FVRR - 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	4.32%	3.88%	3.95%	5.57%	3.62%	3.71%	11.26	12.11	10.86	12.56
Weekly	9.42%	9.54%	9.61%	13.01%	7.98%	8.17%	10.78	12.65	9.96	13.70
Monthly	18.37%	18.56%	17.89%	26.88%	16.60%	17.00%	9.89	13.79	8.38	16.28
Quarterly	38.93%	36.09%	35.28%	45.54%	28.76%	29.44%	8.76	15.57	6.57	20.76
Annual	—	—	—	—	57.51%	58.89%	6.57	20.76	3.70	36.90
Option Time Horizon	—	—	—	—	22.12%	22.65%	9.36	14.57	7.50	18.18

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $11.68 | Strike (K): $12.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.9250 (Bid $0.8000 / Ask $1.0500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 57.51% (CRR binomial tree, American, n=20 steps) | BS IV: 57.92% (European Black-Scholes) | Yahoo IV (Annual): 58.89% → 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 0.26. Further, an Excess Kurtosis of 4.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.93%	8	0.48%	0.48%
-12.93% to -9.69%	13	0.77%	1.25%
-9.69% to -6.45%	65	3.87%	5.12%
-6.45% to -3.22%	221	13.15%	18.26%
-3.22% to 0.02%	557	33.14%	51.40%
0.02% to 3.26%	505	30.04%	81.44%
3.26% to 6.49%	210	12.49%	93.93%
6.49% to 9.73%	76	4.52%	98.45%
9.73% to 12.97%	12	0.71%	99.17%
Greater than 12.97%	14	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.30%	4.34%	75.55%	68.27%
±2σ	-8.61%	8.65%	95.72%	95.45%
±3σ	-12.93%	12.97%	98.69%	99.73%

Descriptive Statistics

Mean	0.020%
Standard Error	0.105%
Median	-0.125%
Mode	0.000%
Standard Deviation	4.316%
Sample Variance	18.629%
Kurtosis	4.42
Skewness	0.26
Range	55.006%
Minimum	-25.642%
Maximum	29.364%
Count	1681

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.227%	818	48.66%	1.570%
Negative	-3.048%	855	50.86%	-1.550%
Zero	0.000%	8	0.48%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	12.60%
20	1 Month	6.98%
60	1 Quarter	4.48%
250	1 Year	4.17%
750	3 Years	4.61%
1,250	5 Years	5.57%
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 5.50. Further, an Excess Kurtosis of 65.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.77%	0	0.00%	0.00%
-5.77% to -2.86%	0	0.00%	0.00%
-2.86% to 0.04%	0	0.00%	0.00%
0.04% to 2.95%	224	13.32%	13.32%
2.95% to 5.86%	817	48.57%	61.89%
5.86% to 8.77%	406	24.14%	86.03%
8.77% to 11.68%	145	8.62%	94.65%
11.68% to 14.58%	47	2.79%	97.44%
14.58% to 17.49%	16	0.95%	98.39%
Greater than 17.49%	27	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.98%	9.74%	88.53%	68.27%
±2σ	-1.89%	13.61%	97.09%	95.45%
±3σ	-5.77%	17.49%	98.39%	99.73%

Descriptive Statistics

Mean	5.860%
Standard Error	0.095%
Median	4.960%
Mode	3.838%
Standard Deviation	3.877%
Sample Variance	15.034%
Kurtosis	65.70
Skewness	5.50
Range	63.761%
Minimum	1.333%
Maximum	65.094%
Count	1682

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.860%	1682	100.00%	5.860%
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 -0.05. Further, an Excess Kurtosis of 7.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.67%	10	0.59%	0.59%
-11.67% to -8.70%	13	0.77%	1.37%
-8.70% to -5.74%	64	3.80%	5.17%
-5.74% to -2.78%	216	12.84%	18.01%
-2.78% to 0.19%	552	32.82%	50.83%
0.19% to 3.15%	514	30.56%	81.39%
3.15% to 6.12%	210	12.49%	93.88%
6.12% to 9.08%	74	4.40%	98.28%
9.08% to 12.04%	21	1.25%	99.52%
Greater than 12.04%	8	0.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.76%	4.14%	75.27%	68.27%
±2σ	-7.72%	8.09%	95.54%	95.45%
±3σ	-11.67%	12.04%	98.93%	99.73%

