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	4.21%	3.10%	3.77%	6.01%	5.94%	5.96%	17.96	20.23	16.93	21.46
Weekly	9.45%	7.78%	9.45%	14.27%	13.07%	13.12%	16.72	21.72	14.68	24.75
Monthly	17.23%	15.07%	18.14%	29.06%	27.21%	27.32%	14.52	25.02	11.06	32.85
Quarterly	35.00%	31.93%	38.74%	52.21%	47.13%	47.31%	11.90	30.54	7.43	48.92
Annual	—	—	—	—	94.26%	94.63%	7.43	48.92	2.89	125.56
Option Time Horizon	—	—	—	—	35.58%	35.72%	13.35	27.20	9.36	38.83

Calculation Notes: Computed at 2026-03-23T16:40 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $19.06 | Strike (K): $20.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3750 (Bid $1.9500 / Ask $2.8000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 94.26% (CRR binomial tree, American, n=20 steps) | BS IV: 95.04% (European Black-Scholes) | Yahoo IV (Annual): 94.63% → 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 0.18. Further, an Excess Kurtosis of 3.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.59%	8	0.49%	0.49%
-12.59% to -9.44%	17	1.04%	1.53%
-9.44% to -6.28%	65	3.97%	5.49%
-6.28% to -3.13%	203	12.39%	17.88%
-3.13% to 0.03%	554	33.80%	51.68%
0.03% to 3.18%	488	29.77%	81.45%
3.18% to 6.33%	214	13.06%	94.51%
6.33% to 9.49%	55	3.36%	97.86%
9.49% to 12.64%	23	1.40%	99.27%
Greater than 12.64%	12	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.18%	4.23%	75.47%	68.27%
±2σ	-8.39%	8.44%	94.87%	95.45%
±3σ	-12.59%	12.64%	98.78%	99.73%

Descriptive Statistics

Mean	0.026%
Standard Error	0.104%
Median	-0.066%
Mode	0.000%
Standard Deviation	4.206%
Sample Variance	17.687%
Kurtosis	3.51
Skewness	0.18
Range	49.067%
Minimum	-24.700%
Maximum	24.367%
Count	1639

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.164%	796	48.57%	1.537%
Negative	-2.976%	832	50.76%	-1.511%
Zero	0.000%	11	0.67%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.44%
20	1 Month	6.93%
60	1 Quarter	6.46%
250	1 Year	6.34%
750	3 Years	5.66%
1,250	5 Years	6.01%
2,500	10 Years	5.98%
5,000	20 Years	5.98%
12,500	50 Years	5.98%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.86. Further, an Excess Kurtosis of 5.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.42%	0	0.00%	0.00%
-3.42% to -1.10%	0	0.00%	0.00%
-1.10% to 1.23%	1	0.06%	0.06%
1.23% to 3.55%	333	20.30%	20.37%
3.55% to 5.87%	673	41.04%	61.40%
5.87% to 8.19%	352	21.46%	82.87%
8.19% to 10.51%	155	9.45%	92.32%
10.51% to 12.84%	66	4.02%	96.34%
12.84% to 15.16%	31	1.89%	98.23%
Greater than 15.16%	29	1.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.77%	8.97%	78.48%	68.27%
±2σ	-0.32%	12.06%	95.24%	95.45%
±3σ	-3.42%	15.16%	98.23%	99.73%

Descriptive Statistics

Mean	5.870%
Standard Error	0.076%
Median	5.072%
Mode	2.742%
Standard Deviation	3.096%
Sample Variance	9.585%
Kurtosis	5.47
Skewness	1.86
Range	26.454%
Minimum	1.212%
Maximum	27.666%
Count	1640

