MDB - 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	4.11%	2.70%	3.22%	5.27%	4.73%	4.77%	328.64	361.25	313.46	378.75
Weekly	9.51%	8.27%	9.66%	12.93%	10.41%	10.51%	310.49	382.37	279.78	424.33
Monthly	16.97%	14.77%	17.84%	27.20%	21.68%	21.88%	277.42	427.96	223.36	531.54
Quarterly	30.20%	26.18%	27.44%	47.61%	37.54%	37.89%	236.71	501.55	162.62	730.06
Annual	—	—	—	—	75.09%	75.78%	162.62	730.06	76.75	1546.85
Option Time Horizon	—	—	—	—	28.88%	29.15%	258.13	459.93	193.38	613.93

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $344.56 | Strike (K): $350.00 (first OTM call ≥ spot) | Observed Mid-Price: $37.9500 (Bid $35.6500 / Ask $40.2500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 75.09% (CRR binomial tree, American, n=20 steps) | BS IV: 74.94% (European Black-Scholes) | Yahoo IV (Annual): 75.78% → 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 0.79. Further, an Excess Kurtosis of 9.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.14%	10	0.48%	0.48%
-12.14% to -9.06%	14	0.67%	1.15%
-9.06% to -5.97%	81	3.87%	5.01%
-5.97% to -2.89%	237	11.32%	16.33%
-2.89% to 0.20%	728	34.77%	51.10%
0.20% to 3.28%	704	33.62%	84.72%
3.28% to 6.37%	221	10.55%	95.27%
6.37% to 9.45%	67	3.20%	98.47%
9.45% to 12.54%	10	0.48%	98.95%
Greater than 12.54%	22	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.92%	4.31%	79.27%	68.27%
±2σ	-8.03%	8.42%	96.08%	95.45%
±3σ	-12.14%	12.54%	98.47%	99.73%

Descriptive Statistics

Mean	0.197%
Standard Error	0.090%
Median	0.115%
Mode	-1.626%
Standard Deviation	4.114%
Sample Variance	16.923%
Kurtosis	9.93
Skewness	0.79
Range	64.895%
Minimum	-26.937%
Maximum	37.958%
Count	2094

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.906%	1079	51.53%	1.497%
Negative	-2.691%	1012	48.33%	-1.301%
Zero	0.000%	3	0.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.90%
20	1 Month	6.32%
60	1 Quarter	4.90%
250	1 Year	4.85%
750	3 Years	4.57%
1,250	5 Years	5.27%
2,500	10 Years	5.31%
5,000	20 Years	5.31%
12,500	50 Years	5.31%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.04%	0	0.00%	0.00%
-3.04% to -1.02%	0	0.00%	0.00%
-1.02% to 1.01%	0	0.00%	0.00%
1.01% to 3.03%	420	20.05%	20.05%
3.03% to 5.06%	866	41.34%	61.38%
5.06% to 7.08%	451	21.53%	82.91%
7.08% to 9.10%	200	9.55%	92.46%
9.10% to 11.13%	77	3.68%	96.13%
11.13% to 13.15%	41	1.96%	98.09%
Greater than 13.15%	40	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.36%	7.75%	79.43%	68.27%
±2σ	-0.34%	10.45%	95.42%	95.45%
±3σ	-3.04%	13.15%	98.09%	99.73%

Descriptive Statistics

Mean	5.056%
Standard Error	0.059%
Median	4.329%
Mode	3.258%
Standard Deviation	2.699%
Sample Variance	7.287%
Kurtosis	8.77
Skewness	2.11
Range	29.719%
Minimum	1.062%
Maximum	30.781%
Count	2095

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.056%	2095	100.00%	5.056%
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 1.71 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.64%	11	0.53%	0.53%
-9.64% to -7.22%	22	1.05%	1.58%
-7.22% to -4.81%	81	3.87%	5.44%
-4.81% to -2.39%	306	14.61%	20.05%
-2.39% to 0.02%	657	31.36%	51.41%
0.02% to 2.44%	632	30.17%	81.58%
2.44% to 4.85%	246	11.74%	93.32%
4.85% to 7.27%	98	4.68%	98.00%
7.27% to 9.68%	26	1.24%	99.24%
Greater than 9.68%	16	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.20%	3.24%	73.41%	68.27%
±2σ	-6.42%	6.46%	94.61%	95.45%
±3σ	-9.64%	9.68%	98.71%	99.73%

