MVIS - 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	6.12%	6.33%	5.17%	8.49%	5.64%	5.51%	0.80	0.90	0.76	0.95
Weekly	16.43%	19.21%	13.47%	20.00%	12.42%	12.13%	0.75	0.96	0.66	1.09
Monthly	27.74%	41.15%	24.83%	40.44%	25.86%	25.26%	0.66	1.10	0.51	1.43
Quarterly	64.18%	100.10%	44.16%	76.94%	44.80%	43.75%	0.54	1.33	0.35	2.08
Annual	—	—	—	—	89.60%	87.50%	0.35	2.08	0.14	5.10
Option Time Horizon	—	—	—	—	29.29%	28.60%	0.63	1.14	0.47	1.53

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $0.85 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0500 (Bid $0.0000 / Ask $0.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 89.60% (CRR binomial tree, American, n=20 steps) | BS IV: 89.92% (European Black-Scholes) | Yahoo IV (Annual): 87.50% → 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 4.20. Further, an Excess Kurtosis of 78.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.25%	26	0.35%	0.35%
-18.25% to -13.66%	33	0.44%	0.80%
-13.66% to -9.07%	157	2.12%	2.91%
-9.07% to -4.47%	897	12.09%	15.01%
-4.47% to 0.12%	3062	41.28%	56.29%
0.12% to 4.71%	2223	29.97%	86.26%
4.71% to 9.30%	661	8.91%	95.17%
9.30% to 13.90%	216	2.91%	98.09%
13.90% to 18.49%	78	1.05%	99.14%
Greater than 18.49%	64	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.01%	6.24%	81.35%	68.27%
±2σ	-12.13%	12.37%	96.14%	95.45%
±3σ	-18.25%	18.49%	98.79%	99.73%

Descriptive Statistics

Mean	0.118%
Standard Error	0.071%
Median	-0.142%
Mode	0.000%
Standard Deviation	6.124%
Sample Variance	37.499%
Kurtosis	78.23
Skewness	4.20
Range	203.448%
Minimum	-53.448%
Maximum	150.000%
Count	7417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.527%	3246	43.76%	1.981%
Negative	-3.711%	3724	50.21%	-1.863%
Zero	0.000%	447	6.03%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.16%
20	1 Month	8.10%
60	1 Quarter	6.80%
250	1 Year	7.77%
750	3 Years	7.97%
1,250	5 Years	8.49%
2,500	10 Years	8.82%
5,000	20 Years	8.08%
12,500	50 Years	7.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.81. Further, an Excess Kurtosis of 258.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.06%	0	0.00%	0.00%
-11.06% to -6.31%	0	0.00%	0.00%
-6.31% to -1.56%	0	0.00%	0.00%
-1.56% to 3.18%	598	8.06%	8.06%
3.18% to 7.93%	4132	55.70%	63.76%
7.93% to 12.68%	1781	24.01%	87.77%
12.68% to 17.43%	550	7.41%	95.19%
17.43% to 22.18%	185	2.49%	97.68%
22.18% to 26.93%	80	1.08%	98.76%
Greater than 26.93%	92	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.60%	14.27%	90.87%	68.27%
±2σ	-4.73%	20.60%	97.17%	95.45%
±3σ	-11.06%	26.93%	98.76%	99.73%

Descriptive Statistics

Mean	7.933%
Standard Error	0.074%
Median	6.481%
Mode	5.263%
Standard Deviation	6.332%
Sample Variance	40.099%
Kurtosis	258.84
Skewness	9.81
Range	234.488%
Minimum	0.806%
Maximum	235.294%
Count	7418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.933%	7418	100.00%	7.933%
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 6.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.89%	49	0.66%	0.66%
-14.89% to -11.01%	97	1.31%	1.97%
-11.01% to -7.13%	250	3.37%	5.34%
-7.13% to -3.25%	843	11.36%	16.70%
-3.25% to 0.62%	2431	32.77%	49.47%
0.62% to 4.50%	2467	33.26%	82.73%
4.50% to 8.38%	903	12.17%	94.90%
8.38% to 12.26%	255	3.44%	98.34%
12.26% to 16.14%	75	1.01%	99.35%
Greater than 16.14%	48	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.55%	5.80%	76.96%	68.27%
±2σ	-9.72%	10.97%	94.94%	95.45%
±3σ	-14.89%	16.14%	98.69%	99.73%

