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%	3.88%	4.72%	7.11%	5.01%	5.01%	54.51	60.25	51.85	63.35
Weekly	12.92%	11.68%	11.93%	16.85%	11.02%	11.03%	51.33	63.99	45.97	71.44
Monthly	27.28%	24.06%	23.07%	36.01%	22.94%	22.96%	45.56	72.09	36.22	90.68
Quarterly	56.49%	51.12%	46.48%	65.96%	39.74%	39.77%	38.52	85.27	25.89	126.88
Annual	—	—	—	—	79.48%	79.54%	25.89	126.88	11.69	280.92
Option Time Horizon	—	—	—	—	25.98%	26.00%	44.20	74.31	34.09	96.36

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $57.31 | Strike (K): $58.00 (first OTM call ≥ spot) | Observed Mid-Price: $5.7000 (Bid $5.2000 / Ask $6.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 79.48% (CRR binomial tree, American, n=20 steps) | BS IV: 79.21% (European Black-Scholes) | Yahoo IV (Annual): 79.54% → 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 1.11. Further, an Excess Kurtosis of 7.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.08%	5	0.35%	0.35%
-16.08% to -12.03%	6	0.42%	0.78%
-12.03% to -7.98%	42	2.97%	3.75%
-7.98% to -3.92%	219	15.48%	19.22%
-3.92% to 0.13%	492	34.77%	53.99%
0.13% to 4.18%	393	27.77%	81.77%
4.18% to 8.23%	177	12.51%	94.28%
8.23% to 12.29%	52	3.67%	97.95%
12.29% to 16.34%	17	1.20%	99.15%
Greater than 16.34%	12	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.27%	5.53%	75.83%	68.27%
±2σ	-10.68%	10.93%	96.04%	95.45%
±3σ	-16.08%	16.34%	98.80%	99.73%

Descriptive Statistics

Mean	0.128%
Standard Error	0.144%
Median	-0.384%
Mode	0.000%
Standard Deviation	5.403%
Sample Variance	29.193%
Kurtosis	7.55
Skewness	1.11
Range	74.716%
Minimum	-27.716%
Maximum	47.000%
Count	1415

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.362%	656	46.36%	2.022%
Negative	-3.555%	754	53.29%	-1.894%
Zero	0.000%	5	0.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.76%
20	1 Month	8.35%
60	1 Quarter	7.27%
250	1 Year	7.54%
750	3 Years	6.79%
1,250	5 Years	7.11%
2,500	10 Years	7.39%
5,000	20 Years	7.39%
12,500	50 Years	7.39%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.34%	0	0.00%	0.00%
-4.34% to -1.44%	0	0.00%	0.00%
-1.44% to 1.47%	0	0.00%	0.00%
1.47% to 4.38%	270	19.07%	19.07%
4.38% to 7.28%	598	42.23%	61.30%
7.28% to 10.19%	328	23.16%	84.46%
10.19% to 13.10%	127	8.97%	93.43%
13.10% to 16.00%	48	3.39%	96.82%
16.00% to 18.91%	16	1.13%	97.95%
Greater than 18.91%	29	2.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.41%	11.16%	81.07%	68.27%
±2σ	-0.47%	15.03%	96.26%	95.45%
±3σ	-4.34%	18.91%	97.95%	99.73%

