TXG - 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	4.19%	3.08%	3.74%	6.02%	4.76%	4.88%	18.00	19.80	17.17	20.76
Weekly	9.32%	7.74%	9.32%	14.24%	10.47%	10.75%	17.00	20.96	15.31	23.28
Monthly	17.17%	15.20%	18.09%	28.82%	21.79%	22.38%	15.18	23.48	12.21	29.19
Quarterly	35.00%	33.11%	38.73%	51.28%	37.75%	38.77%	12.94	27.54	8.87	40.17
Annual	—	—	—	—	75.50%	77.54%	8.87	40.17	4.17	85.46
Option Time Horizon	—	—	—	—	35.78%	36.75%	13.20	27.00	9.23	38.62

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $18.88 | Strike (K): $20.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3250 (Bid $1.6500 / Ask $3.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 75.50% (CRR binomial tree, American, n=20 steps) | BS IV: 76.26% (European Black-Scholes) | Yahoo IV (Annual): 77.54% → 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 Fairly Symmetrical with a Skewness factor of 0.17. Further, an Excess Kurtosis of 3.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.56%	9	0.56%	0.56%
-12.56% to -9.41%	15	0.93%	1.48%
-9.41% to -6.27%	68	4.20%	5.69%
-6.27% to -3.12%	197	12.18%	17.86%
-3.12% to 0.02%	548	33.87%	51.73%
0.02% to 3.17%	481	29.73%	81.46%
3.17% to 6.32%	212	13.10%	94.56%
6.32% to 9.46%	54	3.34%	97.90%
9.46% to 12.61%	22	1.36%	99.26%
Greater than 12.61%	12	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.17%	4.22%	75.40%	68.27%
±2σ	-8.36%	8.41%	94.81%	95.45%
±3σ	-12.56%	12.61%	98.70%	99.73%

Descriptive Statistics

Mean	0.024%
Standard Error	0.104%
Median	-0.068%
Mode	0.000%
Standard Deviation	4.194%
Sample Variance	17.586%
Kurtosis	3.57
Skewness	0.17
Range	49.067%
Minimum	-24.700%
Maximum	24.367%
Count	1618

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.158%	785	48.52%	1.532%
Negative	-2.964%	823	50.87%	-1.508%
Zero	0.000%	10	0.62%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.96%
20	1 Month	6.42%
60	1 Quarter	5.99%
250	1 Year	6.37%
750	3 Years	5.63%
1,250	5 Years	6.02%
2,500	10 Years	5.97%
5,000	20 Years	5.97%
12,500	50 Years	5.97%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.85. Further, an Excess Kurtosis of 5.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.38%	0	0.00%	0.00%
-3.38% to -1.07%	0	0.00%	0.00%
-1.07% to 1.24%	1	0.06%	0.06%
1.24% to 3.55%	330	20.38%	20.44%
3.55% to 5.86%	665	41.07%	61.52%
5.86% to 8.16%	342	21.12%	82.64%
8.16% to 10.47%	156	9.64%	92.28%
10.47% to 12.78%	65	4.01%	96.29%
12.78% to 15.09%	32	1.98%	98.27%
Greater than 15.09%	28	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.78%	8.93%	78.20%	68.27%
±2σ	-0.30%	12.01%	95.31%	95.45%
±3σ	-3.38%	15.09%	98.27%	99.73%

Descriptive Statistics

Mean	5.856%
Standard Error	0.077%
Median	5.063%
Mode	2.742%
Standard Deviation	3.078%
Sample Variance	9.477%
Kurtosis	5.41
Skewness	1.85
Range	26.454%
Minimum	1.212%
Maximum	27.666%
Count	1619

