INVZ - 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	5.38%	4.71%	4.72%	8.10%	8.56%	8.61%	0.86	1.03	0.79	1.12
Weekly	12.31%	13.09%	11.70%	18.99%	18.84%	18.96%	0.78	1.14	0.65	1.37
Monthly	28.25%	35.27%	26.83%	43.28%	39.21%	39.47%	0.64	1.39	0.43	2.06
Quarterly	54.10%	120.18%	57.77%	87.33%	67.92%	68.36%	0.48	1.86	0.24	3.66
Annual	—	—	—	—	135.84%	136.72%	0.24	3.66	0.06	14.24
Option Time Horizon	—	—	—	—	52.25%	52.59%	0.56	1.59	0.33	2.68

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $0.94 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1750 (Bid $0.0000 / Ask $0.3500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 135.84% (CRR binomial tree, American, n=20 steps) | BS IV: 136.69% (European Black-Scholes) | Yahoo IV (Annual): 136.72% → 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 1.03. Further, an Excess Kurtosis of 4.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.17%	2	0.14%	0.14%
-16.17% to -12.13%	7	0.50%	0.64%
-12.13% to -8.10%	36	2.56%	3.20%
-8.10% to -4.06%	220	15.65%	18.85%
-4.06% to -0.03%	502	35.70%	54.55%
-0.03% to 4.01%	414	29.45%	84.00%
4.01% to 8.04%	132	9.39%	93.39%
8.04% to 12.08%	52	3.70%	97.08%
12.08% to 16.11%	21	1.49%	98.58%
Greater than 16.11%	20	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.41%	5.35%	77.24%	68.27%
±2σ	-10.79%	10.73%	95.31%	95.45%
±3σ	-16.17%	16.11%	98.44%	99.73%

Descriptive Statistics

Mean	-0.027%
Standard Error	0.143%
Median	-0.460%
Mode	0.000%
Standard Deviation	5.380%
Sample Variance	28.941%
Kurtosis	4.67
Skewness	1.03
Range	61.068%
Minimum	-28.025%
Maximum	33.043%
Count	1406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.368%	601	42.74%	1.867%
Negative	-3.467%	768	54.62%	-1.894%
Zero	0.000%	37	2.63%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.03%
20	1 Month	6.83%
60	1 Quarter	7.83%
250	1 Year	9.05%
750	3 Years	8.85%
1,250	5 Years	8.10%
2,500	10 Years	7.60%
5,000	20 Years	7.60%
12,500	50 Years	7.60%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.51%	0	0.00%	0.00%
-6.51% to -2.98%	0	0.00%	0.00%
-2.98% to 0.55%	35	2.49%	2.49%
0.55% to 4.08%	177	12.58%	15.07%
4.08% to 7.62%	641	45.56%	60.63%
7.62% to 11.15%	331	23.53%	84.15%
11.15% to 14.68%	134	9.52%	93.67%
14.68% to 18.21%	44	3.13%	96.80%
18.21% to 21.74%	19	1.35%	98.15%
Greater than 21.74%	26	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.91%	12.32%	80.38%	68.27%
±2σ	-1.80%	17.03%	96.09%	95.45%
±3σ	-6.51%	21.74%	98.22%	99.73%

Descriptive Statistics

Mean	7.615%
Standard Error	0.126%
Median	6.707%
Mode	5.263%
Standard Deviation	4.708%
Sample Variance	22.163%
Kurtosis	9.60
Skewness	2.18
Range	48.012%
Minimum	0.101%
Maximum	48.113%
Count	1407

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.615%	1407	100.00%	7.615%
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 0.04. Further, an Excess Kurtosis of 2.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.41%	9	0.64%	0.64%
-13.41% to -9.87%	23	1.63%	2.27%
-9.87% to -6.34%	56	3.98%	6.25%
-6.34% to -2.80%	166	11.80%	18.05%
-2.80% to 0.74%	455	32.34%	50.39%
0.74% to 4.28%	439	31.20%	81.59%
4.28% to 7.81%	176	12.51%	94.10%
7.81% to 11.35%	56	3.98%	98.08%
11.35% to 14.89%	22	1.56%	99.64%
Greater than 14.89%	5	0.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.98%	5.45%	75.05%	68.27%
±2σ	-8.69%	10.17%	94.10%	95.45%
±3σ	-13.41%	14.89%	99.00%	99.73%

