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	5.50%	5.25%	4.56%	7.02%	4.87%	4.92%	9.81	10.82	9.35	11.36
Weekly	11.78%	12.73%	10.96%	16.70%	10.73%	10.82%	9.26	11.47	8.32	12.77
Monthly	26.82%	35.85%	22.47%	36.65%	22.33%	22.52%	8.24	12.88	6.59	16.11
Quarterly	40.55%	57.18%	34.43%	57.85%	38.68%	39.01%	7.00	15.17	4.75	22.33
Annual	—	—	—	—	77.35%	78.03%	4.75	22.33	2.19	48.41
Option Time Horizon	—	—	—	—	29.20%	29.45%	7.70	13.80	5.75	18.48

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $10.31 | Strike (K): $11.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.9550 (Bid $0.8100 / Ask $1.1000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 77.35% (CRR binomial tree, American, n=20 steps) | BS IV: 78.30% (European Black-Scholes) | Yahoo IV (Annual): 78.03% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 9.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.50%	6	0.43%	0.43%
-16.50% to -12.38%	9	0.65%	1.09%
-12.38% to -8.26%	38	2.75%	3.84%
-8.26% to -4.14%	173	12.52%	16.35%
-4.14% to -0.02%	503	36.40%	52.75%
-0.02% to 4.10%	429	31.04%	83.79%
4.10% to 8.23%	147	10.64%	94.43%
8.23% to 12.35%	50	3.62%	98.05%
12.35% to 16.47%	13	0.94%	98.99%
Greater than 16.47%	14	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.51%	5.48%	79.23%	68.27%
±2σ	-11.01%	10.97%	96.16%	95.45%
±3σ	-16.50%	16.47%	98.55%	99.73%

Descriptive Statistics

Mean	-0.017%
Standard Error	0.148%
Median	-0.295%
Mode	0.000%
Standard Deviation	5.495%
Sample Variance	30.191%
Kurtosis	9.82
Skewness	1.20
Range	81.626%
Minimum	-38.626%
Maximum	43.000%
Count	1382

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.100%	621	44.94%	1.842%
Negative	-3.524%	729	52.75%	-1.859%
Zero	0.000%	32	2.31%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.41%
20	1 Month	6.19%
60	1 Quarter	6.04%
250	1 Year	6.19%
750	3 Years	6.59%
1,250	5 Years	7.02%
2,500	10 Years	7.07%
5,000	20 Years	7.07%
12,500	50 Years	7.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.16. Further, an Excess Kurtosis of 81.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.81%	0	0.00%	0.00%
-8.81% to -4.88%	0	0.00%	0.00%
-4.88% to -0.94%	0	0.00%	0.00%
-0.94% to 3.00%	129	9.33%	9.33%
3.00% to 6.93%	729	52.71%	62.04%
6.93% to 10.87%	361	26.10%	88.14%
10.87% to 14.81%	100	7.23%	95.37%
14.81% to 18.75%	33	2.39%	97.76%
18.75% to 22.68%	13	0.94%	98.70%
Greater than 22.68%	18	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.68%	12.18%	85.68%	68.27%
±2σ	-3.57%	17.43%	97.32%	95.45%
±3σ	-8.82%	22.68%	98.70%	99.73%

Descriptive Statistics

Mean	6.935%
Standard Error	0.141%
Median	5.918%
Mode	4.369%
Standard Deviation	5.250%
Sample Variance	27.565%
Kurtosis	81.92
Skewness	6.16
Range	99.688%
Minimum	0.200%
Maximum	99.888%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.935%	1383	100.00%	6.935%
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 -0.56. Further, an Excess Kurtosis of 4.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.35%	11	0.80%	0.80%
-13.35% to -9.94%	18	1.30%	2.10%
-9.94% to -6.51%	46	3.33%	5.42%
-6.51% to -3.10%	174	12.58%	18.00%
-3.10% to 0.32%	424	30.66%	48.66%
0.32% to 3.74%	461	33.33%	82.00%
3.74% to 7.16%	158	11.42%	93.42%
7.16% to 10.58%	77	5.57%	98.99%
10.58% to 14.00%	9	0.65%	99.64%
Greater than 14.00%	5	0.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.24%	4.88%	74.84%	68.27%
±2σ	-8.79%	9.44%	95.37%	95.45%
±3σ	-13.35%	14.00%	98.84%	99.73%