Descriptive Statistics

Mean	7.284%
Standard Error	0.103%
Median	6.374%
Mode	4.258%
Standard Deviation	3.875%
Sample Variance	15.014%
Kurtosis	11.46
Skewness	2.44
Range	42.633%
Minimum	1.798%
Maximum	44.431%
Count	1416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.284%	1416	100.00%	7.284%
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 -0.29. Further, an Excess Kurtosis of 2.09 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	0.71%	0.71%
-14.04% to -10.50%	13	0.92%	1.62%
-10.50% to -6.96%	66	4.66%	6.29%
-6.96% to -3.42%	198	13.98%	20.27%
-3.42% to 0.11%	404	28.53%	48.80%
0.11% to 3.65%	447	31.57%	80.37%
3.65% to 7.19%	196	13.84%	94.21%
7.19% to 10.72%	64	4.52%	98.73%
10.72% to 14.26%	14	0.99%	99.72%
Greater than 14.26%	4	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.60%	4.83%	72.67%	68.27%
±2σ	-9.32%	9.54%	95.69%	95.45%
±3σ	-14.04%	14.26%	99.01%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.125%
Median	0.288%
Mode	0.000%
Standard Deviation	4.716%
Sample Variance	22.239%
Kurtosis	2.09
Skewness	-0.29
Range	48.791%
Minimum	-27.878%
Maximum	20.913%
Count	1416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.556%	734	51.84%	1.843%
Negative	-3.620%	677	47.81%	-1.731%
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 1.27. Further, an Excess Kurtosis of 3.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.10%	0	0.00%	0.00%
-38.10% to -28.41%	2	0.68%	0.68%
-28.41% to -18.73%	9	3.06%	3.74%
-18.73% to -9.04%	48	16.33%	20.07%
-9.04% to 0.65%	104	35.37%	55.44%
0.65% to 10.34%	82	27.89%	83.33%
10.34% to 20.03%	33	11.22%	94.56%
20.03% to 29.72%	8	2.72%	97.28%
29.72% to 39.41%	1	0.34%	97.62%
Greater than 39.41%	7	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.27%	13.57%	76.87%	68.27%
±2σ	-25.19%	26.49%	95.24%	95.45%
±3σ	-38.10%	39.41%	97.62%	99.73%

Descriptive Statistics

Mean	0.653%
Standard Error	0.753%
Median	-0.660%
Mode	18.554%
Standard Deviation	12.919%
Sample Variance	166.903%
Kurtosis	3.92
Skewness	1.27
Range	96.156%
Minimum	-34.494%
Maximum	61.662%
Count	294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.441%	138	46.94%	4.901%
Negative	-8.058%	155	52.72%	-4.248%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	21.17%
12	1 Quarter	17.29%
52	1 Year	17.06%
156	3 Years	16.33%
260	5 Years	16.85%
520	10 Years	17.56%
1,040	20 Years	17.56%
2,600	50 Years	17.56%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.63%	0	0.00%	0.00%
-15.63% to -6.87%	0	0.00%	0.00%
-6.87% to 1.89%	0	0.00%	0.00%
1.89% to 10.65%	54	18.31%	18.31%
10.65% to 19.41%	128	43.39%	61.69%
19.41% to 28.17%	68	23.05%	84.75%
28.17% to 36.93%	25	8.47%	93.22%
36.93% to 45.69%	8	2.71%	95.93%
45.69% to 54.45%	4	1.36%	97.29%
Greater than 54.45%	8	2.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.73%	31.09%	83.73%	68.27%
±2σ	-3.95%	42.77%	95.59%	95.45%
±3σ	-15.63%	54.45%	97.29%	99.73%

Descriptive Statistics

Mean	19.409%
Standard Error	0.680%
Median	16.507%
Mode	8.951%
Standard Deviation	11.679%
Sample Variance	136.399%
Kurtosis	9.22
Skewness	2.43
Range	91.032%
Minimum	5.847%
Maximum	96.879%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.409%	295	100.00%	19.409%
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 -0.10. Further, an Excess Kurtosis of 1.45 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.06%	2	0.68%	0.68%
-35.06% to -26.12%	5	1.69%	2.37%
-26.12% to -17.17%	9	3.05%	5.42%
-17.17% to -8.22%	44	14.92%	20.34%
-8.22% to 0.72%	86	29.15%	49.49%
0.72% to 9.66%	93	31.53%	81.02%
9.66% to 18.61%	40	13.56%	94.58%
18.61% to 27.56%	10	3.39%	97.97%
27.56% to 36.50%	3	1.02%	98.98%
Greater than 36.50%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.21%	12.65%	74.92%	68.27%
±2σ	-23.13%	24.57%	94.24%	95.45%
±3σ	-35.06%	36.50%	98.31%	99.73%

