% to 18.55%	138	48.59%	63.03%
18.55% to 28.16%	63	22.18%	85.21%
28.16% to 37.76%	22	7.75%	92.96%
37.76% to 47.36%	11	3.87%	96.83%
47.36% to 56.97%	3	1.06%	97.89%
Greater than 56.97%	6	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.74%	31.36%	82.39%	68.27%
±2σ	-7.06%	44.16%	96.13%	95.45%
±3σ	-19.87%	56.97%	97.89%	99.73%

Descriptive Statistics

Mean	18.551%
Standard Error	0.760%
Median	15.646%
Mode	16.667%
Standard Deviation	12.806%
Sample Variance	163.982%
Kurtosis	14.11
Skewness	2.72
Range	115.932%
Minimum	0.999%
Maximum	116.931%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.551%	284	100.00%	18.551%
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 -0.01. Further, an Excess Kurtosis of 0.86 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.62%	1	0.35%	0.35%
-31.62% to -23.36%	7	2.46%	2.82%
-23.36% to -15.11%	13	4.58%	7.39%
-15.11% to -6.85%	28	9.86%	17.25%
-6.85% to 1.41%	100	35.21%	52.46%
1.41% to 9.67%	77	27.11%	79.58%
9.67% to 17.93%	40	14.08%	93.66%
17.93% to 26.18%	14	4.93%	98.59%
26.18% to 34.44%	3	1.06%	99.65%
Greater than 34.44%	1	0.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.60%	12.42%	72.18%	68.27%
±2σ	-20.61%	23.43%	94.37%	95.45%
±3σ	-31.62%	34.44%	99.30%	99.73%

Descriptive Statistics

Mean	1.410%
Standard Error	0.653%
Median	0.936%
Mode	0.000%
Standard Deviation	11.011%
Sample Variance	121.234%
Kurtosis	0.86
Skewness	-0.01
Range	69.101%
Minimum	-33.293%
Maximum	35.808%
Count	284

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.920%	153	53.87%	4.805%
Negative	-7.593%	127	44.72%	-3.395%
Zero	0.000%	4	1.41%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.21. Further, an Excess Kurtosis of 7.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.78%	0	0.00%	0.00%
-81.78% to -61.49%	0	0.00%	0.00%
-61.49% to -41.21%	0	0.00%	0.00%
-41.21% to -20.92%	12	18.46%	18.46%
-20.92% to -0.64%	29	44.62%	63.08%
-0.64% to 19.65%	14	21.54%	84.62%
19.65% to 39.93%	5	7.69%	92.31%
39.93% to 60.22%	3	4.62%	96.92%
60.22% to 80.50%	1	1.54%	98.46%
Greater than 80.50%	1	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.69%	26.41%	78.46%	68.27%
±2σ	-54.73%	53.46%	96.92%	95.45%
±3σ	-81.78%	80.50%	98.46%	99.73%

Descriptive Statistics

Mean	-0.638%
Standard Error	3.355%
Median	-8.099%
Mode	-37.394%
Standard Deviation	27.047%
Sample Variance	731.526%
Kurtosis	7.52
Skewness	2.21
Range	165.965%
Minimum	-37.394%
Maximum	128.571%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.505%	23	35.38%	9.025%
Negative	-14.954%	42	64.61%	-9.663%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	23.58%
12	1 Year	30.72%
36	3 Years	31.99%
60	5 Years	36.96%
120	10 Years	39.65%
240	20 Years	39.65%
600	50 Years	39.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.50. Further, an Excess Kurtosis of 7.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.79%	0	0.00%	0.00%
-60.79% to -33.80%	0	0.00%	0.00%
-33.80% to -6.81%	0	0.00%	0.00%
-6.81% to 20.18%	7	10.61%	10.61%
20.18% to 47.18%	36	54.55%	65.15%
47.18% to 74.17%	16	24.24%	89.39%
74.17% to 101.16%	4	6.06%	95.45%
101.16% to 128.15%	0	0.00%	95.45%
128.15% to 155.14%	0	0.00%	95.45%
Greater than 155.14%	3	4.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.19%	83.16%	84.85%	68.27%
±2σ	-24.80%	119.15%	95.45%	95.45%
±3σ	-60.79%	155.14%	95.45%	99.73%

