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%	3.05%	3.22%	5.19%	4.45%	4.47%	14.03	15.34	13.42	16.03
Weekly	9.12%	8.85%	9.00%	12.62%	9.79%	9.83%	13.30	16.18	12.06	17.84
Monthly	18.19%	18.83%	17.77%	27.74%	20.38%	20.47%	11.97	17.99	9.76	22.05
Quarterly	38.60%	39.87%	38.14%	52.15%	35.30%	35.45%	10.31	20.88	7.24	29.72
Annual	—	—	—	—	70.60%	70.90%	7.24	29.72	3.57	60.21
Option Time Horizon	—	—	—	—	26.65%	26.76%	11.24	19.15	8.61	25.00

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $14.67 | Strike (K): $15.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.4500 (Bid $1.3000 / Ask $1.6000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 70.60% (CRR binomial tree, American, n=20 steps) | BS IV: 70.78% (European Black-Scholes) | Yahoo IV (Annual): 70.90% → 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 0.85. Further, an Excess Kurtosis of 14.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.00%	10	0.35%	0.35%
-12.00% to -9.00%	26	0.92%	1.27%
-9.00% to -6.00%	94	3.32%	4.59%
-6.00% to -3.00%	335	11.82%	16.41%
-3.00% to 0.01%	1044	36.84%	53.25%
0.01% to 3.01%	853	30.10%	83.35%
3.01% to 6.01%	338	11.93%	95.27%
6.01% to 9.01%	76	2.68%	97.95%
9.01% to 12.02%	32	1.13%	99.08%
Greater than 12.02%	26	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.00%	4.01%	78.97%	68.27%
±2σ	-8.00%	8.01%	95.52%	95.45%
±3σ	-12.00%	12.02%	98.73%	99.73%

Descriptive Statistics

Mean	0.006%
Standard Error	0.075%
Median	-0.130%
Mode	0.000%
Standard Deviation	4.003%
Sample Variance	16.023%
Kurtosis	14.37
Skewness	0.85
Range	82.745%
Minimum	-34.930%
Maximum	47.815%
Count	2834

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.924%	1325	46.75%	1.367%
Negative	-2.664%	1448	51.09%	-1.361%
Zero	0.000%	61	2.15%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.48%
20	1 Month	5.64%
60	1 Quarter	5.19%
250	1 Year	4.82%
750	3 Years	4.56%
1,250	5 Years	5.19%
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 3.56. Further, an Excess Kurtosis of 32.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.10%	0	0.00%	0.00%
-4.10% to -1.80%	0	0.00%	0.00%
-1.80% to 0.48%	0	0.00%	0.00%
0.48% to 2.78%	458	16.16%	16.16%
2.78% to 5.07%	1346	47.48%	63.63%
5.07% to 7.36%	600	21.16%	84.80%
7.36% to 9.65%	237	8.36%	93.16%
9.65% to 11.94%	95	3.35%	96.51%
11.94% to 14.23%	52	1.83%	98.34%
Greater than 14.23%	47	1.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.01%	8.12%	84.90%	68.27%
±2σ	-1.04%	11.17%	95.84%	95.45%
±3σ	-4.10%	14.23%	98.34%	99.73%

Descriptive Statistics

Mean	5.066%
Standard Error	0.057%
Median	4.312%
Mode	5.000%
Standard Deviation	3.054%
Sample Variance	9.327%
Kurtosis	32.38
Skewness	3.56
Range	53.661%
Minimum	1.080%
Maximum	54.741%
Count	2835

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.066%	2835	100.00%	5.066%
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 0.04. 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 -9.50%	18	0.63%	0.63%
-9.50% to -7.09%	33	1.16%	1.80%
-7.09% to -4.67%	89	3.14%	4.94%
-4.67% to -2.25%	376	13.26%	18.20%
-2.25% to 0.16%	923	32.56%	50.76%
0.16% to 2.58%	880	31.04%	81.80%
2.58% to 4.99%	335	11.82%	93.62%
4.99% to 7.41%	126	4.44%	98.06%
7.41% to 9.82%	35	1.23%	99.29%
Greater than 9.82%	20	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.06%	3.38%	74.36%	68.27%
±2σ	-6.28%	6.60%	94.32%	95.45%
±3σ	-9.50%	9.82%	98.66%	99.73%