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.870%	1640	100.00%	5.870%
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 0.15. Further, an Excess Kurtosis of 1.96 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.23%	7	0.43%	0.43%
-11.23% to -8.41%	21	1.28%	1.71%
-8.41% to -5.59%	66	4.02%	5.73%
-5.59% to -2.76%	228	13.90%	19.63%
-2.76% to 0.06%	507	30.91%	50.55%
0.06% to 2.88%	517	31.52%	82.07%
2.88% to 5.71%	187	11.40%	93.48%
5.71% to 8.53%	73	4.45%	97.93%
8.53% to 11.36%	20	1.22%	99.15%
Greater than 11.36%	14	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.71%	3.83%	74.15%	68.27%
±2σ	-7.47%	7.59%	94.33%	95.45%
±3σ	-11.23%	11.36%	98.72%	99.73%

Descriptive Statistics

Mean	0.060%
Standard Error	0.093%
Median	0.030%
Mode	0.000%
Standard Deviation	3.765%
Sample Variance	14.176%
Kurtosis	1.96
Skewness	0.15
Range	37.855%
Minimum	-19.954%
Maximum	17.901%
Count	1640

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.838%	822	50.12%	1.422%
Negative	-2.752%	812	49.51%	-1.363%
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 0.72 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.23%	1	0.29%	0.29%
-28.23% to -21.14%	3	0.88%	1.18%
-21.14% to -14.05%	16	4.71%	5.88%
-14.05% to -6.96%	55	16.18%	22.06%
-6.96% to 0.13%	103	30.29%	52.35%
0.13% to 7.22%	92	27.06%	79.41%
7.22% to 14.31%	47	13.82%	93.24%
14.31% to 21.40%	14	4.12%	97.35%
21.40% to 28.49%	9	2.65%	100.00%
Greater than 28.49%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.32%	9.58%	73.24%	68.27%
±2σ	-18.77%	19.04%	94.12%	95.45%
±3σ	-28.23%	28.49%	99.71%	99.73%

Descriptive Statistics

Mean	0.131%
Standard Error	0.513%
Median	-0.428%
Mode	2.258%
Standard Deviation	9.452%
Sample Variance	89.347%
Kurtosis	0.72
Skewness	0.23
Range	58.293%
Minimum	-29.982%
Maximum	28.311%
Count	340

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.718%	162	47.65%	3.677%
Negative	-6.774%	178	52.35%	-3.546%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	20.26%
12	1 Quarter	16.94%
52	1 Year	15.46%
156	3 Years	13.52%
260	5 Years	14.27%
520	10 Years	14.04%
1,040	20 Years	14.04%
2,600	50 Years	14.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.71. Further, an Excess Kurtosis of 4.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.13%	0	0.00%	0.00%
-8.13% to -2.29%	0	0.00%	0.00%
-2.29% to 3.54%	0	0.00%	0.00%
3.54% to 9.38%	69	20.23%	20.23%
9.38% to 15.22%	132	38.71%	58.94%
15.22% to 21.05%	82	24.05%	82.99%
21.05% to 26.89%	32	9.38%	92.38%
26.89% to 32.73%	14	4.11%	96.48%
32.73% to 38.56%	6	1.76%	98.24%
Greater than 38.56%	6	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.44%	23.00%	77.13%	68.27%
±2σ	-0.35%	30.78%	95.01%	95.45%
±3σ	-8.13%	38.56%	98.24%	99.73%

Descriptive Statistics

Mean	15.218%
Standard Error	0.421%
Median	13.541%
Mode	11.530%
Standard Deviation	7.782%
Sample Variance	60.552%
Kurtosis	4.54
Skewness	1.71
Range	53.574%
Minimum	3.996%
Maximum	57.570%
Count	341