Descriptive Statistics

Mean	0.625%
Standard Error	0.060%
Median	0.671%
Mode	0.000%
Standard Deviation	5.171%
Sample Variance	26.737%
Kurtosis	6.43
Skewness	-0.26
Range	89.178%
Minimum	-52.124%
Maximum	37.054%
Count	7418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.941%	4042	54.49%	2.147%
Negative	-3.770%	2996	40.39%	-1.523%
Zero	0.000%	380	5.12%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.77. Further, an Excess Kurtosis of 109.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.57%	1	0.07%	0.07%
-48.57% to -36.24%	3	0.20%	0.26%
-36.24% to -23.92%	29	1.89%	2.15%
-23.92% to -11.59%	156	10.14%	12.29%
-11.59% to 0.73%	692	44.99%	57.28%
0.73% to 13.06%	474	30.82%	88.10%
13.06% to 25.38%	128	8.32%	96.42%
25.38% to 37.71%	29	1.89%	98.31%
37.71% to 50.03%	10	0.65%	98.96%
Greater than 50.03%	16	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.70%	17.17%	85.31%	68.27%
±2σ	-32.13%	33.60%	97.33%	95.45%
±3σ	-48.57%	50.03%	98.89%	99.73%

Descriptive Statistics

Mean	0.733%
Standard Error	0.419%
Median	-1.051%
Mode	0.000%
Standard Deviation	16.433%
Sample Variance	270.048%
Kurtosis	109.51
Skewness	6.77
Range	374.690%
Minimum	-51.613%
Maximum	323.077%
Count	1538

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.467%	680	44.21%	5.070%
Negative	-8.165%	817	53.12%	-4.337%
Zero	0.000%	41	2.67%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.90%
12	1 Quarter	14.33%
52	1 Year	16.97%
156	3 Years	18.12%
260	5 Years	20.00%
520	10 Years	21.34%
1,040	20 Years	19.17%
2,600	50 Years	18.47%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.83. Further, an Excess Kurtosis of 104.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.94%	0	0.00%	0.00%
-36.94% to -22.53%	0	0.00%	0.00%
-22.53% to -8.13%	0	0.00%	0.00%
-8.13% to 6.28%	52	3.38%	3.38%
6.28% to 20.69%	960	62.38%	65.76%
20.69% to 35.09%	377	24.50%	90.25%
35.09% to 49.50%	91	5.91%	96.17%
49.50% to 63.91%	32	2.08%	98.25%
63.91% to 78.31%	10	0.65%	98.90%
Greater than 78.31%	17	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.48%	39.90%	92.85%	68.27%
±2σ	-17.73%	59.11%	97.60%	95.45%
±3σ	-36.94%	78.31%	98.90%	99.73%

Descriptive Statistics

Mean	20.687%
Standard Error	0.490%
Median	16.477%
Mode	14.286%
Standard Deviation	19.209%
Sample Variance	368.993%
Kurtosis	104.75
Skewness	7.83
Range	371.809%
Minimum	3.191%
Maximum	375.000%
Count	1539

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.687%	1539	100.00%	20.687%
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 0.97. Further, an Excess Kurtosis of 9.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.79%	6	0.39%	0.39%
-38.79% to -28.69%	14	0.91%	1.30%
-28.69% to -18.59%	53	3.44%	4.74%
-18.59% to -8.49%	180	11.70%	16.44%
-8.49% to 1.61%	541	35.15%	51.59%
1.61% to 11.71%	508	33.01%	84.60%
11.71% to 21.81%	172	11.18%	95.78%
21.81% to 31.91%	32	2.08%	97.86%
31.91% to 42.01%	18	1.17%	99.03%
Greater than 42.01%	15	0.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.86%	15.07%	78.82%	68.27%
±2σ	-25.32%	28.54%	95.52%	95.45%
±3σ	-38.79%	42.01%	98.64%	99.73%