Descriptive Statistics

Mean	0.720%
Standard Error	0.694%
Median	0.857%
Mode	-38.342%
Standard Deviation	11.927%
Sample Variance	142.260%
Kurtosis	1.45
Skewness	-0.10
Range	77.391%
Minimum	-38.342%
Maximum	39.049%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.306%	153	51.86%	4.826%
Negative	-8.591%	141	47.80%	-4.106%
Zero	0.000%	1	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.70. Further, an Excess Kurtosis of 4.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -78.87%	0	0.00%	0.00%
-78.87% to -58.41%	0	0.00%	0.00%
-58.41% to -37.95%	1	1.49%	1.49%
-37.95% to -17.48%	12	17.91%	19.40%
-17.48% to 2.98%	30	44.78%	64.18%
2.98% to 23.44%	14	20.90%	85.07%
23.44% to 43.90%	5	7.46%	92.54%
43.90% to 64.36%	3	4.48%	97.01%
64.36% to 84.82%	1	1.49%	98.51%
Greater than 84.82%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.30%	30.26%	79.10%	68.27%
±2σ	-51.59%	57.54%	94.03%	95.45%
±3σ	-78.87%	84.82%	98.51%	99.73%

Descriptive Statistics

Mean	2.978%
Standard Error	3.333%
Median	-1.922%
Mode	-40.817%
Standard Deviation	27.282%
Sample Variance	744.285%
Kurtosis	4.36
Skewness	1.70
Range	158.781%
Minimum	-40.817%
Maximum	117.964%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.718%	32	47.76%	10.850%
Negative	-15.071%	35	52.24%	-7.873%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	32.34%
12	1 Year	33.85%
36	3 Years	37.20%
60	5 Years	36.01%
120	10 Years	37.57%
240	20 Years	37.57%
600	50 Years	37.57%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.33. Further, an Excess Kurtosis of 1.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.26%	0	0.00%	0.00%
-26.26% to -8.21%	0	0.00%	0.00%
-8.21% to 9.84%	0	0.00%	0.00%
9.84% to 27.89%	14	20.59%	20.59%
27.89% to 45.93%	29	42.65%	63.24%
45.93% to 63.98%	10	14.71%	77.94%
63.98% to 82.03%	10	14.71%	92.65%
82.03% to 100.07%	3	4.41%	97.06%
100.07% to 118.12%	0	0.00%	97.06%
Greater than 118.12%	2	2.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.87%	70.00%	75.00%	68.27%
±2σ	-2.19%	94.06%	95.59%	95.45%
±3σ	-26.26%	118.12%	97.06%	99.73%

Descriptive Statistics

Mean	45.932%
Standard Error	2.918%
Median	41.992%
Mode	14.634%
Standard Deviation	24.063%
Sample Variance	579.037%
Kurtosis	1.91
Skewness	1.33
Range	114.515%
Minimum	14.634%
Maximum	129.149%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	45.932%	68	100.00%	45.932%
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 0.11. Further, an Excess Kurtosis of 0.26 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -66.17%	0	0.00%	0.00%
-66.17% to -48.86%	1	1.47%	1.47%
-48.86% to -31.56%	3	4.41%	5.88%
-31.56% to -14.26%	9	13.24%	19.12%
-14.26% to 3.04%	23	33.82%	52.94%
3.04% to 20.35%	18	26.47%	79.41%
20.35% to 37.65%	10	14.71%	94.12%
37.65% to 54.95%	3	4.41%	98.53%
54.95% to 72.25%	1	1.47%	100.00%
Greater than 72.25%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.03%	26.11%	69.12%	68.27%
±2σ	-43.10%	49.18%	95.59%	95.45%
±3σ	-66.17%	72.25%	100.00%	99.73%

