LMND - 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	5.40%	3.86%	4.71%	7.06%	5.72%	5.78%	62.96	70.60	59.46	74.75
Weekly	12.91%	11.71%	11.95%	16.71%	12.60%	12.72%	58.78	75.62	51.82	85.77
Monthly	27.40%	24.21%	23.72%	36.15%	26.22%	26.49%	51.29	86.66	39.46	112.64
Quarterly	56.15%	50.50%	45.87%	66.40%	45.41%	45.87%	42.33	104.99	26.88	165.35
Annual	—	—	—	—	90.83%	91.75%	26.88	165.35	10.84	410.07
Option Time Horizon	—	—	—	—	34.28%	34.63%	47.32	93.93	33.59	132.35

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $66.67 | Strike (K): $70.00 (first OTM call ≥ spot) | Observed Mid-Price: $7.9500 (Bid $7.4000 / Ask $8.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 90.83% (CRR binomial tree, American, n=20 steps) | BS IV: 91.63% (European Black-Scholes) | Yahoo IV (Annual): 91.75% → 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 1.10. Further, an Excess Kurtosis of 7.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.07%	5	0.35%	0.35%
-16.07% to -12.02%	6	0.42%	0.77%
-12.02% to -7.96%	44	3.06%	3.83%
-7.96% to -3.91%	220	15.32%	19.15%
-3.91% to 0.14%	498	34.68%	53.83%
0.14% to 4.19%	401	27.92%	81.75%
4.19% to 8.24%	180	12.53%	94.29%
8.24% to 12.29%	52	3.62%	97.91%
12.29% to 16.34%	18	1.25%	99.16%
Greater than 16.34%	12	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.26%	5.54%	75.70%	68.27%
±2σ	-10.67%	10.94%	95.96%	95.45%
±3σ	-16.07%	16.34%	98.82%	99.73%

Descriptive Statistics

Mean	0.139%
Standard Error	0.143%
Median	-0.360%
Mode	0.000%
Standard Deviation	5.402%
Sample Variance	29.187%
Kurtosis	7.46
Skewness	1.10
Range	74.716%
Minimum	-27.716%
Maximum	47.000%
Count	1436

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.356%	668	46.52%	2.026%
Negative	-3.552%	763	53.13%	-1.887%
Zero	0.000%	5	0.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.57%
20	1 Month	6.90%
60	1 Quarter	7.34%
250	1 Year	7.25%
750	3 Years	6.80%
1,250	5 Years	7.06%
2,500	10 Years	7.38%
5,000	20 Years	7.38%
12,500	50 Years	7.38%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.44. Further, an Excess Kurtosis of 11.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.30%	0	0.00%	0.00%
-4.30% to -1.41%	0	0.00%	0.00%
-1.41% to 1.49%	0	0.00%	0.00%
1.49% to 4.38%	276	19.21%	19.21%
4.38% to 7.27%	605	42.10%	61.31%
7.27% to 10.17%	331	23.03%	84.34%
10.17% to 13.06%	130	9.05%	93.39%
13.06% to 15.95%	50	3.48%	96.87%
15.95% to 18.85%	16	1.11%	97.98%
Greater than 18.85%	29	2.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.42%	11.13%	81.14%	68.27%
±2σ	-0.44%	14.99%	96.17%	95.45%
±3σ	-4.30%	18.85%	97.98%	99.73%

Descriptive Statistics

Mean	7.274%
Standard Error	0.102%
Median	6.382%
Mode	4.258%
Standard Deviation	3.858%
Sample Variance	14.884%
Kurtosis	11.53
Skewness	2.44
Range	42.633%
Minimum	1.798%
Maximum	44.431%
Count	1437