Descriptive Statistics

Mean	1.609%
Standard Error	0.343%
Median	1.227%
Mode	0.000%
Standard Deviation	13.466%
Sample Variance	181.341%
Kurtosis	9.19
Skewness	0.97
Range	183.031%
Minimum	-76.364%
Maximum	106.667%
Count	1539

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.064%	831	54.00%	5.434%
Negative	-8.878%	663	43.08%	-3.825%
Zero	0.000%	45	2.92%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.97. Further, an Excess Kurtosis of 6.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.21%	0	0.00%	0.00%
-81.21% to -60.41%	1	0.28%	0.28%
-60.41% to -39.61%	3	0.85%	1.13%
-39.61% to -18.80%	56	15.82%	16.95%
-18.80% to 2.00%	151	42.66%	59.60%
2.00% to 22.81%	90	25.42%	85.03%
22.81% to 43.61%	28	7.91%	92.94%
43.61% to 64.42%	14	3.95%	96.89%
64.42% to 85.22%	5	1.41%	98.31%
Greater than 85.22%	6	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.74%	29.74%	79.94%	68.27%
±2σ	-53.48%	57.48%	95.48%	95.45%
±3σ	-81.21%	85.22%	98.31%	99.73%

Descriptive Statistics

Mean	2.003%
Standard Error	1.474%
Median	-2.708%
Mode	0.000%
Standard Deviation	27.739%
Sample Variance	769.460%
Kurtosis	6.47
Skewness	1.97
Range	212.967%
Minimum	-61.538%
Maximum	151.429%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.863%	159	44.91%	10.269%
Negative	-15.241%	192	54.24%	-8.266%
Zero	0.000%	3	0.85%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	23.80%
12	1 Year	31.19%
36	3 Years	39.15%
60	5 Years	40.44%
120	10 Years	49.51%
240	20 Years	43.03%
600	50 Years	41.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.66. Further, an Excess Kurtosis of 19.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.57%	0	0.00%	0.00%
-72.57% to -41.70%	0	0.00%	0.00%
-41.70% to -10.84%	0	0.00%	0.00%
-10.84% to 20.02%	29	8.17%	8.17%
20.02% to 50.89%	212	59.72%	67.89%
50.89% to 81.75%	72	20.28%	88.17%
81.75% to 112.62%	20	5.63%	93.80%
112.62% to 143.48%	11	3.10%	96.90%
143.48% to 174.35%	3	0.85%	97.75%
Greater than 174.35%	8	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.74%	92.04%	90.70%	68.27%
±2σ	-31.42%	133.19%	95.49%	95.45%
±3σ	-72.57%	174.35%	97.75%	99.73%

Descriptive Statistics

Mean	50.889%
Standard Error	2.184%
Median	39.535%
Mode	66.667%
Standard Deviation	41.153%
Sample Variance	1693.571%
Kurtosis	19.69
Skewness	3.66
Range	367.958%
Minimum	10.989%
Maximum	378.947%
Count	355

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.889%	355	100.00%	50.889%
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 0.89. Further, an Excess Kurtosis of 4.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.64%	0	0.00%	0.00%
-69.64% to -51.02%	4	1.13%	1.13%
-51.02% to -32.40%	15	4.23%	5.35%
-32.40% to -13.77%	46	12.96%	18.31%
-13.77% to 4.85%	126	35.49%	53.80%
4.85% to 23.48%	99	27.89%	81.69%
23.48% to 42.10%	40	11.27%	92.96%
42.10% to 60.72%	18	5.07%	98.03%
60.72% to 79.35%	4	1.13%	99.15%
Greater than 79.35%	3	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.98%	29.68%	74.37%	68.27%
±2σ	-44.81%	54.52%	94.65%	95.45%
±3σ	-69.65%	79.35%	99.15%	99.73%

Descriptive Statistics

Mean	4.851%
Standard Error	1.318%
Median	2.966%
Mode	0.000%
Standard Deviation	24.832%
Sample Variance	616.634%
Kurtosis	4.32
Skewness	0.89
Range	217.143%
Minimum	-57.143%
Maximum	160.000%
Count	355

