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	4.14%	2.71%	3.23%	5.27%	3.73%	3.76%	265.51	286.09	255.79	296.96
Weekly	9.54%	8.26%	9.68%	12.97%	8.21%	8.28%	253.87	299.20	233.85	324.82
Monthly	17.03%	14.72%	17.88%	27.22%	17.10%	17.23%	232.29	327.00	195.78	387.99
Quarterly	30.71%	25.27%	28.10%	48.81%	29.62%	29.84%	204.96	370.61	152.42	498.36
Annual	—	—	—	—	59.23%	59.68%	152.42	498.36	84.29	901.15
Option Time Horizon	—	—	—	—	22.36%	22.53%	220.39	344.66	176.24	431.01

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $275.61 | Strike (K): $280.00 (first OTM call ≥ spot) | Observed Mid-Price: $23.2500 (Bid $22.0000 / Ask $24.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 59.23% (CRR binomial tree, American, n=20 steps) | BS IV: 59.27% (European Black-Scholes) | Yahoo IV (Annual): 59.68% → 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 0.69. 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 -12.23%	11	0.52%	0.52%
-12.23% to -9.13%	15	0.71%	1.23%
-9.13% to -6.02%	78	3.69%	4.92%
-6.02% to -2.92%	235	11.11%	16.03%
-2.92% to 0.19%	739	34.94%	50.97%
0.19% to 3.29%	716	33.85%	84.82%
3.29% to 6.40%	221	10.45%	95.27%
6.40% to 9.50%	68	3.22%	98.49%
9.50% to 12.61%	10	0.47%	98.96%
Greater than 12.61%	22	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.95%	4.33%	79.43%	68.27%
±2σ	-8.09%	8.47%	96.08%	95.45%
±3σ	-12.23%	12.61%	98.44%	99.73%

Descriptive Statistics

Mean	0.187%
Standard Error	0.090%
Median	0.113%
Mode	0.470%
Standard Deviation	4.140%
Sample Variance	17.139%
Kurtosis	9.93
Skewness	0.69
Range	64.895%
Minimum	-26.937%
Maximum	37.958%
Count	2115

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.905%	1090	51.54%	1.497%
Negative	-2.712%	1022	48.32%	-1.310%
Zero	0.000%	3	0.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.56%
20	1 Month	7.08%
60	1 Quarter	6.04%
250	1 Year	4.88%
750	3 Years	4.62%
1,250	5 Years	5.27%
2,500	10 Years	5.33%
5,000	20 Years	5.33%
12,500	50 Years	5.33%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.05%	0	0.00%	0.00%
-3.05% to -1.02%	0	0.00%	0.00%
-1.02% to 1.01%	0	0.00%	0.00%
1.01% to 3.04%	423	19.99%	19.99%
3.04% to 5.07%	877	41.45%	61.44%
5.07% to 7.09%	456	21.55%	82.99%
7.09% to 9.12%	202	9.55%	92.53%
9.12% to 11.15%	77	3.64%	96.17%
11.15% to 13.18%	40	1.89%	98.06%
Greater than 13.18%	41	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.36%	7.77%	79.58%	68.27%
±2σ	-0.34%	10.48%	95.37%	95.45%
±3σ	-3.05%	13.18%	98.06%	99.73%

Descriptive Statistics

Mean	5.065%
Standard Error	0.059%
Median	4.342%
Mode	3.258%
Standard Deviation	2.705%
Sample Variance	7.315%
Kurtosis	8.67
Skewness	2.11
Range	29.719%
Minimum	1.062%
Maximum	30.781%
Count	2116

