CVNA - 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	6.32%	5.87%	5.32%	8.42%	4.71%	4.73%	321.15	352.84	306.39	369.83
Weekly	13.90%	16.86%	14.13%	20.45%	10.36%	10.42%	303.50	373.36	273.64	414.10
Monthly	30.76%	43.12%	29.37%	44.92%	21.56%	21.70%	271.33	417.62	218.71	518.11
Quarterly	101.80%	139.68%	52.92%	106.34%	37.35%	37.58%	231.71	489.02	159.50	710.43
Annual	—	—	—	—	74.69%	75.17%	159.50	710.43	75.58	1499.34
Option Time Horizon	—	—	—	—	28.73%	28.91%	252.56	448.65	189.50	597.97

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $336.62 | Strike (K): $340.00 (first OTM call ≥ spot) | Observed Mid-Price: $37.5750 (Bid $36.8000 / Ask $38.3500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 74.69% (CRR binomial tree, American, n=20 steps) | BS IV: 74.29% (European Black-Scholes) | Yahoo IV (Annual): 75.17% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.21. Further, an Excess Kurtosis of 10.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.61%	9	0.41%	0.41%
-18.61% to -13.87%	19	0.86%	1.26%
-13.87% to -9.13%	63	2.84%	4.11%
-9.13% to -4.39%	246	11.11%	15.21%
-4.39% to 0.35%	842	38.01%	53.23%
0.35% to 5.09%	735	33.18%	86.41%
5.09% to 9.83%	197	8.89%	95.30%
9.83% to 14.57%	54	2.44%	97.74%
14.57% to 19.31%	20	0.90%	98.65%
Greater than 19.31%	30	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.97%	6.67%	81.49%	68.27%
±2σ	-12.29%	12.99%	95.21%	95.45%
±3σ	-18.61%	19.31%	98.24%	99.73%

Descriptive Statistics

Mean	0.348%
Standard Error	0.134%
Median	0.110%
Mode	-0.071%
Standard Deviation	6.320%
Sample Variance	39.947%
Kurtosis	10.86
Skewness	1.21
Range	98.942%
Minimum	-42.921%
Maximum	56.021%
Count	2215

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.293%	1139	51.42%	2.208%
Negative	-3.840%	1073	48.44%	-1.860%
Zero	0.000%	3	0.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.91%
20	1 Month	8.25%
60	1 Quarter	5.83%
250	1 Year	6.04%
750	3 Years	7.54%
1,250	5 Years	8.42%
2,500	10 Years	7.80%
5,000	20 Years	7.80%
12,500	50 Years	7.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.31. Further, an Excess Kurtosis of 18.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.88%	0	0.00%	0.00%
-9.88% to -5.47%	0	0.00%	0.00%
-5.47% to -1.07%	0	0.00%	0.00%
-1.07% to 3.34%	306	13.81%	13.81%
3.34% to 7.74%	1111	50.14%	63.94%
7.74% to 12.15%	503	22.70%	86.64%
12.15% to 16.55%	162	7.31%	93.95%
16.55% to 20.96%	69	3.11%	97.07%
20.96% to 25.36%	25	1.13%	98.19%
Greater than 25.36%	40	1.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.87%	13.62%	88.67%	68.27%
±2σ	-4.00%	19.49%	96.21%	95.45%
±3σ	-9.88%	25.37%	98.19%	99.73%

Descriptive Statistics

Mean	7.743%
Standard Error	0.125%
Median	6.139%
Mode	2.987%
Standard Deviation	5.874%
Sample Variance	34.505%
Kurtosis	18.09
Skewness	3.31
Range	60.154%
Minimum	1.136%
Maximum	61.290%
Count	2216