Descriptive Statistics

Mean	47.176%
Standard Error	4.430%
Median	36.252%
Mode	2.604%
Standard Deviation	35.989%
Sample Variance	1295.172%
Kurtosis	7.81
Skewness	2.50
Range	189.843%
Minimum	2.604%
Maximum	192.447%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	47.176%	66	100.00%	47.176%
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 -0.22. Further, an Excess Kurtosis of 0.21 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.84%	0	0.00%	0.00%
-61.84% to -44.88%	1	1.52%	1.52%
-44.88% to -27.93%	4	6.06%	7.58%
-27.93% to -10.97%	8	12.12%	19.70%
-10.97% to 5.99%	19	28.79%	48.48%
5.99% to 22.95%	21	31.82%	80.30%
22.95% to 39.91%	7	10.61%	90.91%
39.91% to 56.87%	5	7.58%	98.48%
56.87% to 73.83%	1	1.52%	100.00%
Greater than 73.83%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.62%	28.61%	69.70%	68.27%
±2σ	-39.23%	51.22%	95.45%	95.45%
±3σ	-61.84%	73.83%	100.00%	99.73%

Descriptive Statistics

Mean	5.994%
Standard Error	2.783%
Median	6.888%
Mode	-56.163%
Standard Deviation	22.613%
Sample Variance	511.358%
Kurtosis	0.21
Skewness	-0.22
Range	115.439%
Minimum	-56.163%
Maximum	59.276%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.994%	40	60.61%	12.118%
Negative	-15.544%	26	39.39%	-6.123%
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 2.28. Further, an Excess Kurtosis of 6.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -125.85%	0	0.00%	0.00%
-125.85% to -95.40%	0	0.00%	0.00%
-95.40% to -64.94%	0	0.00%	0.00%
-64.94% to -34.49%	4	18.18%	18.18%
-34.49% to -4.04%	11	50.00%	68.18%
-4.04% to 26.41%	4	18.18%	86.36%
26.41% to 56.86%	2	9.09%	95.45%
56.86% to 87.31%	0	0.00%	95.45%
87.31% to 117.76%	0	0.00%	95.45%
Greater than 117.76%	1	4.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-44.64%	36.56%	81.82%	68.27%
±2σ	-85.25%	77.16%	95.45%	95.45%
±3σ	-125.85%	117.76%	95.45%	99.73%

Descriptive Statistics

Mean	-4.044%
Standard Error	8.656%
Median	-15.846%
Mode	-45.861%
Standard Deviation	40.601%
Sample Variance	1648.407%
Kurtosis	6.50
Skewness	2.28
Range	183.452%
Minimum	-45.861%
Maximum	137.591%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	44.978%	6	27.27%	12.267%
Negative	-22.427%	16	72.73%	-16.310%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	40.71%
12	3 Years	52.84%
20	5 Years	57.67%
40	10 Years	69.87%
80	20 Years	69.87%
200	50 Years	69.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.41. 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 -75.48%	0	0.00%	0.00%
-75.48% to -32.37%	0	0.00%	0.00%
-32.37% to 10.75%	1	4.35%	4.35%
10.75% to 53.86%	2	8.70%	13.04%
53.86% to 96.98%	13	56.52%	69.57%
96.98% to 140.09%	3	13.04%	82.61%
140.09% to 183.21%	1	4.35%	86.96%
183.21% to 226.33%	2	8.70%	95.65%
226.33% to 269.44%	1	4.35%	100.00%
Greater than 269.44%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	39.49%	154.47%	73.91%	68.27%
±2σ	-18.00%	211.95%	95.65%	95.45%
±3σ	-75.48%	269.44%	100.00%	99.73%

Descriptive Statistics

Mean	96.979%
Standard Error	11.987%
Median	80.402%
Mode	6.771%
Standard Deviation	57.488%
Sample Variance	3304.856%
Kurtosis	2.68
Skewness	1.41
Range	261.333%
Minimum	6.771%
Maximum	268.104%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	96.979%	23	100.00%	96.979%
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 -0.17. Further, an Excess Kurtosis of -0.13 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.96%	0	0.00%	0.00%
-85.96% to -60.19%	0	0.00%	0.00%
-60.19% to -34.41%	2	8.70%	8.70%
-34.41% to -8.63%	3	13.04%	21.74%
-8.63% to 17.14%	7	30.43%	52.17%
17.14% to 42.92%	6	26.09%	78.26%
42.92% to 68.70%	3	13.04%	91.30%
68.70% to 94.47%	2	8.70%	100.00%
94.47% to 120.25%	0	0.00%	100.00%
Greater than 120.25%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.23%	51.51%	65.22%	68.27%
±2σ	-51.59%	85.88%	95.65%	95.45%
±3σ	-85.96%	120.25%	100.00%	99.73%

Descriptive Statistics

Mean	17.144%
Standard Error	7.166%
Median	15.916%
Mode	-57.911%
Standard Deviation	34.369%
Sample Variance	1181.248%
Kurtosis	-0.13
Skewness	-0.17
Range	139.100%
Minimum	-57.911%
Maximum	81.189%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.110%	17	73.91%	23.733%
Negative	-25.260%	6	26.09%	-6.590%
Zero	0.000%	0	0.00%	0.000%

LCID Deep Analytical Report