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.856%	1619	100.00%	5.856%
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 0.14. Further, an Excess Kurtosis of 1.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.15%	7	0.43%	0.43%
-11.15% to -8.34%	20	1.24%	1.67%
-8.34% to -5.54%	63	3.89%	5.56%
-5.54% to -2.73%	233	14.39%	19.95%
-2.73% to 0.07%	499	30.82%	50.77%
0.07% to 2.88%	503	31.07%	81.84%
2.88% to 5.68%	188	11.61%	93.45%
5.68% to 8.49%	71	4.39%	97.84%
8.49% to 11.29%	22	1.36%	99.20%
Greater than 11.29%	13	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.67%	3.81%	73.56%	68.27%
±2σ	-7.41%	7.55%	94.44%	95.45%
±3σ	-11.15%	11.29%	98.76%	99.73%

Descriptive Statistics

Mean	0.071%
Standard Error	0.093%
Median	0.039%
Mode	0.000%
Standard Deviation	3.740%
Sample Variance	13.988%
Kurtosis	1.94
Skewness	0.14
Range	37.855%
Minimum	-19.954%
Maximum	17.901%
Count	1619

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.831%	813	50.22%	1.422%
Negative	-2.732%	800	49.41%	-1.350%
Zero	0.000%	6	0.37%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of 0.80 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.85%	1	0.30%	0.30%
-27.85% to -20.86%	3	0.89%	1.19%
-20.86% to -13.87%	15	4.46%	5.65%
-13.87% to -6.88%	54	16.07%	21.73%
-6.88% to 0.11%	103	30.65%	52.38%
0.11% to 7.10%	91	27.08%	79.46%
7.10% to 14.09%	46	13.69%	93.15%
14.09% to 21.08%	15	4.46%	97.62%
21.08% to 28.07%	6	1.79%	99.40%
Greater than 28.07%	2	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.21%	9.43%	73.21%	68.27%
±2σ	-18.53%	18.75%	94.05%	95.45%
±3σ	-27.85%	28.07%	99.11%	99.73%

Descriptive Statistics

Mean	0.114%
Standard Error	0.508%
Median	-0.428%
Mode	2.258%
Standard Deviation	9.320%
Sample Variance	86.858%
Kurtosis	0.80
Skewness	0.23
Range	58.293%
Minimum	-29.982%
Maximum	28.311%
Count	336

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.589%	160	47.62%	3.614%
Negative	-6.682%	176	52.38%	-3.500%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.81%
12	1 Quarter	13.74%
52	1 Year	15.23%
156	3 Years	13.28%
260	5 Years	14.24%
520	10 Years	13.96%
1,040	20 Years	13.96%
2,600	50 Years	13.96%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.75. Further, an Excess Kurtosis of 4.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.10%	0	0.00%	0.00%
-8.10% to -2.29%	0	0.00%	0.00%
-2.29% to 3.52%	0	0.00%	0.00%
3.52% to 9.32%	68	20.18%	20.18%
9.32% to 15.13%	130	38.58%	58.75%
15.13% to 20.93%	78	23.15%	81.90%
20.93% to 26.74%	36	10.68%	92.58%
26.74% to 32.55%	14	4.15%	96.74%
32.55% to 38.35%	5	1.48%	98.22%
Greater than 38.35%	6	1.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.39%	22.87%	77.15%	68.27%
±2σ	-0.36%	30.61%	94.96%	95.45%
±3σ	-8.10%	38.35%	98.22%	99.73%

Descriptive Statistics

Mean	15.129%
Standard Error	0.422%
Median	13.421%
Mode	11.530%
Standard Deviation	7.742%
Sample Variance	59.940%
Kurtosis	4.76
Skewness	1.75
Range	53.574%
Minimum	3.996%
Maximum	57.570%
Count	337

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.129%	337	100.00%	15.129%
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 0.61. Further, an Excess Kurtosis of 1.62 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.23%	0	0.00%	0.00%
-27.23% to -20.24%	3	0.89%	0.89%
-20.24% to -13.24%	16	4.75%	5.64%
-13.24% to -6.25%	52	15.43%	21.07%
-6.25% to 0.74%	107	31.75%	52.82%
0.74% to 7.74%	92	27.30%	80.12%
7.74% to 14.73%	44	13.06%	93.18%
14.73% to 21.72%	15	4.45%	97.63%
21.72% to 28.71%	4	1.19%	98.81%
Greater than 28.71%	4	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.58%	10.07%	71.81%	68.27%
±2σ	-17.91%	19.39%	95.55%	95.45%
±3σ	-27.23%	28.71%	98.81%	99.73%

