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	4.31%	3.86%	3.95%	5.51%	4.19%	4.21%	9.66	10.50	9.26	10.95
Weekly	9.43%	9.50%	9.68%	12.86%	9.23%	9.26%	9.18	11.04	8.37	12.11
Monthly	18.38%	18.58%	18.13%	26.48%	19.22%	19.28%	8.31	12.20	6.86	14.79
Quarterly	39.27%	36.07%	36.29%	45.64%	33.28%	33.40%	7.22	14.05	5.18	19.59
Annual	—	—	—	—	66.57%	66.80%	5.18	19.59	2.66	38.12
Option Time Horizon	—	—	—	—	25.12%	25.21%	7.83	12.95	6.09	16.64

Calculation Notes: Computed at 2026-03-23T16:36 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $10.07 | Strike (K): $11.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.6750 (Bid $0.5000 / Ask $0.8500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 66.57% (CRR binomial tree, American, n=20 steps) | BS IV: 66.84% (European Black-Scholes) | Yahoo IV (Annual): 66.80% → 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 0.25. Further, an Excess Kurtosis of 4.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.92%	8	0.47%	0.47%
-12.92% to -9.69%	13	0.76%	1.23%
-9.69% to -6.45%	67	3.94%	5.17%
-6.45% to -3.22%	225	13.22%	18.39%
-3.22% to 0.01%	563	33.08%	51.47%
0.01% to 3.24%	510	29.96%	81.43%
3.24% to 6.48%	214	12.57%	94.01%
6.48% to 9.71%	76	4.47%	98.47%
9.71% to 12.94%	12	0.71%	99.18%
Greater than 12.94%	14	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.30%	4.32%	75.44%	68.27%
±2σ	-8.61%	8.63%	95.71%	95.45%
±3σ	-12.92%	12.94%	98.71%	99.73%

Descriptive Statistics

Mean	0.012%
Standard Error	0.104%
Median	-0.126%
Mode	0.000%
Standard Deviation	4.310%
Sample Variance	18.578%
Kurtosis	4.39
Skewness	0.25
Range	55.006%
Minimum	-25.642%
Maximum	29.364%
Count	1702

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.222%	827	48.59%	1.566%
Negative	-3.053%	866	50.88%	-1.553%
Zero	0.000%	9	0.53%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.68%
20	1 Month	5.66%
60	1 Quarter	5.46%
250	1 Year	4.25%
750	3 Years	4.64%
1,250	5 Years	5.51%
2,500	10 Years	5.96%
5,000	20 Years	5.96%
12,500	50 Years	5.96%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.51. Further, an Excess Kurtosis of 66.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.72%	0	0.00%	0.00%
-5.72% to -2.83%	0	0.00%	0.00%
-2.83% to 0.07%	0	0.00%	0.00%
0.07% to 2.96%	227	13.33%	13.33%
2.96% to 5.86%	825	48.44%	61.77%
5.86% to 8.75%	414	24.31%	86.08%
8.75% to 11.65%	147	8.63%	94.72%
11.65% to 14.54%	47	2.76%	97.48%
14.54% to 17.44%	16	0.94%	98.41%
Greater than 17.44%	27	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.00%	9.72%	88.43%	68.27%
±2σ	-1.86%	13.58%	97.12%	95.45%
±3σ	-5.72%	17.44%	98.41%	99.73%

Descriptive Statistics

Mean	5.858%
Standard Error	0.094%
Median	4.974%
Mode	3.838%
Standard Deviation	3.860%
Sample Variance	14.901%
Kurtosis	66.07
Skewness	5.51
Range	63.761%
Minimum	1.333%
Maximum	65.094%
Count	1703