Descriptive Statistics

Mean	0.738%
Standard Error	0.126%
Median	0.717%
Mode	0.000%
Standard Deviation	4.716%
Sample Variance	22.237%
Kurtosis	2.57
Skewness	0.04
Range	47.431%
Minimum	-21.168%
Maximum	26.263%
Count	1407

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.644%	813	57.78%	2.106%
Negative	-3.525%	546	38.81%	-1.368%
Zero	0.000%	48	3.41%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.32. Further, an Excess Kurtosis of 4.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.04%	0	0.00%	0.00%
-37.04% to -27.80%	1	0.34%	0.34%
-27.80% to -18.57%	8	2.72%	3.06%
-18.57% to -9.33%	43	14.63%	17.69%
-9.33% to -0.09%	122	41.50%	59.18%
-0.09% to 9.14%	73	24.83%	84.01%
9.14% to 18.38%	24	8.16%	92.18%
18.38% to 27.61%	13	4.42%	96.60%
27.61% to 36.85%	7	2.38%	98.98%
Greater than 36.85%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.41%	12.22%	75.51%	68.27%
±2σ	-24.72%	24.54%	94.90%	95.45%
±3σ	-37.04%	36.85%	98.98%	99.73%

Descriptive Statistics

Mean	-0.094%
Standard Error	0.718%
Median	-1.514%
Mode	-12.500%
Standard Deviation	12.315%
Sample Variance	151.666%
Kurtosis	4.01
Skewness	1.32
Range	103.189%
Minimum	-34.844%
Maximum	68.345%
Count	294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.928%	116	39.46%	4.312%
Negative	-7.360%	176	59.86%	-4.406%
Zero	0.000%	2	0.68%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.59%
12	1 Quarter	17.46%
52	1 Year	20.89%
156	3 Years	20.72%
260	5 Years	18.99%
520	10 Years	17.68%
1,040	20 Years	17.68%
2,600	50 Years	17.68%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.25. Further, an Excess Kurtosis of 9.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.50%	0	0.00%	0.00%
-19.50% to -9.68%	0	0.00%	0.00%
-9.68% to 0.14%	1	0.34%	0.34%
0.14% to 9.96%	40	13.56%	13.90%
9.96% to 19.78%	138	46.78%	60.68%
19.78% to 29.60%	69	23.39%	84.07%
29.60% to 39.42%	30	10.17%	94.24%
39.42% to 49.24%	7	2.37%	96.61%
49.24% to 59.06%	4	1.36%	97.97%
Greater than 59.06%	6	2.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.68%	32.87%	82.37%	68.27%
±2σ	-6.41%	45.96%	95.59%	95.45%
±3σ	-19.50%	59.06%	97.97%	99.73%

Descriptive Statistics

Mean	19.777%
Standard Error	0.762%
Median	16.949%
Mode	1.227%
Standard Deviation	13.093%
Sample Variance	171.435%
Kurtosis	9.80
Skewness	2.25
Range	109.232%
Minimum	0.101%
Maximum	109.333%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.777%	295	100.00%	19.777%
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 0.51. Further, an Excess Kurtosis of 4.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.83%	1	0.34%	0.34%
-32.83% to -24.06%	5	1.69%	2.03%
-24.06% to -15.28%	14	4.75%	6.78%
-15.28% to -6.51%	28	9.49%	16.27%
-6.51% to 2.26%	105	35.59%	51.86%
2.26% to 11.04%	87	29.49%	81.36%
11.04% to 19.81%	37	12.54%	93.90%
19.81% to 28.59%	15	5.08%	98.98%
28.59% to 37.36%	1	0.34%	99.32%
Greater than 37.36%	2	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.43%	13.96%	75.93%	68.27%
±2σ	-21.13%	25.66%	94.58%	95.45%
±3σ	-32.83%	37.36%	98.98%	99.73%