Descriptive Statistics

Mean	0.323%
Standard Error	0.123%
Median	0.398%
Mode	0.000%
Standard Deviation	4.559%
Sample Variance	20.783%
Kurtosis	4.33
Skewness	-0.56
Range	54.329%
Minimum	-30.148%
Maximum	24.181%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.321%	750	54.23%	1.801%
Negative	-3.418%	598	43.24%	-1.478%
Zero	0.000%	35	2.53%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.69. Further, an Excess Kurtosis of 2.30 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.43%	1	0.35%	0.35%
-35.43% to -26.60%	1	0.35%	0.70%
-26.60% to -17.77%	10	3.48%	4.18%
-17.77% to -8.94%	42	14.63%	18.82%
-8.94% to -0.11%	100	34.84%	53.66%
-0.11% to 8.72%	91	31.71%	85.37%
8.72% to 17.55%	17	5.92%	91.29%
17.55% to 26.39%	14	4.88%	96.17%
26.39% to 35.22%	7	2.44%	98.61%
Greater than 35.22%	4	1.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.88%	11.67%	77.70%	68.27%
±2σ	-23.66%	23.44%	94.08%	95.45%
±3σ	-35.43%	35.22%	98.26%	99.73%

Descriptive Statistics

Mean	-0.108%
Standard Error	0.695%
Median	-0.670%
Mode	-11.111%
Standard Deviation	11.775%
Sample Variance	138.656%
Kurtosis	2.30
Skewness	0.69
Range	90.107%
Minimum	-46.610%
Maximum	43.497%
Count	287

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.098%	130	45.30%	4.121%
Negative	-7.780%	156	54.35%	-4.229%
Zero	0.000%	1	0.35%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.29%
12	1 Quarter	13.81%
52	1 Year	14.39%
156	3 Years	15.51%
260	5 Years	16.70%
520	10 Years	17.01%
1,040	20 Years	17.01%
2,600	50 Years	17.01%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.75. Further, an Excess Kurtosis of 14.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.73%	0	0.00%	0.00%
-19.73% to -10.18%	0	0.00%	0.00%
-10.18% to -0.63%	0	0.00%	0.00%
-0.63% to 8.92%	41	14.24%	14.24%
8.92% to 18.47%	142	49.31%	63.54%
18.47% to 28.02%	62	21.53%	85.07%
28.02% to 37.57%	23	7.99%	93.06%
37.57% to 47.12%	11	3.82%	96.88%
47.12% to 56.67%	3	1.04%	97.92%
Greater than 56.67%	6	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.74%	31.21%	82.64%	68.27%
±2σ	-7.00%	43.94%	96.18%	95.45%
±3σ	-19.73%	56.67%	97.92%	99.73%

Descriptive Statistics

Mean	18.473%
Standard Error	0.750%
Median	15.511%
Mode	16.667%
Standard Deviation	12.734%
Sample Variance	162.151%
Kurtosis	14.32
Skewness	2.75
Range	115.932%
Minimum	0.999%
Maximum	116.931%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.473%	288	100.00%	18.473%
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 0.00. Further, an Excess Kurtosis of 0.88 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.50%	1	0.35%	0.35%
-31.50% to -23.29%	7	2.43%	2.78%
-23.29% to -15.07%	13	4.51%	7.29%
-15.07% to -6.85%	28	9.72%	17.01%
-6.85% to 1.37%	101	35.07%	52.08%
1.37% to 9.59%	80	27.78%	79.86%
9.59% to 17.81%	40	13.89%	93.75%
17.81% to 26.03%	14	4.86%	98.61%
26.03% to 34.25%	2	0.69%	99.31%
Greater than 34.25%	2	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.59%	12.33%	72.22%	68.27%
±2σ	-20.55%	23.29%	94.10%	95.45%
±3σ	-31.50%	34.25%	98.96%	99.73%

