TRVG - 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	4.18%	5.34%	3.70%	5.77%	8.04%	8.07%	2.68	3.14	2.47	3.41
Weekly	8.93%	12.10%	8.73%	12.91%	17.71%	17.77%	2.43	3.46	2.04	4.13
Monthly	17.96%	26.01%	21.19%	25.30%	36.86%	36.99%	2.01	4.19	1.39	6.06
Quarterly	35.28%	63.09%	45.28%	44.57%	63.84%	64.06%	1.53	5.49	0.81	10.40
Annual	—	—	—	—	127.68%	128.13%	0.81	10.40	0.23	37.28
Option Time Horizon	—	—	—	—	48.65%	48.82%	1.78	4.72	1.10	7.67

Calculation Notes: Computed at 2026-02-23T14:06 UTC | Reference Contract: Call option expiring 2026-04-17 (53 days) | Spot Price (S): $2.90 | Strike (K): $5.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1250 (Bid $0.0000 / Ask $0.2500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 127.68% (CRR binomial tree, American, n=20 steps) | BS IV: 128.58% (European Black-Scholes) | Yahoo IV (Annual): 128.13% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2023-11-14	$2.8250

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.55%	11	0.48%	0.48%
-12.55% to -9.42%	11	0.48%	0.95%
-9.42% to -6.28%	51	2.21%	3.17%
-6.28% to -3.15%	280	12.15%	15.31%
-3.15% to -0.01%	840	36.44%	51.76%
-0.01% to 3.12%	762	33.06%	84.82%
3.12% to 6.26%	241	10.46%	95.27%
6.26% to 9.39%	57	2.47%	97.74%
9.39% to 12.52%	24	1.04%	98.79%
Greater than 12.52%	28	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.19%	4.17%	80.61%	68.27%
±2σ	-8.37%	8.35%	96.01%	95.45%
±3σ	-12.55%	12.52%	98.31%	99.73%

Descriptive Statistics

Mean	-0.013%
Standard Error	0.087%
Median	-0.264%
Mode	0.000%
Standard Deviation	4.179%
Sample Variance	17.466%
Kurtosis	16.86
Skewness	1.32
Range	79.769%
Minimum	-27.864%
Maximum	51.905%
Count	2305

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.249%	961	41.69%	1.355%
Negative	-2.642%	1193	51.76%	-1.367%
Zero	0.000%	151	6.55%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.68%
20	1 Month	4.25%
60	1 Quarter	3.62%
250	1 Year	5.78%
750	3 Years	5.54%
1,250	5 Years	5.77%
2,500	10 Years	6.04%
5,000	20 Years	6.04%
12,500	50 Years	6.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 17.01. Further, an Excess Kurtosis of 537.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.01%	0	0.00%	0.00%
-10.01% to -6.00%	0	0.00%	0.00%
-6.00% to -2.00%	0	0.00%	0.00%
-2.00% to 2.01%	115	4.99%	4.99%
2.01% to 6.02%	1380	59.84%	64.83%
6.02% to 10.03%	571	24.76%	89.59%
10.03% to 14.03%	135	5.85%	95.45%
14.03% to 18.04%	63	2.73%	98.18%
18.04% to 22.05%	24	1.04%	99.22%
Greater than 22.05%	18	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.68%	11.36%	92.45%	68.27%
±2σ	-4.67%	16.70%	97.53%	95.45%
±3σ	-10.01%	22.05%	99.22%	99.73%

Descriptive Statistics

Mean	6.019%
Standard Error	0.111%
Median	4.982%
Mode	4.167%
Standard Deviation	5.343%
Sample Variance	28.546%
Kurtosis	537.31
Skewness	17.01
Range	183.681%
Minimum	0.377%
Maximum	184.058%
Count	2306