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.274%	1437	100.00%	7.274%
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 -0.26. Further, an Excess Kurtosis of 2.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.04%	10	0.70%	0.70%
-14.04% to -10.51%	13	0.90%	1.60%
-10.51% to -6.97%	67	4.66%	6.26%
-6.97% to -3.44%	202	14.06%	20.32%
-3.44% to 0.09%	411	28.60%	48.92%
0.09% to 3.63%	452	31.45%	80.38%
3.63% to 7.16%	198	13.78%	94.15%
7.16% to 10.70%	64	4.45%	98.61%
10.70% to 14.23%	16	1.11%	99.72%
Greater than 14.23%	4	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.62%	4.81%	72.58%	68.27%
±2σ	-9.33%	9.52%	95.62%	95.45%
±3σ	-14.04%	14.23%	99.03%	99.73%

Descriptive Statistics

Mean	0.094%
Standard Error	0.124%
Median	0.264%
Mode	0.000%
Standard Deviation	4.713%
Sample Variance	22.208%
Kurtosis	2.07
Skewness	-0.26
Range	48.791%
Minimum	-27.878%
Maximum	20.913%
Count	1437

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.555%	741	51.57%	1.833%
Negative	-3.617%	691	48.09%	-1.739%
Zero	0.000%	5	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.23. Further, an Excess Kurtosis of 3.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.03%	0	0.00%	0.00%
-38.03% to -28.34%	2	0.67%	0.67%
-28.34% to -18.66%	10	3.36%	4.03%
-18.66% to -8.98%	48	16.11%	20.13%
-8.98% to 0.70%	103	34.56%	54.70%
0.70% to 10.39%	85	28.52%	83.22%
10.39% to 20.07%	34	11.41%	94.63%
20.07% to 29.75%	8	2.68%	97.32%
29.75% to 39.44%	1	0.34%	97.65%
Greater than 39.44%	7	2.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.21%	13.62%	76.51%	68.27%
±2σ	-25.12%	26.53%	95.30%	95.45%
±3σ	-38.03%	39.44%	97.65%	99.73%

Descriptive Statistics

Mean	0.705%
Standard Error	0.748%
Median	-0.585%
Mode	18.554%
Standard Deviation	12.911%
Sample Variance	166.689%
Kurtosis	3.86
Skewness	1.23
Range	96.156%
Minimum	-34.494%
Maximum	61.662%
Count	298

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.351%	142	47.65%	4.932%
Negative	-8.127%	155	52.01%	-4.227%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.80%
12	1 Quarter	18.67%
52	1 Year	16.77%
156	3 Years	16.43%
260	5 Years	16.71%
520	10 Years	17.57%
1,040	20 Years	17.57%
2,600	50 Years	17.57%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.43. Further, an Excess Kurtosis of 9.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.72%	0	0.00%	0.00%
-15.72% to -6.94%	0	0.00%	0.00%
-6.94% to 1.83%	0	0.00%	0.00%
1.83% to 10.61%	53	17.73%	17.73%
10.61% to 19.39%	133	44.48%	62.21%
19.39% to 28.17%	68	22.74%	84.95%
28.17% to 36.95%	24	8.03%	92.98%
36.95% to 45.73%	8	2.68%	95.65%
45.73% to 54.51%	5	1.67%	97.32%
Greater than 54.51%	8	2.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.69%	31.10%	83.95%	68.27%
±2σ	-4.02%	42.80%	95.32%	95.45%
±3σ	-15.72%	54.51%	97.32%	99.73%

Descriptive Statistics

Mean	19.393%
Standard Error	0.677%
Median	16.217%
Mode	8.951%
Standard Deviation	11.705%
Sample Variance	137.004%
Kurtosis	9.08
Skewness	2.43
Range	91.032%
Minimum	5.847%
Maximum	96.879%
Count	299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.393%	299	100.00%	19.393%
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 -0.06. Further, an Excess Kurtosis of 1.43 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.16%	2	0.67%	0.67%
-35.16% to -26.20%	5	1.67%	2.34%
-26.20% to -17.24%	9	3.01%	5.35%
-17.24% to -8.28%	43	14.38%	19.73%
-8.28% to 0.68%	91	30.43%	50.17%
0.68% to 9.64%	92	30.77%	80.94%
9.64% to 18.61%	40	13.38%	94.31%
18.61% to 27.57%	11	3.68%	97.99%
27.57% to 36.53%	3	1.00%	99.00%
Greater than 36.53%	3	1.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.27%	12.63%	75.25%	68.27%
±2σ	-23.21%	24.58%	93.98%	95.45%
±3σ	-35.16%	36.53%	98.33%	99.73%