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.218%	341	100.00%	15.218%
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 1.54 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.62%	0	0.00%	0.00%
-27.62% to -20.53%	3	0.88%	0.88%
-20.53% to -13.44%	17	4.99%	5.87%
-13.44% to -6.35%	51	14.96%	20.82%
-6.35% to 0.73%	108	31.67%	52.49%
0.73% to 7.82%	95	27.86%	80.35%
7.82% to 14.91%	43	12.61%	92.96%
14.91% to 22.00%	16	4.69%	97.65%
22.00% to 29.09%	4	1.17%	98.83%
Greater than 29.09%	4	1.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.72%	10.19%	72.43%	68.27%
±2σ	-18.17%	19.64%	95.01%	95.45%
±3σ	-27.62%	29.09%	98.83%	99.73%

Descriptive Statistics

Mean	0.734%
Standard Error	0.512%
Median	0.151%
Mode	-1.673%
Standard Deviation	9.451%
Sample Variance	89.320%
Kurtosis	1.54
Skewness	0.61
Range	62.432%
Minimum	-22.355%
Maximum	40.077%
Count	341

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.650%	175	51.32%	3.926%
Negative	-6.558%	166	48.68%	-3.192%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.06. Further, an Excess Kurtosis of -0.52 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 -38.52%	0	0.00%	0.00%
-38.52% to -25.60%	4	5.13%	5.13%
-25.60% to -12.67%	18	23.08%	28.21%
-12.67% to 0.25%	18	23.08%	51.28%
0.25% to 13.17%	19	24.36%	75.64%
13.17% to 26.10%	14	17.95%	93.59%
26.10% to 39.02%	4	5.13%	98.72%
39.02% to 51.95%	1	1.28%	100.00%
Greater than 51.95%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.98%	17.48%	66.67%	68.27%
±2σ	-34.21%	34.71%	94.87%	95.45%
±3σ	-51.45%	51.95%	100.00%	99.73%

Descriptive Statistics

Mean	0.250%
Standard Error	1.951%
Median	-0.377%
Mode	-37.216%
Standard Deviation	17.232%
Sample Variance	296.944%
Kurtosis	-0.52
Skewness	0.06
Range	79.453%
Minimum	-37.216%
Maximum	42.237%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.687%	39	50.00%	7.344%
Negative	-14.186%	39	50.00%	-7.093%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	35.63%
12	1 Year	30.80%
36	3 Years	27.34%
60	5 Years	29.06%
120	10 Years	29.08%
240	20 Years	29.08%
600	50 Years	29.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 1.00. Further, an Excess Kurtosis of 1.06 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.80%	0	0.00%	0.00%
-9.80% to 1.50%	0	0.00%	0.00%
1.50% to 12.80%	1	1.27%	1.27%
12.80% to 24.11%	18	22.78%	24.05%
24.11% to 35.41%	27	34.18%	58.23%
35.41% to 46.72%	18	22.78%	81.01%
46.72% to 58.02%	8	10.13%	91.14%
58.02% to 69.33%	5	6.33%	97.47%
69.33% to 80.63%	0	0.00%	97.47%
Greater than 80.63%	2	2.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	20.34%	50.49%	72.15%	68.27%
±2σ	5.27%	65.56%	96.20%	95.45%
±3σ	-9.80%	80.63%	97.47%	99.73%

Descriptive Statistics

Mean	35.414%
Standard Error	1.696%
Median	33.641%
Mode	10.673%
Standard Deviation	15.073%
Sample Variance	227.204%
Kurtosis	1.06
Skewness	1.00
Range	73.285%
Minimum	10.673%
Maximum	83.958%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.414%	79	100.00%	35.414%
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 0.57 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.64%	0	0.00%	0.00%
-51.64% to -38.03%	0	0.00%	0.00%
-38.03% to -24.43%	3	3.80%	3.80%
-24.43% to -10.83%	17	21.52%	25.32%
-10.83% to 2.77%	21	26.58%	51.90%
2.77% to 16.37%	19	24.05%	75.95%
16.37% to 29.98%	14	17.72%	93.67%
29.98% to 43.58%	3	3.80%	97.47%
43.58% to 57.18%	1	1.27%	98.73%
Greater than 57.18%	1	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.36%	20.91%	73.42%	68.27%
±2σ	-33.50%	39.04%	96.20%	95.45%
±3σ	-51.64%	57.18%	98.73%	99.73%