Descriptive Statistics

Mean	0.743%
Standard Error	0.508%
Median	0.151%
Mode	-1.673%
Standard Deviation	9.324%
Sample Variance	86.935%
Kurtosis	1.62
Skewness	0.61
Range	62.432%
Minimum	-22.355%
Maximum	40.077%
Count	337

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.568%	173	51.34%	3.885%
Negative	-6.456%	164	48.66%	-3.142%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.07. Further, an Excess Kurtosis of -0.46 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.28%	0	0.00%	0.00%
-51.28% to -38.41%	0	0.00%	0.00%
-38.41% to -25.53%	5	6.49%	6.49%
-25.53% to -12.66%	16	20.78%	27.27%
-12.66% to 0.22%	19	24.68%	51.95%
0.22% to 13.09%	19	24.68%	76.62%
13.09% to 25.96%	13	16.88%	93.51%
25.96% to 38.84%	4	5.19%	98.70%
38.84% to 51.71%	1	1.30%	100.00%
Greater than 51.71%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.95%	17.38%	66.23%	68.27%
±2σ	-34.12%	34.55%	94.81%	95.45%
±3σ	-51.28%	51.71%	100.00%	99.73%

Descriptive Statistics

Mean	0.216%
Standard Error	1.956%
Median	-0.811%
Mode	-37.216%
Standard Deviation	17.166%
Sample Variance	294.679%
Kurtosis	-0.46
Skewness	0.07
Range	79.453%
Minimum	-37.216%
Maximum	42.237%
Count	77

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.702%	38	49.35%	7.256%
Negative	-13.899%	39	50.65%	-7.040%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.55%
12	1 Year	29.57%
36	3 Years	26.87%
60	5 Years	28.82%
120	10 Years	28.89%
240	20 Years	28.89%
600	50 Years	28.89%

High-to-Low 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 1.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.50%	0	0.00%	0.00%
-10.50% to 0.90%	0	0.00%	0.00%
0.90% to 12.30%	1	1.28%	1.28%
12.30% to 23.71%	18	23.08%	24.36%
23.71% to 35.11%	25	32.05%	56.41%
35.11% to 46.51%	19	24.36%	80.77%
46.51% to 57.91%	8	10.26%	91.03%
57.91% to 69.31%	5	6.41%	97.44%
69.31% to 80.71%	0	0.00%	97.44%
Greater than 80.71%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.91%	50.31%	71.79%	68.27%
±2σ	4.70%	65.51%	96.15%	95.45%
±3σ	-10.50%	80.71%	97.44%	99.73%

Descriptive Statistics

Mean	35.107%
Standard Error	1.721%
Median	32.624%
Mode	10.673%
Standard Deviation	15.202%
Sample Variance	231.107%
Kurtosis	1.07
Skewness	1.03
Range	73.285%
Minimum	10.673%
Maximum	83.958%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.107%	78	100.00%	35.107%
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 0.76. Further, an Excess Kurtosis of 0.63 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.45%	0	0.00%	0.00%
-51.45% to -37.89%	0	0.00%	0.00%
-37.89% to -24.32%	3	3.85%	3.85%
-24.32% to -10.75%	17	21.79%	25.64%
-10.75% to 2.82%	20	25.64%	51.28%
2.82% to 16.39%	20	25.64%	76.92%
16.39% to 29.96%	13	16.67%	93.59%
29.96% to 43.53%	3	3.85%	97.44%
43.53% to 57.10%	1	1.28%	98.72%
Greater than 57.10%	1	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.27%	20.91%	73.08%	68.27%
±2σ	-33.36%	39.00%	96.15%	95.45%
±3σ	-51.45%	57.10%	98.72%	99.73%