Descriptive Statistics

Mean	0.683%
Standard Error	0.691%
Median	0.671%
Mode	-38.342%
Standard Deviation	11.948%
Sample Variance	142.744%
Kurtosis	1.43
Skewness	-0.06
Range	77.391%
Minimum	-38.342%
Maximum	39.049%
Count	299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.403%	153	51.17%	4.812%
Negative	-8.513%	145	48.49%	-4.128%
Zero	0.000%	1	0.33%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.61. Further, an Excess Kurtosis of 4.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -78.93%	0	0.00%	0.00%
-78.93% to -58.38%	0	0.00%	0.00%
-58.38% to -37.83%	2	2.94%	2.94%
-37.83% to -17.29%	11	16.18%	19.12%
-17.29% to 3.26%	31	45.59%	64.71%
3.26% to 23.81%	13	19.12%	83.82%
23.81% to 44.36%	7	10.29%	94.12%
44.36% to 64.90%	2	2.94%	97.06%
64.90% to 85.45%	1	1.47%	98.53%
Greater than 85.45%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.14%	30.66%	77.94%	68.27%
±2σ	-51.53%	58.05%	94.12%	95.45%
±3σ	-78.93%	85.45%	98.53%	99.73%

Descriptive Statistics

Mean	3.261%
Standard Error	3.322%
Median	-0.991%
Mode	-40.817%
Standard Deviation	27.397%
Sample Variance	750.613%
Kurtosis	4.11
Skewness	1.61
Range	158.781%
Minimum	-40.817%
Maximum	117.964%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.897%	33	48.53%	11.112%
Negative	-15.254%	35	51.47%	-7.851%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	42.20%
12	1 Year	35.76%
36	3 Years	37.88%
60	5 Years	36.15%
120	10 Years	37.75%
240	20 Years	37.75%
600	50 Years	37.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.29. Further, an Excess Kurtosis of 1.70 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.40%	0	0.00%	0.00%
-26.40% to -8.25%	0	0.00%	0.00%
-8.25% to 9.91%	0	0.00%	0.00%
9.91% to 28.07%	14	20.29%	20.29%
28.07% to 46.22%	30	43.48%	63.77%
46.22% to 64.38%	9	13.04%	76.81%
64.38% to 82.53%	11	15.94%	92.75%
82.53% to 100.69%	3	4.35%	97.10%
100.69% to 118.84%	0	0.00%	97.10%
Greater than 118.84%	2	2.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.01%	70.43%	73.91%	68.27%
±2σ	-2.19%	94.63%	95.65%	95.45%
±3σ	-26.40%	118.84%	97.10%	99.73%

Descriptive Statistics

Mean	46.220%
Standard Error	2.914%
Median	41.718%
Mode	14.634%
Standard Deviation	24.207%
Sample Variance	585.978%
Kurtosis	1.70
Skewness	1.29
Range	114.515%
Minimum	14.634%
Maximum	129.149%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.220%	69	100.00%	46.220%
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 0.27. Further, an Excess Kurtosis of 0.47 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.31%	0	0.00%	0.00%
-68.31% to -50.52%	1	1.45%	1.45%
-50.52% to -32.72%	3	4.35%	5.80%
-32.72% to -14.93%	10	14.49%	20.29%
-14.93% to 2.86%	23	33.33%	53.62%
2.86% to 20.66%	19	27.54%	81.16%
20.66% to 38.45%	9	13.04%	94.20%
38.45% to 56.24%	2	2.90%	97.10%
56.24% to 74.03%	2	2.90%	100.00%
Greater than 74.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.86%	26.59%	69.57%	68.27%
±2σ	-44.59%	50.31%	95.65%	95.45%
±3σ	-68.31%	74.03%	100.00%	99.73%