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.858%	1703	100.00%	5.858%
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 7.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.65%	10	0.59%	0.59%
-11.65% to -8.69%	13	0.76%	1.35%
-8.69% to -5.73%	64	3.76%	5.11%
-5.73% to -2.77%	222	13.04%	18.14%
-2.77% to 0.19%	558	32.77%	50.91%
0.19% to 3.15%	520	30.53%	81.44%
3.15% to 6.11%	212	12.45%	93.89%
6.11% to 9.07%	75	4.40%	98.30%
9.07% to 12.03%	21	1.23%	99.53%
Greater than 12.03%	8	0.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.76%	4.13%	75.10%	68.27%
±2σ	-7.71%	8.08%	95.54%	95.45%
±3σ	-11.65%	12.03%	98.94%	99.73%

Descriptive Statistics

Mean	0.187%
Standard Error	0.096%
Median	0.126%
Mode	0.000%
Standard Deviation	3.946%
Sample Variance	15.572%
Kurtosis	7.25
Skewness	-0.05
Range	67.069%
Minimum	-34.837%
Maximum	32.232%
Count	1703

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.950%	874	51.32%	1.514%
Negative	-2.750%	822	48.27%	-1.327%
Zero	0.000%	7	0.41%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.28. Further, an Excess Kurtosis of 1.04 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.20%	1	0.28%	0.28%
-28.20% to -21.13%	4	1.13%	1.42%
-21.13% to -14.05%	12	3.40%	4.82%
-14.05% to -6.98%	52	14.73%	19.55%
-6.98% to 0.10%	119	33.71%	53.26%
0.10% to 7.17%	96	27.20%	80.45%
7.17% to 14.25%	42	11.90%	92.35%
14.25% to 21.32%	18	5.10%	97.45%
21.32% to 28.40%	7	1.98%	99.43%
Greater than 28.40%	2	0.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.34%	9.53%	70.82%	68.27%
±2σ	-18.77%	18.96%	93.77%	95.45%
±3σ	-28.20%	28.40%	99.15%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.502%
Median	-0.454%
Mode	-2.499%
Standard Deviation	9.433%
Sample Variance	88.984%
Kurtosis	1.04
Skewness	0.28
Range	66.472%
Minimum	-32.212%
Maximum	34.260%
Count	353

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.412%	168	47.59%	3.528%
Negative	-6.581%	184	52.12%	-3.430%
Zero	0.000%	1	0.28%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.81%
12	1 Quarter	12.72%
52	1 Year	10.06%
156	3 Years	10.82%
260	5 Years	12.86%
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 2.29. Further, an Excess Kurtosis of 8.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.18%	0	0.00%	0.00%
-13.18% to -6.05%	0	0.00%	0.00%
-6.05% to 1.07%	0	0.00%	0.00%
1.07% to 8.19%	70	19.77%	19.77%
8.19% to 15.32%	150	42.37%	62.15%
15.32% to 22.44%	76	21.47%	83.62%
22.44% to 29.56%	34	9.60%	93.22%
29.56% to 36.69%	12	3.39%	96.61%
36.69% to 43.81%	6	1.69%	98.31%
Greater than 43.81%	6	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.82%	24.81%	83.05%	68.27%
±2σ	-3.68%	34.31%	94.92%	95.45%
±3σ	-13.18%	43.81%	98.31%	99.73%

Descriptive Statistics

Mean	15.316%
Standard Error	0.505%
Median	12.994%
Mode	7.409%
Standard Deviation	9.498%
Sample Variance	90.215%
Kurtosis	8.39
Skewness	2.29
Range	69.435%
Minimum	3.755%
Maximum	73.190%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.316%	354	100.00%	15.316%
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 2.08 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.13%	0	0.00%	0.00%
-28.13% to -20.87%	3	0.85%	0.85%
-20.87% to -13.61%	15	4.24%	5.08%
-13.61% to -6.35%	59	16.67%	21.75%
-6.35% to 0.92%	109	30.79%	52.54%
0.92% to 8.18%	107	30.23%	82.77%
8.18% to 15.44%	35	9.89%	92.66%
15.44% to 22.70%	18	5.08%	97.74%
22.70% to 29.96%	4	1.13%	98.87%
Greater than 29.96%	4	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.77%	10.60%	73.16%	68.27%
±2σ	-18.45%	20.28%	95.76%	95.45%
±3σ	-28.13%	29.96%	98.87%	99.73%