Descriptive Statistics

Mean	2.772%
Standard Error	2.040%
Median	0.693%
Mode	-27.326%
Standard Deviation	18.136%
Sample Variance	328.926%
Kurtosis	0.57
Skewness	0.76
Range	87.125%
Minimum	-27.326%
Maximum	59.799%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.180%	40	50.63%	8.699%
Negative	-12.006%	39	49.37%	-5.927%
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 -103.41%	0	0.00%	0.00%
-103.41% to -77.16%	0	0.00%	0.00%
-77.16% to -50.91%	0	0.00%	0.00%
-50.91% to -24.66%	7	26.92%	26.92%
-24.66% to 1.59%	8	30.77%	57.69%
1.59% to 27.84%	6	23.08%	80.77%
27.84% to 54.09%	2	7.69%	88.46%
54.09% to 80.34%	3	11.54%	100.00%
80.34% to 106.59%	0	0.00%	100.00%
Greater than 106.59%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.41%	36.59%	65.38%	68.27%
±2σ	-68.41%	71.59%	96.15%	95.45%
±3σ	-103.41%	106.59%	100.00%	99.73%

Descriptive Statistics

Mean	1.587%
Standard Error	6.864%
Median	-6.269%
Mode	-50.390%
Standard Deviation	35.000%
Sample Variance	1225.017%
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	-25.276%	14	53.85%	-13.610%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	57.09%
12	3 Years	51.88%
20	5 Years	52.21%
40	10 Years	53.35%
80	20 Years	53.35%
200	50 Years	53.35%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of -1.08 proves the distribution possesses Thin Tails (Platykurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.50%	0	0.00%	0.00%
-22.50% to 1.45%	0	0.00%	0.00%
1.45% to 25.40%	1	3.70%	3.70%
25.40% to 49.35%	8	29.63%	33.33%
49.35% to 73.31%	4	14.81%	48.15%
73.31% to 97.26%	8	29.63%	77.78%
97.26% to 121.21%	3	11.11%	88.89%
121.21% to 145.16%	3	11.11%	100.00%
145.16% to 169.11%	0	0.00%	100.00%
Greater than 169.11%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	41.37%	105.24%	55.56%	68.27%
±2σ	9.44%	137.18%	100.00%	95.45%
±3σ	-22.50%	169.11%	100.00%	99.73%

Descriptive Statistics

Mean	73.305%
Standard Error	6.146%
Median	76.605%
Mode	25.015%
Standard Deviation	31.935%
Sample Variance	1019.843%
Kurtosis	-1.08
Skewness	0.23
Range	105.363%
Minimum	25.015%
Maximum	130.378%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	73.305%	27	100.00%	73.305%
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 -106.51%	0	0.00%	0.00%
-106.51% to -77.46%	0	0.00%	0.00%
-77.46% to -48.41%	0	0.00%	0.00%
-48.41% to -19.36%	7	25.93%	25.93%
-19.36% to 9.70%	9	33.33%	59.26%
9.70% to 38.75%	5	18.52%	77.78%
38.75% to 67.80%	3	11.11%	88.89%
67.80% to 96.85%	2	7.41%	96.30%
96.85% to 125.91%	1	3.70%	100.00%
Greater than 125.91%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.04%	48.43%	70.37%	68.27%
±2σ	-67.77%	87.17%	96.30%	95.45%
±3σ	-106.51%	125.91%	100.00%	99.73%

Descriptive Statistics

Mean	9.697%
Standard Error	7.455%
Median	6.512%
Mode	-39.739%
Standard Deviation	38.736%
Sample Variance	1500.480%
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	38.623%	14	51.85%	20.027%
Negative	-21.453%	13	48.15%	-10.329%
Zero	0.000%	0	0.00%	0.000%

TXG Deep Analytical Report