Descriptive Statistics

Mean	1.372%
Standard Error	0.646%
Median	0.887%
Mode	0.000%
Standard Deviation	10.959%
Sample Variance	120.106%
Kurtosis	0.88
Skewness	0.00
Range	69.101%
Minimum	-33.293%
Maximum	35.808%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.918%	154	53.47%	4.769%
Negative	-7.525%	130	45.14%	-3.397%
Zero	0.000%	4	1.39%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.22. Further, an Excess Kurtosis of 7.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.97%	0	0.00%	0.00%
-80.97% to -60.86%	0	0.00%	0.00%
-60.86% to -40.75%	0	0.00%	0.00%
-40.75% to -20.63%	12	18.18%	18.18%
-20.63% to -0.52%	29	43.94%	62.12%
-0.52% to 19.59%	15	22.73%	84.85%
19.59% to 39.70%	5	7.58%	92.42%
39.70% to 59.81%	3	4.55%	96.97%
59.81% to 79.92%	1	1.52%	98.48%
Greater than 79.92%	1	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.34%	26.29%	78.79%	68.27%
±2σ	-54.15%	53.11%	96.97%	95.45%
±3σ	-80.97%	79.92%	98.48%	99.73%

Descriptive Statistics

Mean	-0.523%
Standard Error	3.301%
Median	-7.298%
Mode	-37.394%
Standard Deviation	26.815%
Sample Variance	719.067%
Kurtosis	7.67
Skewness	2.22
Range	165.965%
Minimum	-37.394%
Maximum	128.571%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.563%	24	36.36%	8.932%
Negative	-14.858%	42	63.64%	-9.455%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.86%
12	1 Year	30.30%
36	3 Years	31.94%
60	5 Years	36.65%
120	10 Years	39.36%
240	20 Years	39.36%
600	50 Years	39.36%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 7.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.74%	0	0.00%	0.00%
-60.74% to -33.85%	0	0.00%	0.00%
-33.85% to -6.97%	0	0.00%	0.00%
-6.97% to 19.92%	7	10.45%	10.45%
19.92% to 46.80%	37	55.22%	65.67%
46.80% to 73.69%	16	23.88%	89.55%
73.69% to 100.58%	4	5.97%	95.52%
100.58% to 127.47%	0	0.00%	95.52%
127.47% to 154.35%	0	0.00%	95.52%
Greater than 154.35%	3	4.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.96%	82.65%	85.07%	68.27%
±2σ	-24.89%	118.50%	95.52%	95.45%
±3σ	-60.74%	154.35%	95.52%	99.73%

Descriptive Statistics

Mean	46.805%
Standard Error	4.380%
Median	36.111%
Mode	2.604%
Standard Deviation	35.849%
Sample Variance	1285.182%
Kurtosis	7.92
Skewness	2.52
Range	189.843%
Minimum	2.604%
Maximum	192.447%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.805%	67	100.00%	46.805%
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 -0.18. 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 -61.70%	0	0.00%	0.00%
-61.70% to -44.85%	1	1.49%	1.49%
-44.85% to -27.99%	4	5.97%	7.46%
-27.99% to -11.14%	8	11.94%	19.40%
-11.14% to 5.72%	20	29.85%	49.25%
5.72% to 22.57%	21	31.34%	80.60%
22.57% to 39.43%	7	10.45%	91.04%
39.43% to 56.28%	5	7.46%	98.51%
56.28% to 73.14%	1	1.49%	100.00%
Greater than 73.14%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.75%	28.19%	70.15%	68.27%
±2σ	-39.23%	50.66%	95.52%	95.45%
±3σ	-61.70%	73.14%	100.00%	99.73%