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.019%	2306	100.00%	6.019%
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 -0.29. Further, an Excess Kurtosis of 6.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.91%	19	0.82%	0.82%
-10.91% to -8.13%	32	1.39%	2.21%
-8.13% to -5.36%	68	2.95%	5.16%
-5.36% to -2.58%	271	11.75%	16.91%
-2.58% to 0.19%	772	33.48%	50.39%
0.19% to 2.97%	754	32.70%	83.09%
2.97% to 5.74%	269	11.67%	94.75%
5.74% to 8.52%	84	3.64%	98.40%
8.52% to 11.30%	21	0.91%	99.31%
Greater than 11.30%	16	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.51%	3.89%	77.58%	68.27%
±2σ	-7.21%	7.59%	94.84%	95.45%
±3σ	-10.91%	11.30%	98.48%	99.73%

Descriptive Statistics

Mean	0.193%
Standard Error	0.077%
Median	0.164%
Mode	0.000%
Standard Deviation	3.701%
Sample Variance	13.695%
Kurtosis	6.45
Skewness	-0.29
Range	55.137%
Minimum	-32.915%
Maximum	22.222%
Count	2306

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.730%	1165	50.52%	1.379%
Negative	-2.730%	1002	43.45%	-1.186%
Zero	0.000%	139	6.03%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.02. Further, an Excess Kurtosis of 6.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.89%	2	0.42%	0.42%
-26.89% to -20.19%	7	1.46%	1.88%
-20.19% to -13.49%	13	2.71%	4.59%
-13.49% to -6.79%	56	11.69%	16.28%
-6.79% to -0.09%	177	36.95%	53.24%
-0.09% to 6.61%	148	30.90%	84.13%
6.61% to 13.31%	47	9.81%	93.95%
13.31% to 20.01%	15	3.13%	97.08%
20.01% to 26.70%	8	1.67%	98.75%
Greater than 26.70%	6	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.02%	8.84%	79.54%	68.27%
±2σ	-17.96%	17.77%	93.95%	95.45%
±3σ	-26.89%	26.70%	98.33%	99.73%

Descriptive Statistics

Mean	-0.091%
Standard Error	0.408%
Median	-0.676%
Mode	0.000%
Standard Deviation	8.932%
Sample Variance	79.787%
Kurtosis	6.42
Skewness	1.02
Range	93.038%
Minimum	-31.908%
Maximum	61.130%
Count	479

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.106%	204	42.59%	3.026%
Negative	-5.856%	255	53.24%	-3.118%
Zero	0.000%	20	4.17%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.41%
12	1 Quarter	7.14%
52	1 Year	13.17%
156	3 Years	12.62%
260	5 Years	12.91%
520	10 Years	13.62%
1,040	20 Years	13.62%
2,600	50 Years	13.62%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.85. Further, an Excess Kurtosis of 82.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.71%	0	0.00%	0.00%
-21.71% to -12.64%	0	0.00%	0.00%
-12.64% to -3.56%	0	0.00%	0.00%
-3.56% to 5.51%	27	5.62%	5.62%
5.51% to 14.58%	287	59.79%	65.42%
14.58% to 23.65%	110	22.92%	88.33%
23.65% to 32.72%	32	6.67%	95.00%
32.72% to 41.79%	11	2.29%	97.29%
41.79% to 50.86%	6	1.25%	98.54%
Greater than 50.86%	7	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.48%	26.67%	91.88%	68.27%
±2σ	-9.61%	38.77%	97.08%	95.45%
±3σ	-21.71%	50.86%	98.54%	99.73%

Descriptive Statistics

Mean	14.578%
Standard Error	0.552%
Median	11.598%
Mode	9.091%
Standard Deviation	12.095%
Sample Variance	146.297%
Kurtosis	82.61
Skewness	6.85
Range	181.392%
Minimum	2.666%
Maximum	184.058%
Count	480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.578%	480	100.00%	14.578%
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 0.62. Further, an Excess Kurtosis of 4.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.18%	2	0.42%	0.42%
-25.18% to -18.63%	5	1.04%	1.46%
-18.63% to -12.08%	15	3.12%	4.58%
-12.08% to -5.53%	68	14.17%	18.75%
-5.53% to 1.02%	157	32.71%	51.46%
1.02% to 7.57%	156	32.50%	83.96%
7.57% to 14.12%	53	11.04%	95.00%
14.12% to 20.67%	12	2.50%	97.50%
20.67% to 27.22%	6	1.25%	98.75%
Greater than 27.22%	6	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.72%	9.75%	75.83%	68.27%
±2σ	-16.45%	18.48%	95.00%	95.45%
±3σ	-25.18%	27.22%	98.33%	99.73%