Descriptive Statistics

Mean	3.044%
Standard Error	2.798%
Median	2.072%
Mode	-53.117%
Standard Deviation	23.070%
Sample Variance	532.221%
Kurtosis	0.26
Skewness	0.11
Range	120.195%
Minimum	-53.117%
Maximum	67.078%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.262%	37	54.41%	10.481%
Negative	-16.313%	31	45.59%	-7.437%
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 1.63. Further, an Excess Kurtosis of 3.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -158.50%	0	0.00%	0.00%
-158.50% to -116.12%	0	0.00%	0.00%
-116.12% to -73.76%	0	0.00%	0.00%
-73.76% to -31.39%	7	30.43%	30.43%
-31.39% to 10.98%	7	30.43%	60.87%
10.98% to 53.35%	6	26.09%	86.96%
53.35% to 95.72%	1	4.35%	91.30%
95.72% to 138.09%	1	4.35%	95.65%
138.09% to 180.46%	0	0.00%	95.65%
Greater than 180.46%	1	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-45.51%	67.48%	82.61%	68.27%
±2σ	-102.00%	123.97%	95.65%	95.45%
±3σ	-158.50%	180.46%	95.65%	99.73%

Descriptive Statistics

Mean	10.984%
Standard Error	11.780%
Median	-3.695%
Mode	-52.946%
Standard Deviation	56.493%
Sample Variance	3191.493%
Kurtosis	3.45
Skewness	1.63
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	-28.472%	12	52.17%	-14.855%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	60.95%
12	3 Years	71.62%
20	5 Years	65.96%
40	10 Years	73.59%
80	20 Years	73.59%
200	50 Years	73.59%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.11. Further, an Excess Kurtosis of 5.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -56.07%	0	0.00%	0.00%
-56.07% to -17.73%	0	0.00%	0.00%
-17.73% to 20.61%	0	0.00%	0.00%
20.61% to 58.95%	4	16.67%	16.67%
58.95% to 97.29%	13	54.17%	70.83%
97.29% to 135.63%	5	20.83%	91.67%
135.63% to 173.97%	0	0.00%	91.67%
173.97% to 212.31%	1	4.17%	95.83%
212.31% to 250.65%	0	0.00%	95.83%
Greater than 250.65%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	46.17%	148.41%	87.50%	68.27%
±2σ	-4.95%	199.53%	91.67%	95.45%
±3σ	-56.07%	250.65%	95.83%	99.73%

Descriptive Statistics

Mean	97.293%
Standard Error	10.435%
Median	86.168%
Mode	45.781%
Standard Deviation	51.120%
Sample Variance	2613.292%
Kurtosis	5.26
Skewness	2.11
Range	223.362%
Minimum	45.781%
Maximum	269.143%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	97.293%	24	100.00%	97.293%
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 0.52. Further, an Excess Kurtosis of -0.49 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -129.86%	0	0.00%	0.00%
-129.86% to -95.00%	0	0.00%	0.00%
-95.00% to -60.14%	1	4.17%	4.17%
-60.14% to -25.28%	5	20.83%	25.00%
-25.28% to 9.58%	8	33.33%	58.33%
9.58% to 44.44%	3	12.50%	70.83%
44.44% to 79.30%	5	20.83%	91.67%
79.30% to 114.16%	2	8.33%	100.00%
114.16% to 149.02%	0	0.00%	100.00%
Greater than 149.02%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.90%	56.06%	70.83%	68.27%
±2σ	-83.38%	102.54%	95.83%	95.45%
±3σ	-129.86%	149.02%	100.00%	99.73%

Descriptive Statistics

Mean	9.581%
Standard Error	9.488%
Median	2.876%
Mode	-63.862%
Standard Deviation	46.479%
Sample Variance	2160.325%
Kurtosis	-0.49
Skewness	0.52
Range	174.008%
Minimum	-63.862%
Maximum	110.146%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.537%	13	54.17%	23.583%
Negative	-30.550%	11	45.83%	-14.002%
Zero	0.000%	0	0.00%	0.000%

LMND Deep Analytical Report