Descriptive Statistics

Mean	5.718%
Standard Error	2.746%
Median	6.667%
Mode	-56.163%
Standard Deviation	22.473%
Sample Variance	505.050%
Kurtosis	0.23
Skewness	-0.18
Range	115.439%
Minimum	-56.163%
Maximum	59.276%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.863%	40	59.70%	11.858%
Negative	-15.239%	27	40.30%	-6.141%
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 2.26. Further, an Excess Kurtosis of 6.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -125.39%	0	0.00%	0.00%
-125.39% to -94.98%	0	0.00%	0.00%
-94.98% to -64.56%	0	0.00%	0.00%
-64.56% to -34.15%	4	18.18%	18.18%
-34.15% to -3.74%	11	50.00%	68.18%
-3.74% to 26.67%	4	18.18%	86.36%
26.67% to 57.09%	2	9.09%	95.45%
57.09% to 87.50%	0	0.00%	95.45%
87.50% to 117.91%	0	0.00%	95.45%
Greater than 117.91%	1	4.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-44.29%	36.81%	81.82%	68.27%
±2σ	-84.84%	77.36%	95.45%	95.45%
±3σ	-125.39%	117.91%	95.45%	99.73%

Descriptive Statistics

Mean	-3.740%
Standard Error	8.645%
Median	-13.509%
Mode	-45.861%
Standard Deviation	40.550%
Sample Variance	1644.271%
Kurtosis	6.46
Skewness	2.26
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	-22.009%	16	72.73%	-16.006%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	41.61%
12	3 Years	53.14%
20	5 Years	57.85%
40	10 Years	70.03%
80	20 Years	70.03%
200	50 Years	70.03%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.44. Further, an Excess Kurtosis of 2.74 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.34%	0	0.00%	0.00%
-74.34% to -31.45%	0	0.00%	0.00%
-31.45% to 11.43%	1	4.35%	4.35%
11.43% to 54.32%	2	8.70%	13.04%
54.32% to 97.20%	13	56.52%	69.57%
97.20% to 140.09%	3	13.04%	82.61%
140.09% to 182.98%	1	4.35%	86.96%
182.98% to 225.86%	2	8.70%	95.65%
225.86% to 268.75%	1	4.35%	100.00%
Greater than 268.75%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	40.02%	154.39%	73.91%	68.27%
±2σ	-17.16%	211.57%	95.65%	95.45%
±3σ	-74.34%	268.75%	100.00%	99.73%

Descriptive Statistics

Mean	97.205%
Standard Error	11.923%
Median	80.402%
Mode	6.771%
Standard Deviation	57.181%
Sample Variance	3269.641%
Kurtosis	2.74
Skewness	1.44
Range	261.333%
Minimum	6.771%
Maximum	268.104%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	97.205%	23	100.00%	97.205%
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 -0.13. Further, an Excess Kurtosis of -0.16 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.50%	0	0.00%	0.00%
-86.50% to -60.68%	0	0.00%	0.00%
-60.68% to -34.86%	1	4.35%	4.35%
-34.86% to -9.04%	4	17.39%	21.74%
-9.04% to 16.78%	7	30.43%	52.17%
16.78% to 42.60%	6	26.09%	78.26%
42.60% to 68.42%	3	13.04%	91.30%
68.42% to 94.24%	2	8.70%	100.00%
94.24% to 120.06%	0	0.00%	100.00%
Greater than 120.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.64%	51.21%	65.22%	68.27%
±2σ	-52.07%	85.64%	95.65%	95.45%
±3σ	-86.50%	120.06%	100.00%	99.73%

Descriptive Statistics

Mean	16.782%
Standard Error	7.178%
Median	12.091%
Mode	-57.911%
Standard Deviation	34.427%
Sample Variance	1185.200%
Kurtosis	-0.16
Skewness	-0.13
Range	139.100%
Minimum	-57.911%
Maximum	81.189%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.620%	17	73.91%	23.371%
Negative	-25.260%	6	26.09%	-6.590%
Zero	0.000%	0	0.00%	0.000%

LCID Deep Analytical Report