Descriptive Statistics

Mean	0.022%
Standard Error	0.070%
Median	-0.056%
Mode	-4.149%
Standard Deviation	3.220%
Sample Variance	10.371%
Kurtosis	1.71
Skewness	0.11
Range	30.218%
Minimum	-15.221%
Maximum	14.997%
Count	2095

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.463%	1028	49.07%	1.209%
Negative	-2.335%	1064	50.79%	-1.186%
Zero	0.000%	3	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.31. Further, an Excess Kurtosis of 2.99 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.52%	3	0.69%	0.69%
-27.52% to -20.39%	7	1.61%	2.30%
-20.39% to -13.26%	12	2.76%	5.06%
-13.26% to -6.12%	60	13.79%	18.85%
-6.12% to 1.01%	147	33.79%	52.64%
1.01% to 8.14%	127	29.20%	81.84%
8.14% to 15.27%	59	13.56%	95.40%
15.27% to 22.40%	11	2.53%	97.93%
22.40% to 29.53%	3	0.69%	98.62%
Greater than 29.53%	6	1.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.50%	10.52%	76.78%	68.27%
±2σ	-18.01%	20.03%	94.94%	95.45%
±3σ	-27.52%	29.53%	97.93%	99.73%

Descriptive Statistics

Mean	1.007%
Standard Error	0.456%
Median	0.603%
Mode	-6.589%
Standard Deviation	9.509%
Sample Variance	90.413%
Kurtosis	2.99
Skewness	0.31
Range	77.403%
Minimum	-32.919%
Maximum	44.484%
Count	435

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.182%	237	54.48%	3.913%
Negative	-6.384%	198	45.52%	-2.906%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.41%
12	1 Quarter	10.57%
52	1 Year	12.07%
156	3 Years	11.24%
260	5 Years	12.93%
520	10 Years	12.66%
1,040	20 Years	12.66%
2,600	50 Years	12.66%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.20. Further, an Excess Kurtosis of 6.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.25%	0	0.00%	0.00%
-11.25% to -5.05%	0	0.00%	0.00%
-5.05% to 1.15%	0	0.00%	0.00%
1.15% to 7.36%	74	16.97%	16.97%
7.36% to 13.56%	212	48.62%	65.60%
13.56% to 19.76%	88	20.18%	85.78%
19.76% to 25.97%	30	6.88%	92.66%
25.97% to 32.17%	16	3.67%	96.33%
32.17% to 38.37%	2	0.46%	96.79%
Greater than 38.37%	14	3.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.29%	21.83%	83.94%	68.27%
±2σ	-2.98%	30.10%	95.87%	95.45%
±3σ	-11.25%	38.37%	96.79%	99.73%

Descriptive Statistics

Mean	13.561%
Standard Error	0.396%
Median	11.516%
Mode	7.374%
Standard Deviation	8.271%
Sample Variance	68.406%
Kurtosis	6.05
Skewness	2.20
Range	51.787%
Minimum	3.378%
Maximum	55.165%
Count	436

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.561%	436	100.00%	13.561%
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 1.12. Further, an Excess Kurtosis of 4.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.84%	1	0.23%	0.23%
-28.84% to -21.60%	6	1.38%	1.61%
-21.60% to -14.36%	9	2.06%	3.67%
-14.36% to -7.12%	64	14.68%	18.35%
-7.12% to 0.13%	155	35.55%	53.90%
0.13% to 7.37%	130	29.82%	83.72%
7.37% to 14.61%	48	11.01%	94.72%
14.61% to 21.85%	13	2.98%	97.71%
21.85% to 29.10%	2	0.46%	98.17%
Greater than 29.10%	8	1.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.53%	9.78%	78.44%	68.27%
±2σ	-19.19%	19.44%	95.64%	95.45%
±3σ	-28.84%	29.10%	97.94%	99.73%