Descriptive Statistics

Mean	2.264%
Standard Error	0.681%
Median	1.961%
Mode	0.000%
Standard Deviation	11.698%
Sample Variance	136.833%
Kurtosis	4.22
Skewness	0.51
Range	108.494%
Minimum	-40.171%
Maximum	68.323%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.660%	182	61.70%	5.343%
Negative	-8.488%	107	36.27%	-3.079%
Zero	0.000%	6	2.03%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.57. Further, an Excess Kurtosis of 4.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.76%	0	0.00%	0.00%
-84.76% to -63.57%	0	0.00%	0.00%
-63.57% to -42.39%	2	2.99%	2.99%
-42.39% to -21.20%	11	16.42%	19.40%
-21.20% to -0.02%	28	41.79%	61.19%
-0.02% to 21.16%	14	20.90%	82.09%
21.16% to 42.35%	7	10.45%	92.54%
42.35% to 63.53%	3	4.48%	97.01%
63.53% to 84.72%	1	1.49%	98.51%
Greater than 84.72%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.27%	28.23%	77.61%	68.27%
±2σ	-56.51%	56.47%	97.01%	95.45%
±3σ	-84.76%	84.72%	98.51%	99.73%

Descriptive Statistics

Mean	-0.020%
Standard Error	3.451%
Median	-6.098%
Mode	-52.323%
Standard Deviation	28.246%
Sample Variance	797.854%
Kurtosis	4.61
Skewness	1.57
Range	173.376%
Minimum	-52.323%
Maximum	121.053%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.796%	26	38.81%	10.010%
Negative	-16.392%	41	61.19%	-10.031%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	41.07%
12	1 Year	46.24%
36	3 Years	49.27%
60	5 Years	43.28%
120	10 Years	40.84%
240	20 Years	40.84%
600	50 Years	40.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.21. Further, an Excess Kurtosis of 8.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.66%	0	0.00%	0.00%
-53.66% to -27.21%	0	0.00%	0.00%
-27.21% to -0.75%	0	0.00%	0.00%
-0.75% to 25.70%	8	11.76%	11.76%
25.70% to 52.15%	32	47.06%	58.82%
52.15% to 78.60%	19	27.94%	86.76%
78.60% to 105.05%	5	7.35%	94.12%
105.05% to 131.50%	2	2.94%	97.06%
131.50% to 157.96%	1	1.47%	98.53%
Greater than 157.96%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.88%	87.42%	83.82%	68.27%
±2σ	-18.39%	122.69%	95.59%	95.45%
±3σ	-53.66%	157.96%	98.53%	99.73%

Descriptive Statistics

Mean	52.149%
Standard Error	4.277%
Median	46.933%
Mode	2.156%
Standard Deviation	35.269%
Sample Variance	1243.926%
Kurtosis	8.09
Skewness	2.21
Range	221.373%
Minimum	2.156%
Maximum	223.529%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.149%	68	100.00%	52.149%
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 0.65. Further, an Excess Kurtosis of 1.44 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -73.41%	0	0.00%	0.00%
-73.41% to -53.28%	1	1.47%	1.47%
-53.28% to -33.16%	1	1.47%	2.94%
-33.16% to -13.04%	12	17.65%	20.59%
-13.04% to 7.09%	22	32.35%	52.94%
7.09% to 27.21%	19	27.94%	80.88%
27.21% to 47.34%	10	14.71%	95.59%
47.34% to 67.46%	1	1.47%	97.06%
67.46% to 87.58%	1	1.47%	98.53%
Greater than 87.58%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.75%	33.92%	67.65%	68.27%
±2σ	-46.58%	60.75%	95.59%	95.45%
±3σ	-73.41%	87.58%	98.53%	99.73%