Descriptive Statistics

Mean	0.915%
Standard Error	0.515%
Median	0.504%
Mode	0.000%
Standard Deviation	9.681%
Sample Variance	93.719%
Kurtosis	2.08
Skewness	0.62
Range	72.967%
Minimum	-25.317%
Maximum	47.650%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.378%	191	53.95%	3.981%
Negative	-6.741%	161	45.48%	-3.066%
Zero	0.000%	2	0.56%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.92. Further, an Excess Kurtosis of 1.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.90%	0	0.00%	0.00%
-54.90% to -41.11%	0	0.00%	0.00%
-41.11% to -27.33%	4	4.94%	4.94%
-27.33% to -13.54%	12	14.81%	19.75%
-13.54% to 0.25%	29	35.80%	55.56%
0.25% to 14.04%	21	25.93%	81.48%
14.04% to 27.82%	10	12.35%	93.83%
27.82% to 41.61%	3	3.70%	97.53%
41.61% to 55.40%	0	0.00%	97.53%
Greater than 55.40%	2	2.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.13%	18.63%	70.37%	68.27%
±2σ	-36.52%	37.02%	97.53%	95.45%
±3σ	-54.90%	55.40%	97.53%	99.73%

Descriptive Statistics

Mean	0.249%
Standard Error	2.043%
Median	-2.658%
Mode	-35.343%
Standard Deviation	18.383%
Sample Variance	337.921%
Kurtosis	1.65
Skewness	0.92
Range	101.338%
Minimum	-35.343%
Maximum	65.995%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.022%	36	44.44%	7.121%
Negative	-12.369%	45	55.56%	-6.872%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.39%
12	1 Year	22.68%
36	3 Years	23.07%
60	5 Years	26.48%
120	10 Years	29.77%
240	20 Years	29.77%
600	50 Years	29.77%

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 -19.60%	0	0.00%	0.00%
-19.60% to -5.66%	0	0.00%	0.00%
-5.66% to 8.28%	0	0.00%	0.00%
8.28% to 22.21%	20	24.39%	24.39%
22.21% to 36.15%	33	40.24%	64.63%
36.15% to 50.09%	14	17.07%	81.71%
50.09% to 64.02%	8	9.76%	91.46%
64.02% to 77.96%	4	4.88%	96.34%
77.96% to 91.90%	2	2.44%	98.78%
Greater than 91.90%	1	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.57%	54.73%	71.95%	68.27%
±2σ	-1.01%	73.31%	96.34%	95.45%
±3σ	-19.60%	91.90%	98.78%	99.73%

Descriptive Statistics

Mean	36.150%
Standard Error	2.052%
Median	32.228%
Mode	12.387%
Standard Deviation	18.582%
Sample Variance	345.308%
Kurtosis	1.54
Skewness	1.26
Range	87.992%
Minimum	12.387%
Maximum	100.379%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.150%	82	100.00%	36.150%
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 0.28. Further, an Excess Kurtosis of 0.45 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.59%	0	0.00%	0.00%
-51.59% to -37.99%	2	2.44%	2.44%
-37.99% to -24.39%	1	1.22%	3.66%
-24.39% to -10.79%	15	18.29%	21.95%
-10.79% to 2.81%	24	29.27%	51.22%
2.81% to 16.41%	24	29.27%	80.49%
16.41% to 30.01%	10	12.20%	92.68%
30.01% to 43.61%	4	4.88%	97.56%
43.61% to 57.21%	2	2.44%	100.00%
Greater than 57.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.32%	20.94%	69.51%	68.27%
±2σ	-33.46%	39.07%	93.90%	95.45%
±3σ	-51.59%	57.21%	100.00%	99.73%