Descriptive Statistics

Mean	0.126%
Standard Error	0.462%
Median	-0.422%
Mode	-5.150%
Standard Deviation	9.657%
Sample Variance	93.259%
Kurtosis	4.48
Skewness	1.12
Range	79.931%
Minimum	-30.956%
Maximum	48.975%
Count	436

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.392%	204	46.79%	3.459%
Negative	-6.262%	232	53.21%	-3.332%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.10. Further, an Excess Kurtosis of 0.29 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -47.01%	0	0.00%	0.00%
-47.01% to -34.29%	3	3.00%	3.00%
-34.29% to -21.56%	4	4.00%	7.00%
-21.56% to -8.83%	10	10.00%	17.00%
-8.83% to 3.90%	36	36.00%	53.00%
3.90% to 16.62%	26	26.00%	79.00%
16.62% to 29.35%	14	14.00%	93.00%
29.35% to 42.08%	5	5.00%	98.00%
42.08% to 54.81%	2	2.00%	100.00%
Greater than 54.81%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.07%	20.87%	74.00%	68.27%
±2σ	-30.04%	37.84%	92.00%	95.45%
±3σ	-47.01%	54.81%	100.00%	99.73%

Descriptive Statistics

Mean	3.897%
Standard Error	1.697%
Median	2.939%
Mode	-1.657%
Standard Deviation	16.970%
Sample Variance	287.995%
Kurtosis	0.29
Skewness	-0.10
Range	83.262%
Minimum	-38.500%
Maximum	44.762%
Count	100

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.687%	58	58.00%	8.518%
Negative	-11.003%	42	42.00%	-4.621%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.88%
12	1 Year	25.76%
36	3 Years	24.86%
60	5 Years	27.20%
120	10 Years	27.36%
240	20 Years	27.36%
600	50 Years	27.36%

High-to-Low 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 0.68 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.76%	0	0.00%	0.00%
-12.76% to -1.68%	0	0.00%	0.00%
-1.68% to 9.39%	0	0.00%	0.00%
9.39% to 20.47%	25	24.75%	24.75%
20.47% to 31.54%	36	35.64%	60.40%
31.54% to 42.62%	22	21.78%	82.18%
42.62% to 53.69%	8	7.92%	90.10%
53.69% to 64.77%	6	5.94%	96.04%
64.77% to 75.84%	4	3.96%	100.00%
Greater than 75.84%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.78%	46.31%	75.25%	68.27%
±2σ	2.01%	61.08%	92.08%	95.45%
±3σ	-12.76%	75.84%	100.00%	99.73%

Descriptive Statistics

Mean	31.543%
Standard Error	1.469%
Median	28.305%
Mode	9.504%
Standard Deviation	14.766%
Sample Variance	218.046%
Kurtosis	0.68
Skewness	1.11
Range	64.177%
Minimum	9.504%
Maximum	73.681%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.543%	101	100.00%	31.543%
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 1.11. Further, an Excess Kurtosis of 1.87 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.62%	0	0.00%	0.00%
-54.62% to -41.24%	0	0.00%	0.00%
-41.24% to -27.85%	3	2.97%	2.97%
-27.85% to -14.47%	19	18.81%	21.78%
-14.47% to -1.09%	32	31.68%	53.47%
-1.09% to 12.30%	32	31.68%	85.15%
12.30% to 25.68%	8	7.92%	93.07%
25.68% to 39.06%	3	2.97%	96.04%
39.06% to 52.45%	2	1.98%	98.02%
Greater than 52.45%	2	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.93%	16.76%	73.27%	68.27%
±2σ	-36.78%	34.60%	95.05%	95.45%
±3σ	-54.62%	52.45%	98.02%	99.73%