Descriptive Statistics

Mean	7.087%
Standard Error	3.254%
Median	5.425%
Mode	-54.167%
Standard Deviation	26.832%
Sample Variance	719.975%
Kurtosis	1.44
Skewness	0.65
Range	151.731%
Minimum	-54.167%
Maximum	97.564%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.841%	41	60.29%	13.772%
Negative	-16.837%	27	39.71%	-6.685%
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 1.54. Further, an Excess Kurtosis of 2.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -160.70%	0	0.00%	0.00%
-160.70% to -120.13%	0	0.00%	0.00%
-120.13% to -79.55%	0	0.00%	0.00%
-79.55% to -38.98%	5	21.74%	21.74%
-38.98% to 1.60%	10	43.48%	65.22%
1.60% to 42.17%	5	21.74%	86.96%
42.17% to 82.75%	1	4.35%	91.30%
82.75% to 123.32%	1	4.35%	95.65%
123.32% to 163.90%	1	4.35%	100.00%
Greater than 163.90%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-52.50%	55.70%	73.91%	68.27%
±2σ	-106.60%	109.80%	91.30%	95.45%
±3σ	-160.70%	163.90%	100.00%	99.73%

Descriptive Statistics

Mean	1.597%
Standard Error	11.281%
Median	-2.183%
Mode	-63.415%
Standard Deviation	54.100%
Sample Variance	2926.853%
Kurtosis	2.69
Skewness	1.54
Range	221.748%
Minimum	-63.415%
Maximum	158.333%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	55.984%	8	34.78%	19.473%
Negative	-29.367%	14	60.87%	-17.876%
Zero	0.000%	1	4.35%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	87.49%
12	3 Years	109.70%
20	5 Years	87.33%
40	10 Years	81.70%
80	20 Years	81.70%
200	50 Years	81.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.96. Further, an Excess Kurtosis of 11.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -240.94%	0	0.00%	0.00%
-240.94% to -150.81%	0	0.00%	0.00%
-150.81% to -60.67%	0	0.00%	0.00%
-60.67% to 29.46%	3	12.50%	12.50%
29.46% to 119.59%	14	58.33%	70.83%
119.59% to 209.73%	4	16.67%	87.50%
209.73% to 299.86%	2	8.33%	95.83%
299.86% to 389.99%	0	0.00%	95.83%
389.99% to 480.12%	0	0.00%	95.83%
Greater than 480.12%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.58%	239.77%	91.67%	68.27%
±2σ	-120.76%	359.95%	95.83%	95.45%
±3σ	-240.94%	480.12%	95.83%	99.73%

Descriptive Statistics

Mean	119.593%
Standard Error	24.531%
Median	89.520%
Mode	4.061%
Standard Deviation	120.177%
Sample Variance	14442.496%
Kurtosis	11.00
Skewness	2.96
Range	593.717%
Minimum	4.061%
Maximum	597.778%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	119.593%	24	100.00%	119.593%
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 0.96. Further, an Excess Kurtosis of 0.67 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -150.43%	0	0.00%	0.00%
-150.43% to -107.10%	0	0.00%	0.00%
-107.10% to -63.77%	0	0.00%	0.00%
-63.77% to -20.43%	5	20.83%	20.83%
-20.43% to 22.90%	9	37.50%	58.33%
22.90% to 66.23%	5	20.83%	79.17%
66.23% to 109.56%	2	8.33%	87.50%
109.56% to 152.89%	2	8.33%	95.83%
152.89% to 196.22%	1	4.17%	100.00%
Greater than 196.22%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.88%	80.67%	70.83%	68.27%
±2σ	-92.65%	138.45%	95.83%	95.45%
±3σ	-150.43%	196.22%	100.00%	99.73%

Descriptive Statistics

Mean	22.896%
Standard Error	11.793%
Median	7.884%
Mode	-61.290%
Standard Deviation	57.775%
Sample Variance	3337.939%
Kurtosis	0.67
Skewness	0.96
Range	233.290%
Minimum	-61.290%
Maximum	172.000%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.615%	16	66.67%	33.077%
Negative	-30.542%	8	33.33%	-10.181%
Zero	0.000%	0	0.00%	0.000%

INVZ Deep Analytical Report