Descriptive Statistics

Mean	1.018%
Standard Error	0.399%
Median	0.828%
Mode	0.000%
Standard Deviation	8.733%
Sample Variance	76.257%
Kurtosis	4.09
Skewness	0.62
Range	83.957%
Minimum	-37.320%
Maximum	46.637%
Count	480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.631%	261	54.38%	3.606%
Negative	-6.030%	206	42.92%	-2.588%
Zero	0.000%	13	2.71%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.24. Further, an Excess Kurtosis of 3.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.44%	0	0.00%	0.00%
-54.44% to -40.97%	0	0.00%	0.00%
-40.97% to -27.50%	5	4.55%	4.55%
-27.50% to -14.03%	16	14.55%	19.09%
-14.03% to -0.56%	42	38.18%	57.27%
-0.56% to 12.91%	30	27.27%	84.55%
12.91% to 26.39%	8	7.27%	91.82%
26.39% to 39.86%	6	5.45%	97.27%
39.86% to 53.33%	1	0.91%	98.18%
Greater than 53.33%	2	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.52%	17.41%	78.18%	68.27%
±2σ	-36.48%	35.37%	96.36%	95.45%
±3σ	-54.44%	53.33%	98.18%	99.73%

Descriptive Statistics

Mean	-0.556%
Standard Error	1.713%
Median	-2.516%
Mode	-35.827%
Standard Deviation	17.962%
Sample Variance	322.634%
Kurtosis	3.09
Skewness	1.24
Range	108.049%
Minimum	-35.827%
Maximum	72.222%
Count	110

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.658%	46	41.82%	6.130%
Negative	-11.491%	64	58.18%	-6.686%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.49%
12	1 Year	24.21%
36	3 Years	24.84%
60	5 Years	25.30%
120	10 Years	29.17%
240	20 Years	29.17%
600	50 Years	29.17%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 13.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.16%	0	0.00%	0.00%
-43.16% to -23.66%	0	0.00%	0.00%
-23.66% to -4.15%	0	0.00%	0.00%
-4.15% to 15.36%	15	13.51%	13.51%
15.36% to 34.87%	62	55.86%	69.37%
34.87% to 54.38%	18	16.22%	85.59%
54.38% to 73.89%	10	9.01%	94.59%
73.89% to 93.39%	2	1.80%	96.40%
93.39% to 112.90%	1	0.90%	97.30%
Greater than 112.90%	3	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.86%	60.88%	90.09%	68.27%
±2σ	-17.15%	86.89%	96.40%	95.45%
±3σ	-43.16%	112.90%	97.30%	99.73%

Descriptive Statistics

Mean	34.870%
Standard Error	2.469%
Median	27.530%
Mode	20.172%
Standard Deviation	26.011%
Sample Variance	676.591%
Kurtosis	13.09
Skewness	3.09
Range	180.284%
Minimum	6.545%
Maximum	186.829%
Count	111

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.870%	111	100.00%	34.870%
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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.18. Further, an Excess Kurtosis of 12.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.72%	0	0.00%	0.00%
-58.72% to -42.83%	0	0.00%	0.00%
-42.83% to -26.94%	3	2.70%	2.70%
-26.94% to -11.04%	14	12.61%	15.32%
-11.04% to 4.84%	45	40.54%	55.86%
4.84% to 20.73%	36	32.43%	88.29%
20.73% to 36.63%	6	5.41%	93.69%
36.63% to 52.52%	5	4.50%	98.20%
52.52% to 68.41%	1	0.90%	99.10%
Greater than 68.41%	1	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.34%	26.03%	81.08%	68.27%
±2σ	-37.53%	47.22%	95.50%	95.45%
±3σ	-58.72%	68.41%	99.10%	99.73%