Descriptive Statistics

Mean	0.161%
Standard Error	0.060%
Median	0.115%
Mode	0.000%
Standard Deviation	3.221%
Sample Variance	10.375%
Kurtosis	2.82
Skewness	0.04
Range	38.316%
Minimum	-20.265%
Maximum	18.051%
Count	2835

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.474%	1437	50.69%	1.254%
Negative	-2.327%	1331	46.95%	-1.093%
Zero	0.000%	67	2.36%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 6.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.33%	3	0.51%	0.51%
-27.33% to -20.49%	3	0.51%	1.02%
-20.49% to -13.64%	23	3.91%	4.93%
-13.64% to -6.80%	80	13.61%	18.54%
-6.80% to 0.04%	192	32.65%	51.19%
0.04% to 6.89%	184	31.29%	82.48%
6.89% to 13.73%	73	12.41%	94.90%
13.73% to 20.57%	16	2.72%	97.62%
20.57% to 27.41%	9	1.53%	99.15%
Greater than 27.41%	5	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.08%	9.17%	76.70%	68.27%
±2σ	-18.21%	18.29%	95.41%	95.45%
±3σ	-27.33%	27.41%	98.64%	99.73%

Descriptive Statistics

Mean	0.043%
Standard Error	0.376%
Median	-0.074%
Mode	0.000%
Standard Deviation	9.124%
Sample Variance	83.247%
Kurtosis	6.07
Skewness	0.86
Range	99.118%
Minimum	-41.740%
Maximum	57.378%
Count	588

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.658%	287	48.81%	3.250%
Negative	-6.370%	296	50.34%	-3.207%
Zero	0.000%	5	0.85%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.48%
12	1 Quarter	12.75%
52	1 Year	11.64%
156	3 Years	11.07%
260	5 Years	12.62%
520	10 Years	12.56%
1,040	20 Years	12.45%
2,600	50 Years	12.45%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.11%	0	0.00%	0.00%
-13.11% to -6.47%	0	0.00%	0.00%
-6.47% to 0.17%	0	0.00%	0.00%
0.17% to 6.80%	97	16.47%	16.47%
6.80% to 13.44%	287	48.73%	65.20%
13.44% to 20.08%	116	19.69%	84.89%
20.08% to 26.72%	46	7.81%	92.70%
26.72% to 33.36%	25	4.24%	96.94%
33.36% to 39.99%	8	1.36%	98.30%
Greater than 39.99%	10	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.59%	22.29%	86.08%	68.27%
±2σ	-4.26%	31.14%	95.76%	95.45%
±3σ	-13.11%	40.00%	98.30%	99.73%

Descriptive Statistics

Mean	13.442%
Standard Error	0.365%
Median	11.028%
Mode	6.213%
Standard Deviation	8.851%
Sample Variance	78.348%
Kurtosis	9.87
Skewness	2.54
Range	67.849%
Minimum	2.908%
Maximum	70.757%
Count	589

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.442%	589	100.00%	13.442%
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 0.68. Further, an Excess Kurtosis of 4.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.16%	3	0.51%	0.51%
-26.16% to -19.41%	4	0.68%	1.19%
-19.41% to -12.66%	19	3.23%	4.41%
-12.66% to -5.90%	80	13.58%	18.00%
-5.90% to 0.85%	214	36.33%	54.33%
0.85% to 7.60%	164	27.84%	82.17%
7.60% to 14.35%	66	11.21%	93.38%
14.35% to 21.11%	26	4.41%	97.79%
21.11% to 27.86%	8	1.36%	99.15%
Greater than 27.86%	5	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.15%	9.85%	75.04%	68.27%
±2σ	-17.16%	18.85%	95.08%	95.45%
±3σ	-26.16%	27.86%	98.64%	99.73%