Descriptive Statistics

Mean	0.188%
Standard Error	0.096%
Median	0.136%
Mode	0.000%
Standard Deviation	3.952%
Sample Variance	15.620%
Kurtosis	7.29
Skewness	-0.05
Range	67.069%
Minimum	-34.837%
Maximum	32.232%
Count	1682

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.945%	865	51.43%	1.515%
Negative	-2.756%	810	48.16%	-1.327%
Zero	0.000%	7	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.31. Further, an Excess Kurtosis of 0.98 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.13%	1	0.29%	0.29%
-28.13% to -21.06%	3	0.86%	1.15%
-21.06% to -14.00%	14	4.01%	5.16%
-14.00% to -6.93%	51	14.61%	19.77%
-6.93% to 0.13%	117	33.52%	53.30%
0.13% to 7.20%	95	27.22%	80.52%
7.20% to 14.26%	41	11.75%	92.26%
14.26% to 21.33%	18	5.16%	97.42%
21.33% to 28.39%	7	2.01%	99.43%
Greater than 28.39%	2	0.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.29%	9.55%	70.49%	68.27%
±2σ	-18.71%	18.97%	93.98%	95.45%
±3σ	-28.13%	28.39%	99.14%	99.73%

Descriptive Statistics

Mean	0.131%
Standard Error	0.504%
Median	-0.377%
Mode	-2.499%
Standard Deviation	9.420%
Sample Variance	88.731%
Kurtosis	0.98
Skewness	0.31
Range	66.472%
Minimum	-32.212%
Maximum	34.260%
Count	349

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.410%	167	47.85%	3.546%
Negative	-6.584%	181	51.86%	-3.415%
Zero	0.000%	1	0.29%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.72%
12	1 Quarter	10.22%
52	1 Year	9.64%
156	3 Years	10.75%
260	5 Years	13.01%
520	10 Years	13.95%
1,040	20 Years	13.95%
2,600	50 Years	13.95%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.28. Further, an Excess Kurtosis of 8.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.30%	0	0.00%	0.00%
-13.30% to -6.14%	0	0.00%	0.00%
-6.14% to 1.01%	0	0.00%	0.00%
1.01% to 8.17%	70	20.00%	20.00%
8.17% to 15.32%	147	42.00%	62.00%
15.32% to 22.48%	75	21.43%	83.43%
22.48% to 29.64%	34	9.71%	93.14%
29.64% to 36.79%	12	3.43%	96.57%
36.79% to 43.95%	6	1.71%	98.29%
Greater than 43.95%	6	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.78%	24.87%	83.14%	68.27%
±2σ	-3.76%	34.41%	95.14%	95.45%
±3σ	-13.30%	43.95%	98.29%	99.73%

Descriptive Statistics

Mean	15.325%
Standard Error	0.510%
Median	12.965%
Mode	7.409%
Standard Deviation	9.542%
Sample Variance	91.053%
Kurtosis	8.30
Skewness	2.28
Range	69.435%
Minimum	3.755%
Maximum	73.190%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.325%	350	100.00%	15.325%
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 0.56. Further, an Excess Kurtosis of 1.90 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.96%	0	0.00%	0.00%
-27.96% to -20.75%	3	0.86%	0.86%
-20.75% to -13.54%	16	4.57%	5.43%
-13.54% to -6.33%	57	16.29%	21.71%
-6.33% to 0.88%	108	30.86%	52.57%
0.88% to 8.09%	105	30.00%	82.57%
8.09% to 15.29%	35	10.00%	92.57%
15.29% to 22.50%	17	4.86%	97.43%
22.50% to 29.71%	6	1.71%	99.14%
Greater than 29.71%	3	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.73%	10.49%	72.57%	68.27%
±2σ	-18.35%	20.10%	95.43%	95.45%
±3σ	-27.96%	29.71%	99.14%	99.73%