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.743%	2216	100.00%	7.743%
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 6.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.89%	19	0.86%	0.86%
-15.89% to -11.89%	25	1.13%	1.99%
-11.89% to -7.90%	56	2.53%	4.51%
-7.90% to -3.91%	255	11.51%	16.02%
-3.91% to 0.08%	784	35.38%	51.40%
0.08% to 4.08%	724	32.67%	84.07%
4.08% to 8.07%	232	10.47%	94.54%
8.07% to 12.06%	75	3.38%	97.92%
12.06% to 16.06%	28	1.26%	99.19%
Greater than 16.06%	18	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.24%	5.41%	78.93%	68.27%
±2σ	-10.56%	10.73%	94.58%	95.45%
±3σ	-15.89%	16.06%	98.33%	99.73%

Descriptive Statistics

Mean	0.084%
Standard Error	0.113%
Median	-0.030%
Mode	0.000%
Standard Deviation	5.324%
Sample Variance	28.341%
Kurtosis	6.92
Skewness	0.29
Range	78.746%
Minimum	-29.888%
Maximum	48.858%
Count	2216

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.761%	1095	49.41%	1.858%
Negative	-3.533%	1113	50.23%	-1.774%
Zero	0.000%	8	0.36%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.75. Further, an Excess Kurtosis of 2.72 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.01%	1	0.22%	0.22%
-40.01% to -29.59%	4	0.87%	1.09%
-29.59% to -19.17%	20	4.35%	5.43%
-19.17% to -8.75%	51	11.09%	16.52%
-8.75% to 1.67%	176	38.26%	54.78%
1.67% to 12.10%	136	29.57%	84.35%
12.10% to 22.52%	39	8.48%	92.83%
22.52% to 32.94%	19	4.13%	96.96%
32.94% to 43.36%	8	1.74%	98.70%
Greater than 43.36%	6	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.22%	15.57%	77.39%	68.27%
±2σ	-26.12%	29.47%	93.48%	95.45%
±3σ	-40.01%	43.36%	98.48%	99.73%

Descriptive Statistics

Mean	1.674%
Standard Error	0.648%
Median	0.661%
Mode	-4.867%
Standard Deviation	13.896%
Sample Variance	193.091%
Kurtosis	2.72
Skewness	0.75
Range	108.440%
Minimum	-45.381%
Maximum	63.059%
Count	460

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.657%	246	53.48%	5.699%
Negative	-8.652%	214	46.52%	-4.025%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	18.48%
12	1 Quarter	13.48%
52	1 Year	13.81%
156	3 Years	18.13%
260	5 Years	20.45%
520	10 Years	18.67%
1,040	20 Years	18.67%
2,600	50 Years	18.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.74. Further, an Excess Kurtosis of 10.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.63%	0	0.00%	0.00%
-29.63% to -16.98%	0	0.00%	0.00%
-16.98% to -4.33%	0	0.00%	0.00%
-4.33% to 8.31%	64	13.88%	13.88%
8.31% to 20.96%	239	51.84%	65.73%
20.96% to 33.61%	86	18.66%	84.38%
33.61% to 46.26%	43	9.33%	93.71%
46.26% to 58.91%	11	2.39%	96.10%
58.91% to 71.55%	7	1.52%	97.61%
Greater than 71.55%	11	2.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.10%	37.83%	88.07%	68.27%
±2σ	-12.77%	54.69%	95.01%	95.45%
±3σ	-29.63%	71.55%	97.61%	99.73%

Descriptive Statistics

Mean	20.961%
Standard Error	0.785%
Median	15.797%
Mode	8.664%
Standard Deviation	16.864%
Sample Variance	284.401%
Kurtosis	10.92
Skewness	2.74
Range	136.512%
Minimum	4.057%
Maximum	140.569%
Count	461

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.961%	461	100.00%	20.961%
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 1.42. Further, an Excess Kurtosis of 8.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.89%	0	0.00%	0.00%
-41.89% to -31.30%	5	1.08%	1.08%
-31.30% to -20.70%	17	3.69%	4.77%
-20.70% to -10.11%	54	11.71%	16.49%
-10.11% to 0.49%	183	39.70%	56.18%
0.49% to 11.08%	134	29.07%	85.25%
11.08% to 21.68%	39	8.46%	93.71%
21.68% to 32.27%	15	3.25%	96.96%
32.27% to 42.87%	9	1.95%	98.92%
Greater than 42.87%	5	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.64%	14.61%	78.52%	68.27%
±2σ	-27.77%	28.74%	94.36%	95.45%
±3σ	-41.89%	42.87%	98.92%	99.73%