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.757%	198	55.77%	11.577%
Negative	-15.606%	153	43.10%	-6.726%
Zero	0.000%	4	1.13%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.46. Further, an Excess Kurtosis of 27.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -185.43%	0	0.00%	0.00%
-185.43% to -137.29%	0	0.00%	0.00%
-137.29% to -89.15%	0	0.00%	0.00%
-89.15% to -41.01%	10	8.47%	8.47%
-41.01% to 7.12%	64	54.24%	62.71%
7.12% to 55.26%	29	24.58%	87.29%
55.26% to 103.40%	11	9.32%	96.61%
103.40% to 151.54%	2	1.69%	98.31%
151.54% to 199.68%	0	0.00%	98.31%
Greater than 199.68%	2	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-57.06%	71.31%	91.53%	68.27%
±2σ	-121.24%	135.49%	97.46%	95.45%
±3σ	-185.43%	199.68%	98.31%	99.73%

Descriptive Statistics

Mean	7.125%
Standard Error	5.909%
Median	-5.640%
Mode	-46.154%
Standard Deviation	64.184%
Sample Variance	4119.541%
Kurtosis	27.78
Skewness	4.46
Range	547.279%
Minimum	-70.136%
Maximum	477.143%
Count	118

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.204%	51	43.22%	20.834%
Negative	-24.143%	67	56.78%	-13.708%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	42.62%
12	3 Years	78.18%
20	5 Years	76.94%
40	10 Years	100.44%
80	20 Years	82.54%
200	50 Years	76.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.05. Further, an Excess Kurtosis of 22.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -191.87%	0	0.00%	0.00%
-191.87% to -116.80%	0	0.00%	0.00%
-116.80% to -41.73%	0	0.00%	0.00%
-41.73% to 33.34%	6	5.04%	5.04%
33.34% to 108.42%	79	66.39%	71.43%
108.42% to 183.49%	20	16.81%	88.24%
183.49% to 258.56%	7	5.88%	94.12%
258.56% to 333.63%	4	3.36%	97.48%
333.63% to 408.71%	1	0.84%	98.32%
Greater than 408.71%	2	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.32%	208.51%	92.44%	68.27%
±2σ	-91.78%	308.61%	94.96%	95.45%
±3σ	-191.87%	408.71%	98.32%	99.73%

Descriptive Statistics

Mean	108.417%
Standard Error	9.176%
Median	85.938%
Mode	26.429%
Standard Deviation	100.097%
Sample Variance	10019.470%
Kurtosis	22.44
Skewness	4.05
Range	781.466%
Minimum	26.429%
Maximum	807.895%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	108.417%	119	100.00%	108.417%
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 1.36. Further, an Excess Kurtosis of 4.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -119.81%	0	0.00%	0.00%
-119.81% to -86.68%	0	0.00%	0.00%
-86.68% to -53.56%	3	2.52%	2.52%
-53.56% to -20.44%	20	16.81%	19.33%
-20.44% to 12.68%	47	39.50%	58.82%
12.68% to 45.80%	28	23.53%	82.35%
45.80% to 78.93%	11	9.24%	91.60%
78.93% to 112.05%	7	5.88%	97.48%
112.05% to 145.17%	2	1.68%	99.16%
Greater than 145.17%	1	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.48%	56.85%	77.31%	68.27%
±2σ	-75.64%	101.01%	95.80%	95.45%
±3σ	-119.81%	145.17%	99.16%	99.73%

Descriptive Statistics

Mean	12.683%
Standard Error	4.048%
Median	6.330%
Mode	-78.218%
Standard Deviation	44.163%
Sample Variance	1950.393%
Kurtosis	4.93
Skewness	1.36
Range	316.097%
Minimum	-78.218%
Maximum	237.879%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.090%	67	56.30%	22.572%
Negative	-23.075%	51	42.86%	-9.889%
Zero	0.000%	1	0.84%	0.000%

MVIS Deep Analytical Report