Descriptive Statistics

Mean	0.877%
Standard Error	0.514%
Median	0.472%
Mode	0.000%
Standard Deviation	9.612%
Sample Variance	92.392%
Kurtosis	1.90
Skewness	0.56
Range	72.967%
Minimum	-25.317%
Maximum	47.650%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.357%	188	53.71%	3.952%
Negative	-6.726%	160	45.71%	-3.075%
Zero	0.000%	2	0.57%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.95. Further, an Excess Kurtosis of 1.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.71%	0	0.00%	0.00%
-54.71% to -40.93%	0	0.00%	0.00%
-40.93% to -27.16%	4	5.00%	5.00%
-27.16% to -13.38%	13	16.25%	21.25%
-13.38% to 0.40%	27	33.75%	55.00%
0.40% to 14.17%	21	26.25%	81.25%
14.17% to 27.95%	10	12.50%	93.75%
27.95% to 41.72%	3	3.75%	97.50%
41.72% to 55.50%	0	0.00%	97.50%
Greater than 55.50%	2	2.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.97%	18.76%	70.00%	68.27%
±2σ	-36.34%	37.13%	97.50%	95.45%
±3σ	-54.71%	55.50%	97.50%	99.73%

Descriptive Statistics

Mean	0.395%
Standard Error	2.054%
Median	-2.634%
Mode	-30.269%
Standard Deviation	18.368%
Sample Variance	337.376%
Kurtosis	1.61
Skewness	0.95
Range	96.264%
Minimum	-30.269%
Maximum	65.995%
Count	80

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.022%	36	45.00%	7.210%
Negative	-12.390%	44	55.00%	-6.815%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	26.53%
12	1 Year	22.69%
36	3 Years	23.27%
60	5 Years	26.88%
120	10 Years	29.94%
240	20 Years	29.94%
600	50 Years	29.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.26. 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 -19.30%	0	0.00%	0.00%
-19.30% to -5.37%	0	0.00%	0.00%
-5.37% to 8.55%	0	0.00%	0.00%
8.55% to 22.47%	19	23.46%	23.46%
22.47% to 36.40%	33	40.74%	64.20%
36.40% to 50.32%	14	17.28%	81.48%
50.32% to 64.24%	8	9.88%	91.36%
64.24% to 78.16%	4	4.94%	96.30%
78.16% to 92.09%	2	2.47%	98.77%
Greater than 92.09%	1	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.83%	54.96%	72.84%	68.27%
±2σ	-0.73%	73.52%	96.30%	95.45%
±3σ	-19.30%	92.09%	98.77%	99.73%

Descriptive Statistics

Mean	36.395%
Standard Error	2.063%
Median	32.242%
Mode	12.387%
Standard Deviation	18.564%
Sample Variance	344.620%
Kurtosis	1.54
Skewness	1.26
Range	87.992%
Minimum	12.387%
Maximum	100.379%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.395%	81	100.00%	36.395%
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 0.13 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.96%	0	0.00%	0.00%
-50.96% to -37.54%	2	2.47%	2.47%
-37.54% to -24.13%	1	1.23%	3.70%
-24.13% to -10.71%	15	18.52%	22.22%
-10.71% to 2.70%	23	28.40%	50.62%
2.70% to 16.12%	24	29.63%	80.25%
16.12% to 29.53%	10	12.35%	92.59%
29.53% to 42.95%	4	4.94%	97.53%
42.95% to 56.36%	2	2.47%	100.00%
Greater than 56.36%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.19%	20.59%	69.14%	68.27%
±2σ	-33.07%	38.48%	93.83%	95.45%
±3σ	-50.96%	56.36%	100.00%	99.73%