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.065%	2116	100.00%	5.065%
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 0.12. 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 -9.66%	10	0.47%	0.47%
-9.66% to -7.24%	23	1.09%	1.56%
-7.24% to -4.82%	83	3.92%	5.48%
-4.82% to -2.40%	307	14.51%	19.99%
-2.40% to 0.01%	665	31.43%	51.42%
0.01% to 2.43%	639	30.20%	81.62%
2.43% to 4.85%	248	11.72%	93.34%
4.85% to 7.27%	98	4.63%	97.97%
7.27% to 9.69%	26	1.23%	99.20%
Greater than 9.69%	17	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.21%	3.24%	73.63%	68.27%
±2σ	-6.44%	6.46%	94.61%	95.45%
±3σ	-9.66%	9.69%	98.72%	99.73%

Descriptive Statistics

Mean	0.015%
Standard Error	0.070%
Median	-0.058%
Mode	-4.149%
Standard Deviation	3.225%
Sample Variance	10.400%
Kurtosis	1.71
Skewness	0.12
Range	30.218%
Minimum	-15.221%
Maximum	14.997%
Count	2116

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.464%	1036	48.96%	1.206%
Negative	-2.341%	1077	50.90%	-1.192%
Zero	0.000%	3	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 2.92 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.66%	3	0.68%	0.68%
-27.66% to -20.51%	7	1.59%	2.28%
-20.51% to -13.35%	14	3.19%	5.47%
-13.35% to -6.20%	59	13.44%	18.91%
-6.20% to 0.95%	148	33.71%	52.62%
0.95% to 8.11%	128	29.16%	81.78%
8.11% to 15.26%	60	13.67%	95.44%
15.26% to 22.42%	11	2.51%	97.95%
22.42% to 29.57%	3	0.68%	98.63%
Greater than 29.57%	6	1.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.58%	10.49%	76.77%	68.27%
±2σ	-18.12%	20.03%	94.99%	95.45%
±3σ	-27.66%	29.57%	97.95%	99.73%

Descriptive Statistics

Mean	0.955%
Standard Error	0.455%
Median	0.603%
Mode	-6.589%
Standard Deviation	9.539%
Sample Variance	90.995%
Kurtosis	2.92
Skewness	0.29
Range	77.403%
Minimum	-32.919%
Maximum	44.484%
Count	439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.163%	239	54.44%	3.900%
Negative	-6.464%	200	45.56%	-2.945%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.96%
12	1 Quarter	14.08%
52	1 Year	12.37%
156	3 Years	11.45%
260	5 Years	12.97%
520	10 Years	12.74%
1,040	20 Years	12.74%
2,600	50 Years	12.74%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.18. Further, an Excess Kurtosis of 6.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.17%	0	0.00%	0.00%
-11.17% to -4.98%	0	0.00%	0.00%
-4.98% to 1.21%	0	0.00%	0.00%
1.21% to 7.40%	78	17.73%	17.73%
7.40% to 13.59%	209	47.50%	65.23%
13.59% to 19.78%	89	20.23%	85.45%
19.78% to 25.97%	32	7.27%	92.73%
25.97% to 32.16%	16	3.64%	96.36%
32.16% to 38.36%	2	0.45%	96.82%
Greater than 38.36%	14	3.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.34%	21.85%	83.64%	68.27%
±2σ	-2.92%	30.10%	95.91%	95.45%
±3σ	-11.17%	38.36%	96.82%	99.73%

Descriptive Statistics

Mean	13.591%
Standard Error	0.394%
Median	11.580%
Mode	7.374%
Standard Deviation	8.255%
Sample Variance	68.142%
Kurtosis	6.01
Skewness	2.18
Range	51.787%
Minimum	3.378%
Maximum	55.165%
Count	440

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.591%	440	100.00%	13.591%
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 4.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.94%	1	0.23%	0.23%
-28.94% to -21.68%	6	1.36%	1.59%
-21.68% to -14.42%	9	2.05%	3.64%
-14.42% to -7.16%	64	14.55%	18.18%
-7.16% to 0.11%	157	35.68%	53.86%
0.11% to 7.37%	131	29.77%	83.64%
7.37% to 14.63%	48	10.91%	94.55%
14.63% to 21.89%	14	3.18%	97.73%
21.89% to 29.15%	2	0.45%	98.18%
Greater than 29.15%	8	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.58%	9.79%	78.41%	68.27%
±2σ	-19.26%	19.47%	95.68%	95.45%
±3σ	-28.94%	29.15%	97.95%	99.73%