Descriptive Statistics

Mean	0.848%
Standard Error	0.371%
Median	0.253%
Mode	0.000%
Standard Deviation	9.003%
Sample Variance	81.046%
Kurtosis	4.75
Skewness	0.68
Range	97.129%
Minimum	-37.389%
Maximum	59.740%
Count	589

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.159%	298	50.59%	3.622%
Negative	-5.733%	285	48.39%	-2.774%
Zero	0.000%	6	1.02%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.01. Further, an Excess Kurtosis of 2.15 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.61%	0	0.00%	0.00%
-54.61% to -40.97%	0	0.00%	0.00%
-40.97% to -27.33%	5	3.70%	3.70%
-27.33% to -13.69%	23	17.04%	20.74%
-13.69% to -0.04%	52	38.52%	59.26%
-0.04% to 13.60%	26	19.26%	78.52%
13.60% to 27.24%	20	14.81%	93.33%
27.24% to 40.88%	5	3.70%	97.04%
40.88% to 54.52%	2	1.48%	98.52%
Greater than 54.52%	2	1.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.23%	18.14%	73.33%	68.27%
±2σ	-36.42%	36.33%	95.56%	95.45%
±3σ	-54.61%	54.52%	98.52%	99.73%

Descriptive Statistics

Mean	-0.045%
Standard Error	1.565%
Median	-2.993%
Mode	-39.747%
Standard Deviation	18.188%
Sample Variance	330.799%
Kurtosis	2.15
Skewness	1.01
Range	110.625%
Minimum	-39.747%
Maximum	70.878%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.718%	55	40.74%	6.811%
Negative	-11.570%	80	59.26%	-6.856%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.06%
12	1 Year	25.10%
36	3 Years	25.45%
60	5 Years	27.74%
120	10 Years	27.39%
240	20 Years	27.11%
600	50 Years	27.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.88. Further, an Excess Kurtosis of 12.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.56%	0	0.00%	0.00%
-24.56% to -10.44%	0	0.00%	0.00%
-10.44% to 3.68%	0	0.00%	0.00%
3.68% to 17.81%	20	14.71%	14.71%
17.81% to 31.93%	57	41.91%	56.62%
31.93% to 46.05%	40	29.41%	86.03%
46.05% to 60.17%	11	8.09%	94.12%
60.17% to 74.30%	5	3.68%	97.79%
74.30% to 88.42%	1	0.74%	98.53%
Greater than 88.42%	2	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.10%	50.76%	85.29%	68.27%
±2σ	-5.73%	69.59%	95.59%	95.45%
±3σ	-24.56%	88.42%	98.53%	99.73%

Descriptive Statistics

Mean	31.928%
Standard Error	1.615%
Median	28.348%
Mode	7.319%
Standard Deviation	18.830%
Sample Variance	354.571%
Kurtosis	12.63
Skewness	2.88
Range	131.418%
Minimum	7.319%
Maximum	138.737%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.928%	136	100.00%	31.928%
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 -50.13%	0	0.00%	0.00%
-50.13% to -36.80%	2	1.47%	1.47%
-36.80% to -23.47%	4	2.94%	4.41%
-23.47% to -10.15%	24	17.65%	22.06%
-10.15% to 3.18%	40	29.41%	51.47%
3.18% to 16.51%	40	29.41%	80.88%
16.51% to 29.83%	13	9.56%	90.44%
29.83% to 43.16%	10	7.35%	97.79%
43.16% to 56.49%	2	1.47%	99.26%
Greater than 56.49%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.59%	20.95%	72.79%	68.27%
±2σ	-32.36%	38.72%	94.12%	95.45%
±3σ	-50.13%	56.49%	99.26%	99.73%