Descriptive Statistics

Mean	2.702%
Standard Error	1.987%
Median	1.827%
Mode	-42.798%
Standard Deviation	17.887%
Sample Variance	319.943%
Kurtosis	0.13
Skewness	0.15
Range	88.338%
Minimum	-42.798%
Maximum	45.540%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.852%	43	53.09%	8.415%
Negative	-12.177%	38	46.91%	-5.713%
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 1.65. Further, an Excess Kurtosis of 4.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.69%	0	0.00%	0.00%
-113.69% to -84.50%	0	0.00%	0.00%
-84.50% to -55.30%	0	0.00%	0.00%
-55.30% to -26.11%	6	22.22%	22.22%
-26.11% to 3.09%	10	37.04%	59.26%
3.09% to 32.29%	7	25.93%	85.19%
32.29% to 61.48%	3	11.11%	96.30%
61.48% to 90.68%	0	0.00%	96.30%
90.68% to 119.88%	0	0.00%	96.30%
Greater than 119.88%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.84%	42.02%	77.78%	68.27%
±2σ	-74.77%	80.95%	96.30%	95.45%
±3σ	-113.69%	119.87%	96.30%	99.73%

Descriptive Statistics

Mean	3.091%
Standard Error	7.492%
Median	-1.537%
Mode	-49.921%
Standard Deviation	38.928%
Sample Variance	1515.400%
Kurtosis	4.40
Skewness	1.65
Range	188.081%
Minimum	-49.921%
Maximum	138.160%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.035%	13	48.15%	15.424%
Negative	-23.785%	14	51.85%	-12.333%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	38.69%
12	3 Years	40.66%
20	5 Years	45.54%
40	10 Years	55.72%
80	20 Years	55.72%
200	50 Years	55.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.59. Further, an Excess Kurtosis of 3.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.41%	0	0.00%	0.00%
-33.41% to -6.34%	0	0.00%	0.00%
-6.34% to 20.72%	0	0.00%	0.00%
20.72% to 47.79%	5	17.86%	17.86%
47.79% to 74.85%	14	50.00%	67.86%
74.85% to 101.92%	5	17.86%	85.71%
101.92% to 128.98%	2	7.14%	92.86%
128.98% to 156.05%	1	3.57%	96.43%
156.05% to 183.11%	0	0.00%	96.43%
Greater than 183.11%	1	3.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	38.77%	110.94%	78.57%	68.27%
±2σ	2.68%	147.03%	92.86%	95.45%
±3σ	-33.41%	183.11%	96.43%	99.73%

Descriptive Statistics

Mean	74.852%
Standard Error	6.820%
Median	66.684%
Mode	31.261%
Standard Deviation	36.087%
Sample Variance	1302.238%
Kurtosis	3.06
Skewness	1.59
Range	158.768%
Minimum	31.261%
Maximum	190.029%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	74.852%	28	100.00%	74.852%
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 0.55. Further, an Excess Kurtosis of 0.38 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -97.24%	0	0.00%	0.00%
-97.24% to -70.78%	0	0.00%	0.00%
-70.78% to -44.32%	1	3.57%	3.57%
-44.32% to -17.86%	5	17.86%	21.43%
-17.86% to 8.60%	10	35.71%	57.14%
8.60% to 35.06%	6	21.43%	78.57%
35.06% to 61.52%	3	10.71%	89.29%
61.52% to 87.98%	2	7.14%	96.43%
87.98% to 114.45%	1	3.57%	100.00%
Greater than 114.45%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.68%	43.88%	71.43%	68.27%
±2σ	-61.96%	79.16%	96.43%	95.45%
±3σ	-97.24%	114.45%	100.00%	99.73%

Descriptive Statistics

Mean	8.603%
Standard Error	6.667%
Median	2.126%
Mode	-60.131%
Standard Deviation	35.281%
Sample Variance	1244.716%
Kurtosis	0.38
Skewness	0.55
Range	159.568%
Minimum	-60.131%
Maximum	99.437%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.399%	16	57.14%	17.942%
Negative	-21.792%	12	42.86%	-9.339%
Zero	0.000%	0	0.00%	0.000%

FVRR Deep Analytical Report