Descriptive Statistics

Mean	2.821%
Standard Error	2.049%
Median	1.384%
Mode	-27.326%
Standard Deviation	18.092%
Sample Variance	327.332%
Kurtosis	0.63
Skewness	0.76
Range	87.125%
Minimum	-27.326%
Maximum	59.799%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.898%	40	51.28%	8.666%
Negative	-11.997%	38	48.72%	-5.845%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.42. Further, an Excess Kurtosis of -0.71 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.44%	0	0.00%	0.00%
-103.44% to -77.19%	0	0.00%	0.00%
-77.19% to -50.94%	0	0.00%	0.00%
-50.94% to -24.68%	7	26.92%	26.92%
-24.68% to 1.57%	8	30.77%	57.69%
1.57% to 27.82%	6	23.08%	80.77%
27.82% to 54.08%	2	7.69%	88.46%
54.08% to 80.33%	3	11.54%	100.00%
80.33% to 106.58%	0	0.00%	100.00%
Greater than 106.58%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.43%	36.57%	65.38%	68.27%
±2σ	-68.44%	71.58%	96.15%	95.45%
±3σ	-103.44%	106.58%	100.00%	99.73%

Descriptive Statistics

Mean	1.571%
Standard Error	6.865%
Median	-6.480%
Mode	-50.390%
Standard Deviation	35.004%
Sample Variance	1225.283%
Kurtosis	-0.71
Skewness	0.42
Range	122.686%
Minimum	-50.390%
Maximum	72.296%
Count	26

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.927%	12	46.15%	15.197%
Negative	-25.306%	14	53.85%	-13.626%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	52.43%
12	3 Years	50.33%
20	5 Years	51.28%
40	10 Years	52.64%
80	20 Years	52.64%
200	50 Years	52.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.16. Further, an Excess Kurtosis of -1.09 proves the distribution possesses Thin Tails (Platykurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.98%	0	0.00%	0.00%
-26.98% to -2.14%	0	0.00%	0.00%
-2.14% to 22.69%	1	3.70%	3.70%
22.69% to 47.52%	8	29.63%	33.33%
47.52% to 72.36%	4	14.81%	48.15%
72.36% to 97.19%	8	29.63%	77.78%
97.19% to 122.03%	3	11.11%	88.89%
122.03% to 146.86%	3	11.11%	100.00%
146.86% to 171.70%	0	0.00%	100.00%
Greater than 171.70%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	39.25%	105.47%	59.26%	68.27%
±2σ	6.13%	138.59%	100.00%	95.45%
±3σ	-26.98%	171.70%	100.00%	99.73%

Descriptive Statistics

Mean	72.360%
Standard Error	6.373%
Median	76.605%
Mode	21.031%
Standard Deviation	33.113%
Sample Variance	1096.463%
Kurtosis	-1.09
Skewness	0.16
Range	109.347%
Minimum	21.031%
Maximum	130.378%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	72.360%	27	100.00%	72.360%
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 0.85. Further, an Excess Kurtosis of 0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -106.49%	0	0.00%	0.00%
-106.49% to -77.44%	0	0.00%	0.00%
-77.44% to -48.39%	0	0.00%	0.00%
-48.39% to -19.34%	7	25.93%	25.93%
-19.34% to 9.71%	9	33.33%	59.26%
9.71% to 38.77%	5	18.52%	77.78%
38.77% to 67.82%	3	11.11%	88.89%
67.82% to 96.87%	2	7.41%	96.30%
96.87% to 125.92%	1	3.70%	100.00%
Greater than 125.92%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.02%	48.45%	70.37%	68.27%
±2σ	-67.75%	87.19%	96.30%	95.45%
±3σ	-106.49%	125.92%	100.00%	99.73%

Descriptive Statistics

Mean	9.715%
Standard Error	7.454%
Median	6.992%
Mode	-39.739%
Standard Deviation	38.735%
Sample Variance	1500.371%
Kurtosis	0.08
Skewness	0.85
Range	145.267%
Minimum	-39.739%
Maximum	105.528%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.657%	14	51.85%	20.044%
Negative	-21.453%	13	48.15%	-10.329%
Zero	0.000%	0	0.00%	0.000%

TXG Deep Analytical Report