Descriptive Statistics

Mean	3.179%
Standard Error	1.524%
Median	2.377%
Mode	-40.727%
Standard Deviation	17.769%
Sample Variance	315.728%
Kurtosis	0.84
Skewness	0.44
Range	107.744%
Minimum	-40.727%
Maximum	67.017%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.367%	75	55.15%	8.474%
Negative	-12.004%	60	44.12%	-5.296%
Zero	0.000%	1	0.73%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.36. 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 -113.73%	0	0.00%	0.00%
-113.73% to -84.78%	0	0.00%	0.00%
-84.78% to -55.83%	1	2.22%	2.22%
-55.83% to -26.88%	7	15.56%	17.78%
-26.88% to 2.07%	22	48.89%	66.67%
2.07% to 31.03%	7	15.56%	82.22%
31.03% to 59.98%	4	8.89%	91.11%
59.98% to 88.93%	3	6.67%	97.78%
88.93% to 117.88%	0	0.00%	97.78%
Greater than 117.88%	1	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.53%	40.68%	73.33%	68.27%
±2σ	-75.13%	79.28%	95.56%	95.45%
±3σ	-113.73%	117.88%	97.78%	99.73%

Descriptive Statistics

Mean	2.074%
Standard Error	5.755%
Median	-7.044%
Mode	-59.182%
Standard Deviation	38.603%
Sample Variance	1490.193%
Kurtosis	2.10
Skewness	1.36
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	-19.117%	30	66.67%	-12.745%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	44.18%
12	3 Years	49.97%
20	5 Years	52.15%
40	10 Years	51.18%
80	20 Years	50.19%
200	50 Years	50.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.79. Further, an Excess Kurtosis of 3.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.51%	0	0.00%	0.00%
-52.51% to -22.61%	0	0.00%	0.00%
-22.61% to 7.29%	0	0.00%	0.00%
7.29% to 37.19%	9	19.57%	19.57%
37.19% to 67.09%	20	43.48%	63.04%
67.09% to 96.99%	8	17.39%	80.43%
96.99% to 126.89%	5	10.87%	91.30%
126.89% to 156.79%	2	4.35%	95.65%
156.79% to 186.69%	1	2.17%	97.83%
Greater than 186.69%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.22%	106.96%	80.43%	68.27%
±2σ	-12.64%	146.82%	95.65%	95.45%
±3σ	-52.51%	186.69%	97.83%	99.73%

Descriptive Statistics

Mean	67.091%
Standard Error	5.878%
Median	53.938%
Mode	22.460%
Standard Deviation	39.867%
Sample Variance	1589.373%
Kurtosis	3.80
Skewness	1.79
Range	195.614%
Minimum	22.460%
Maximum	218.074%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	67.091%	46	100.00%	67.091%
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 1.13. Further, an Excess Kurtosis of 3.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.23%	0	0.00%	0.00%
-103.23% to -74.63%	0	0.00%	0.00%
-74.63% to -46.02%	1	2.17%	2.17%
-46.02% to -17.42%	8	17.39%	19.57%
-17.42% to 11.19%	17	36.96%	56.52%
11.19% to 39.80%	13	28.26%	84.78%
39.80% to 68.40%	4	8.70%	93.48%
68.40% to 97.01%	2	4.35%	97.83%
97.01% to 125.61%	0	0.00%	97.83%
Greater than 125.61%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.95%	49.33%	69.57%	68.27%
±2σ	-65.09%	87.47%	95.65%	95.45%
±3σ	-103.23%	125.61%	97.83%	99.73%

Descriptive Statistics

Mean	11.189%
Standard Error	5.624%
Median	8.692%
Mode	-56.406%
Standard Deviation	38.141%
Sample Variance	1454.766%
Kurtosis	3.08
Skewness	1.13
Range	207.899%
Minimum	-56.406%
Maximum	151.493%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.439%	31	67.39%	19.839%
Negative	-26.525%	15	32.61%	-8.650%
Zero	0.000%	0	0.00%	0.000%

LC Deep Analytical Report