Descriptive Statistics

Mean	4.845%
Standard Error	2.011%
Median	2.963%
Mode	-3.448%
Standard Deviation	21.187%
Sample Variance	448.904%
Kurtosis	12.02
Skewness	2.18
Range	173.444%
Minimum	-39.401%
Maximum	134.043%
Count	111

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.834%	66	59.46%	9.415%
Negative	-11.795%	43	38.74%	-4.569%
Zero	0.000%	2	1.80%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.01. Further, an Excess Kurtosis of 0.53 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -106.18%	0	0.00%	0.00%
-106.18% to -79.71%	0	0.00%	0.00%
-79.71% to -53.25%	1	2.70%	2.70%
-53.25% to -26.79%	5	13.51%	16.22%
-26.79% to -0.32%	19	51.35%	67.57%
-0.32% to 26.14%	5	13.51%	81.08%
26.14% to 52.60%	3	8.11%	89.19%
52.60% to 79.07%	3	8.11%	97.30%
79.07% to 105.53%	1	2.70%	100.00%
Greater than 105.53%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.61%	34.96%	75.68%	68.27%
±2σ	-70.89%	70.25%	91.89%	95.45%
±3σ	-106.18%	105.53%	100.00%	99.73%

Descriptive Statistics

Mean	-0.323%
Standard Error	5.801%
Median	-10.204%
Mode	-65.632%
Standard Deviation	35.285%
Sample Variance	1245.040%
Kurtosis	0.53
Skewness	1.01
Range	152.299%
Minimum	-65.632%
Maximum	86.667%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.399%	12	32.43%	13.102%
Negative	-19.869%	25	67.57%	-13.425%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.94%
12	3 Years	44.47%
20	5 Years	44.57%
40	10 Years	57.38%
80	20 Years	57.38%
200	50 Years	57.38%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.12. Further, an Excess Kurtosis of 12.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.74%	0	0.00%	0.00%
-113.74% to -66.43%	0	0.00%	0.00%
-66.43% to -19.11%	0	0.00%	0.00%
-19.11% to 28.20%	3	7.89%	7.89%
28.20% to 75.52%	23	60.53%	68.42%
75.52% to 122.83%	7	18.42%	86.84%
122.83% to 170.15%	3	7.89%	94.74%
170.15% to 217.46%	1	2.63%	97.37%
217.46% to 264.77%	0	0.00%	97.37%
Greater than 264.77%	1	2.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.43%	138.60%	89.47%	68.27%
±2σ	-50.66%	201.69%	97.37%	95.45%
±3σ	-113.74%	264.77%	97.37%	99.73%

Descriptive Statistics

Mean	75.517%
Standard Error	10.234%
Median	57.015%
Mode	14.286%
Standard Deviation	63.086%
Sample Variance	3979.838%
Kurtosis	12.68
Skewness	3.12
Range	356.114%
Minimum	14.286%
Maximum	370.400%
Count	38

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.517%	38	100.00%	75.517%
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 1.81. Further, an Excess Kurtosis of 5.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -120.33%	0	0.00%	0.00%
-120.33% to -86.37%	0	0.00%	0.00%
-86.37% to -52.40%	0	0.00%	0.00%
-52.40% to -18.44%	7	18.42%	18.42%
-18.44% to 15.52%	13	34.21%	52.63%
15.52% to 49.49%	15	39.47%	92.11%
49.49% to 83.45%	1	2.63%	94.74%
83.45% to 117.42%	0	0.00%	94.74%
117.42% to 151.38%	1	2.63%	97.37%
Greater than 151.38%	1	2.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.76%	60.81%	76.32%	68.27%
±2σ	-75.05%	106.09%	94.74%	95.45%
±3σ	-120.33%	151.38%	97.37%	99.73%

Descriptive Statistics

Mean	15.524%
Standard Error	7.346%
Median	11.466%
Mode	-3.448%
Standard Deviation	45.285%
Sample Variance	2050.690%
Kurtosis	5.63
Skewness	1.81
Range	237.701%
Minimum	-45.635%
Maximum	192.066%
Count	38

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.784%	24	63.16%	23.864%
Negative	-22.637%	14	36.84%	-8.340%
Zero	0.000%	0	0.00%	0.000%

TRVG Deep Analytical Report