Descriptive Statistics

Mean	0.106%
Standard Error	0.462%
Median	-0.454%
Mode	-5.150%
Standard Deviation	9.682%
Sample Variance	93.738%
Kurtosis	4.39
Skewness	1.12
Range	79.931%
Minimum	-30.956%
Maximum	48.975%
Count	440

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.429%	205	46.59%	3.461%
Negative	-6.283%	235	53.41%	-3.356%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.08. 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 -47.45%	0	0.00%	0.00%
-47.45% to -34.67%	2	1.98%	1.98%
-34.67% to -21.89%	5	4.95%	6.93%
-21.89% to -9.12%	12	11.88%	18.81%
-9.12% to 3.66%	35	34.65%	53.47%
3.66% to 16.43%	26	25.74%	79.21%
16.43% to 29.21%	14	13.86%	93.07%
29.21% to 41.98%	5	4.95%	98.02%
41.98% to 54.76%	2	1.98%	100.00%
Greater than 54.76%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.38%	20.69%	73.27%	68.27%
±2σ	-30.41%	37.72%	92.08%	95.45%
±3σ	-47.44%	54.76%	100.00%	99.73%

Descriptive Statistics

Mean	3.657%
Standard Error	1.695%
Median	2.934%
Mode	-1.657%
Standard Deviation	17.034%
Sample Variance	290.166%
Kurtosis	0.23
Skewness	-0.08
Range	83.262%
Minimum	-38.500%
Maximum	44.762%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.687%	58	57.43%	8.434%
Negative	-11.220%	43	42.57%	-4.777%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.81%
12	1 Year	25.82%
36	3 Years	25.38%
60	5 Years	27.22%
120	10 Years	27.48%
240	20 Years	27.48%
600	50 Years	27.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.07. Further, an Excess Kurtosis of 0.62 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.38%	0	0.00%	0.00%
-12.38% to -1.34%	0	0.00%	0.00%
-1.34% to 9.70%	1	0.98%	0.98%
9.70% to 20.74%	24	23.53%	24.51%
20.74% to 31.79%	35	34.31%	58.82%
31.79% to 42.83%	23	22.55%	81.37%
42.83% to 53.87%	9	8.82%	90.20%
53.87% to 64.91%	6	5.88%	96.08%
64.91% to 75.95%	4	3.92%	100.00%
Greater than 75.95%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.06%	46.51%	74.51%	68.27%
±2σ	2.34%	61.23%	92.16%	95.45%
±3σ	-12.38%	75.95%	100.00%	99.73%

Descriptive Statistics

Mean	31.785%
Standard Error	1.458%
Median	28.859%
Mode	9.504%
Standard Deviation	14.723%
Sample Variance	216.755%
Kurtosis	0.62
Skewness	1.07
Range	64.177%
Minimum	9.504%
Maximum	73.681%
Count	102

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.785%	102	100.00%	31.785%
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 1.07. Further, an Excess Kurtosis of 1.74 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.49%	0	0.00%	0.00%
-54.49% to -41.08%	0	0.00%	0.00%
-41.08% to -27.67%	3	2.94%	2.94%
-27.67% to -14.27%	20	19.61%	22.55%
-14.27% to -0.86%	31	30.39%	52.94%
-0.86% to 12.55%	31	30.39%	83.33%
12.55% to 25.96%	10	9.80%	93.14%
25.96% to 39.37%	3	2.94%	96.08%
39.37% to 52.77%	2	1.96%	98.04%
Greater than 52.77%	2	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.73%	17.02%	73.53%	68.27%
±2σ	-36.61%	34.90%	95.10%	95.45%
±3σ	-54.49%	52.77%	98.04%	99.73%