Descriptive Statistics

Mean	-1.087%
Standard Error	1.776%
Median	-3.520%
Mode	-33.264%
Standard Deviation	17.844%
Sample Variance	318.401%
Kurtosis	1.87
Skewness	1.11
Range	93.880%
Minimum	-33.264%
Maximum	60.616%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.086%	43	42.57%	5.997%
Negative	-12.336%	58	57.43%	-7.084%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.30. Further, an Excess Kurtosis of -0.75 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -79.21%	0	0.00%	0.00%
-79.21% to -56.56%	0	0.00%	0.00%
-56.56% to -33.90%	2	5.88%	5.88%
-33.90% to -11.25%	6	17.65%	23.53%
-11.25% to 11.40%	10	29.41%	52.94%
11.40% to 34.06%	7	20.59%	73.53%
34.06% to 56.71%	7	20.59%	94.12%
56.71% to 79.37%	2	5.88%	100.00%
79.37% to 102.02%	0	0.00%	100.00%
Greater than 102.02%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.80%	41.61%	64.71%	68.27%
±2σ	-49.00%	71.81%	97.06%	95.45%
±3σ	-79.21%	102.02%	100.00%	99.73%

Descriptive Statistics

Mean	11.405%
Standard Error	5.180%
Median	5.174%
Mode	-41.425%
Standard Deviation	30.205%
Sample Variance	912.313%
Kurtosis	-0.75
Skewness	0.30
Range	117.871%
Minimum	-41.425%
Maximum	76.446%
Count	34

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.055%	20	58.82%	18.268%
Negative	-16.666%	14	41.18%	-6.862%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	42.51%
12	3 Years	46.87%
20	5 Years	47.61%
40	10 Years	49.55%
80	20 Years	49.55%
200	50 Years	49.55%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.64. Further, an Excess Kurtosis of 0.55 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.08%	0	0.00%	0.00%
-17.08% to 2.56%	0	0.00%	0.00%
2.56% to 22.19%	2	5.71%	5.71%
22.19% to 41.83%	6	17.14%	22.86%
41.83% to 61.46%	11	31.43%	54.29%
61.46% to 81.10%	9	25.71%	80.00%
81.10% to 100.74%	4	11.43%	91.43%
100.74% to 120.37%	2	5.71%	97.14%
120.37% to 140.01%	1	2.86%	100.00%
Greater than 140.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	35.28%	87.64%	74.29%	68.27%
±2σ	9.10%	113.83%	97.14%	95.45%
±3σ	-17.08%	140.01%	100.00%	99.73%

Descriptive Statistics

Mean	61.464%
Standard Error	4.425%
Median	59.376%
Mode	16.838%
Standard Deviation	26.181%
Sample Variance	685.470%
Kurtosis	0.55
Skewness	0.64
Range	117.746%
Minimum	16.838%
Maximum	134.584%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	61.464%	35	100.00%	61.464%
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 0.71. Further, an Excess Kurtosis of 0.28 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.33%	0	0.00%	0.00%
-85.33% to -64.76%	0	0.00%	0.00%
-64.76% to -44.18%	0	0.00%	0.00%
-44.18% to -23.60%	10	28.57%	28.57%
-23.60% to -3.02%	7	20.00%	48.57%
-3.02% to 17.56%	12	34.29%	82.86%
17.56% to 38.14%	3	8.57%	91.43%
38.14% to 58.72%	2	5.71%	97.14%
58.72% to 79.30%	1	2.86%	100.00%
Greater than 79.30%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.46%	24.42%	65.71%	68.27%
±2σ	-57.90%	51.86%	94.29%	95.45%
±3σ	-85.34%	79.30%	100.00%	99.73%

Descriptive Statistics

Mean	-3.018%
Standard Error	4.638%
Median	-1.355%
Mode	-44.025%
Standard Deviation	27.439%
Sample Variance	752.880%
Kurtosis	0.28
Skewness	0.71
Range	112.320%
Minimum	-44.025%
Maximum	68.295%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.948%	15	42.86%	9.406%
Negative	-21.742%	20	57.14%	-12.424%
Zero	0.000%	0	0.00%	0.000%

MDB Deep Analytical Report