Descriptive Statistics

Mean	2.808%
Standard Error	2.002%
Median	1.733%
Mode	-42.798%
Standard Deviation	18.133%
Sample Variance	328.813%
Kurtosis	0.45
Skewness	0.28
Range	97.092%
Minimum	-42.798%
Maximum	54.294%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.749%	44	53.66%	8.451%
Negative	-12.177%	38	46.34%	-5.643%
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 1.61. Further, an Excess Kurtosis of 4.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.06%	0	0.00%	0.00%
-115.06% to -85.61%	0	0.00%	0.00%
-85.61% to -56.15%	0	0.00%	0.00%
-56.15% to -26.70%	6	22.22%	22.22%
-26.70% to 2.75%	10	37.04%	59.26%
2.75% to 32.20%	7	25.93%	85.19%
32.20% to 61.66%	3	11.11%	96.30%
61.66% to 91.11%	0	0.00%	96.30%
91.11% to 120.56%	0	0.00%	96.30%
Greater than 120.56%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.52%	42.02%	74.07%	68.27%
±2σ	-75.79%	81.29%	96.30%	95.45%
±3σ	-115.06%	120.56%	96.30%	99.73%

Descriptive Statistics

Mean	2.751%
Standard Error	7.557%
Median	-1.537%
Mode	-49.921%
Standard Deviation	39.270%
Sample Variance	1542.124%
Kurtosis	4.24
Skewness	1.61
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	-24.442%	14	51.85%	-12.674%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	39.21%
12	3 Years	40.83%
20	5 Years	45.64%
40	10 Years	55.80%
80	20 Years	55.80%
200	50 Years	55.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.58. Further, an Excess Kurtosis of 3.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.14%	0	0.00%	0.00%
-33.14% to -6.09%	0	0.00%	0.00%
-6.09% to 20.96%	0	0.00%	0.00%
20.96% to 48.02%	5	17.86%	17.86%
48.02% to 75.07%	14	50.00%	67.86%
75.07% to 102.12%	5	17.86%	85.71%
102.12% to 129.17%	2	7.14%	92.86%
129.17% to 156.22%	1	3.57%	96.43%
156.22% to 183.27%	0	0.00%	96.43%
Greater than 183.27%	1	3.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	39.00%	111.13%	78.57%	68.27%
±2σ	2.93%	147.20%	92.86%	95.45%
±3σ	-33.14%	183.27%	96.43%	99.73%

Descriptive Statistics

Mean	75.066%
Standard Error	6.816%
Median	66.684%
Mode	31.261%
Standard Deviation	36.068%
Sample Variance	1300.912%
Kurtosis	3.03
Skewness	1.58
Range	158.768%
Minimum	31.261%
Maximum	190.029%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.066%	28	100.00%	75.066%
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 0.15 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -99.49%	0	0.00%	0.00%
-99.49% to -72.28%	0	0.00%	0.00%
-72.28% to -45.06%	1	3.57%	3.57%
-45.06% to -17.84%	5	17.86%	21.43%
-17.84% to 9.38%	10	35.71%	57.14%
9.38% to 36.60%	6	21.43%	78.57%
36.60% to 63.81%	3	10.71%	89.29%
63.81% to 91.03%	2	7.14%	96.43%
91.03% to 118.25%	1	3.57%	100.00%
Greater than 118.25%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.91%	45.67%	67.86%	68.27%
±2σ	-63.20%	81.96%	96.43%	95.45%
±3σ	-99.49%	118.25%	100.00%	99.73%

Descriptive Statistics

Mean	9.379%
Standard Error	6.858%
Median	2.126%
Mode	-60.131%
Standard Deviation	36.291%
Sample Variance	1317.043%
Kurtosis	0.15
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	32.757%	16	57.14%	18.718%
Negative	-21.792%	12	42.86%	-9.339%
Zero	0.000%	0	0.00%	0.000%

FVRR Deep Analytical Report