Descriptive Statistics

Mean	2.863%
Standard Error	2.856%
Median	1.721%
Mode	-53.117%
Standard Deviation	23.724%
Sample Variance	562.838%
Kurtosis	0.47
Skewness	0.27
Range	120.195%
Minimum	-53.117%
Maximum	67.078%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.700%	37	53.62%	10.564%
Negative	-16.603%	32	46.38%	-7.700%
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 1.65. Further, an Excess Kurtosis of 3.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -157.01%	0	0.00%	0.00%
-157.01% to -114.89%	0	0.00%	0.00%
-114.89% to -72.78%	0	0.00%	0.00%
-72.78% to -30.67%	6	26.09%	26.09%
-30.67% to 11.45%	8	34.78%	60.87%
11.45% to 53.56%	6	26.09%	86.96%
53.56% to 95.67%	1	4.35%	91.30%
95.67% to 137.79%	1	4.35%	95.65%
137.79% to 179.90%	0	0.00%	95.65%
Greater than 179.90%	1	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-44.70%	67.60%	82.61%	68.27%
±2σ	-100.86%	123.75%	95.65%	95.45%
±3σ	-157.01%	179.90%	95.65%	99.73%

Descriptive Statistics

Mean	11.447%
Standard Error	11.708%
Median	-3.695%
Mode	-52.946%
Standard Deviation	56.151%
Sample Variance	3152.911%
Kurtosis	3.54
Skewness	1.65
Range	241.771%
Minimum	-52.946%
Maximum	188.825%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.026%	11	47.83%	25.838%
Negative	-27.583%	12	52.17%	-14.391%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	63.12%
12	3 Years	72.35%
20	5 Years	66.40%
40	10 Years	73.97%
80	20 Years	73.97%
200	50 Years	73.97%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.15. Further, an Excess Kurtosis of 5.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.19%	0	0.00%	0.00%
-53.19% to -15.32%	0	0.00%	0.00%
-15.32% to 22.55%	0	0.00%	0.00%
22.55% to 60.42%	3	12.50%	12.50%
60.42% to 98.30%	14	58.33%	70.83%
98.30% to 136.17%	5	20.83%	91.67%
136.17% to 174.04%	0	0.00%	91.67%
174.04% to 211.91%	1	4.17%	95.83%
211.91% to 249.78%	0	0.00%	95.83%
Greater than 249.78%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	47.80%	148.79%	83.33%	68.27%
±2σ	-2.70%	199.29%	91.67%	95.45%
±3σ	-53.19%	249.78%	95.83%	99.73%

Descriptive Statistics

Mean	98.297%
Standard Error	10.307%
Median	86.346%
Mode	45.781%
Standard Deviation	50.496%
Sample Variance	2549.805%
Kurtosis	5.46
Skewness	2.15
Range	223.362%
Minimum	45.781%
Maximum	269.143%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	98.297%	24	100.00%	98.297%
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 0.58. Further, an Excess Kurtosis of -0.31 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -128.91%	0	0.00%	0.00%
-128.91% to -94.50%	0	0.00%	0.00%
-94.50% to -60.10%	1	4.17%	4.17%
-60.10% to -25.70%	5	20.83%	25.00%
-25.70% to 8.71%	8	33.33%	58.33%
8.71% to 43.12%	4	16.67%	75.00%
43.12% to 77.52%	4	16.67%	91.67%
77.52% to 111.92%	2	8.33%	100.00%
111.92% to 146.33%	0	0.00%	100.00%
Greater than 146.33%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-37.16%	54.58%	70.83%	68.27%
±2σ	-83.04%	100.46%	95.83%	95.45%
±3σ	-128.91%	146.33%	100.00%	99.73%

Descriptive Statistics

Mean	8.710%
Standard Error	9.364%
Median	2.877%
Mode	-63.862%
Standard Deviation	45.873%
Sample Variance	2104.328%
Kurtosis	-0.31
Skewness	0.58
Range	174.008%
Minimum	-63.862%
Maximum	110.146%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.930%	13	54.17%	22.712%
Negative	-30.550%	11	45.83%	-14.002%
Zero	0.000%	0	0.00%	0.000%

LMND Deep Analytical Report