Descriptive Statistics

Mean	-0.858%
Standard Error	1.770%
Median	-3.122%
Mode	-33.264%
Standard Deviation	17.877%
Sample Variance	319.588%
Kurtosis	1.74
Skewness	1.07
Range	93.880%
Minimum	-33.264%
Maximum	60.616%
Count	102

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.272%	44	43.14%	6.157%
Negative	-12.336%	58	56.86%	-7.015%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of -0.82 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.28%	0	0.00%	0.00%
-81.28% to -58.24%	0	0.00%	0.00%
-58.24% to -35.21%	2	5.88%	5.88%
-35.21% to -12.17%	6	17.65%	23.53%
-12.17% to 10.86%	10	29.41%	52.94%
10.86% to 33.90%	7	20.59%	73.53%
33.90% to 56.93%	7	20.59%	94.12%
56.93% to 79.96%	2	5.88%	100.00%
79.96% to 103.00%	0	0.00%	100.00%
Greater than 103.00%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.85%	41.57%	64.71%	68.27%
±2σ	-50.56%	72.28%	97.06%	95.45%
±3σ	-81.27%	103.00%	100.00%	99.73%

Descriptive Statistics

Mean	10.861%
Standard Error	5.267%
Median	5.174%
Mode	-41.425%
Standard Deviation	30.712%
Sample Variance	943.216%
Kurtosis	-0.82
Skewness	0.29
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	-17.987%	14	41.18%	-7.406%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	48.55%
12	3 Years	48.88%
20	5 Years	48.81%
40	10 Years	50.26%
80	20 Years	50.26%
200	50 Years	50.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 0.74 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.00%	0	0.00%	0.00%
-13.00% to 5.95%	0	0.00%	0.00%
5.95% to 24.91%	1	2.86%	2.86%
24.91% to 43.86%	8	22.86%	25.71%
43.86% to 62.82%	9	25.71%	51.43%
62.82% to 81.77%	11	31.43%	82.86%
81.77% to 100.72%	3	8.57%	91.43%
100.72% to 119.68%	2	5.71%	97.14%
119.68% to 138.63%	1	2.86%	100.00%
Greater than 138.63%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	37.54%	88.09%	74.29%	68.27%
±2σ	12.27%	113.36%	97.14%	95.45%
±3σ	-13.00%	138.63%	100.00%	99.73%

Descriptive Statistics

Mean	62.816%
Standard Error	4.272%
Median	61.290%
Mode	16.838%
Standard Deviation	25.272%
Sample Variance	638.657%
Kurtosis	0.74
Skewness	0.67
Range	117.746%
Minimum	16.838%
Maximum	134.584%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	62.816%	35	100.00%	62.816%
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 0.64. Further, an Excess Kurtosis of -0.02 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.55%	0	0.00%	0.00%
-86.55% to -65.47%	0	0.00%	0.00%
-65.47% to -44.40%	0	0.00%	0.00%
-44.40% to -23.33%	10	28.57%	28.57%
-23.33% to -2.25%	7	20.00%	48.57%
-2.25% to 18.82%	11	31.43%	80.00%
18.82% to 39.89%	4	11.43%	91.43%
39.89% to 60.96%	2	5.71%	97.14%
60.96% to 82.04%	1	2.86%	100.00%
Greater than 82.04%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.35%	25.84%	62.86%	68.27%
±2σ	-58.45%	53.94%	94.29%	95.45%
±3σ	-86.55%	82.04%	100.00%	99.73%

Descriptive Statistics

Mean	-2.255%
Standard Error	4.749%
Median	-1.355%
Mode	-44.025%
Standard Deviation	28.097%
Sample Variance	789.460%
Kurtosis	-0.02
Skewness	0.64
Range	112.320%
Minimum	-44.025%
Maximum	68.295%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.727%	15	42.86%	10.169%
Negative	-21.742%	20	57.14%	-12.424%
Zero	0.000%	0	0.00%	0.000%

MDB Deep Analytical Report