Descriptive Statistics

Mean	0.487%
Standard Error	0.658%
Median	-0.596%
Mode	-6.565%
Standard Deviation	14.127%
Sample Variance	199.585%
Kurtosis	8.00
Skewness	1.42
Range	146.407%
Minimum	-39.912%
Maximum	106.495%
Count	461

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.816%	215	46.64%	5.044%
Negative	-8.575%	245	53.15%	-4.557%
Zero	0.000%	1	0.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.11. Further, an Excess Kurtosis of 2.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.97%	0	0.00%	0.00%
-84.97% to -61.90%	0	0.00%	0.00%
-61.90% to -38.83%	3	2.83%	2.83%
-38.83% to -15.76%	21	19.81%	22.64%
-15.76% to 7.30%	32	30.19%	52.83%
7.30% to 30.37%	36	33.96%	86.79%
30.37% to 53.44%	7	6.60%	93.40%
53.44% to 76.51%	2	1.89%	95.28%
76.51% to 99.58%	2	1.89%	97.17%
Greater than 99.58%	3	2.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.45%	38.06%	77.36%	68.27%
±2σ	-54.21%	68.82%	93.40%	95.45%
±3σ	-84.97%	99.58%	97.17%	99.73%

Descriptive Statistics

Mean	7.304%
Standard Error	2.987%
Median	4.273%
Mode	-51.413%
Standard Deviation	30.757%
Sample Variance	945.985%
Kurtosis	2.18
Skewness	1.11
Range	165.970%
Minimum	-51.413%
Maximum	114.557%
Count	106

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.848%	61	57.55%	14.875%
Negative	-17.834%	45	42.45%	-7.571%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.20%
12	1 Year	27.68%
36	3 Years	42.93%
60	5 Years	44.92%
120	10 Years	42.27%
240	20 Years	42.27%
600	50 Years	42.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.48. Further, an Excess Kurtosis of 8.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.27%	0	0.00%	0.00%
-75.27% to -42.93%	0	0.00%	0.00%
-42.93% to -10.59%	0	0.00%	0.00%
-10.59% to 21.75%	11	10.28%	10.28%
21.75% to 54.09%	65	60.75%	71.03%
54.09% to 86.43%	15	14.02%	85.05%
86.43% to 118.78%	6	5.61%	90.65%
118.78% to 151.12%	6	5.61%	96.26%
151.12% to 183.46%	3	2.80%	99.07%
Greater than 183.46%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.97%	97.22%	84.11%	68.27%
±2σ	-32.15%	140.34%	93.46%	95.45%
±3σ	-75.27%	183.46%	99.07%	99.73%

Descriptive Statistics

Mean	54.093%
Standard Error	4.169%
Median	40.890%
Mode	10.004%
Standard Deviation	43.122%
Sample Variance	1859.493%
Kurtosis	8.21
Skewness	2.48
Range	278.899%
Minimum	10.004%
Maximum	288.903%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.093%	107	100.00%	54.093%
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 1.16. Further, an Excess Kurtosis of 2.29 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.88%	0	0.00%	0.00%
-86.88% to -64.85%	0	0.00%	0.00%
-64.85% to -42.82%	5	4.67%	4.67%
-42.82% to -20.79%	14	13.08%	17.76%
-20.79% to 1.23%	43	40.19%	57.94%
1.23% to 23.26%	28	26.17%	84.11%
23.26% to 45.29%	8	7.48%	91.59%
45.29% to 67.32%	6	5.61%	97.20%
67.32% to 89.34%	0	0.00%	97.20%
Greater than 89.34%	3	2.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.14%	30.60%	78.50%	68.27%
±2σ	-57.51%	59.97%	96.26%	95.45%
±3σ	-86.88%	89.34%	97.20%	99.73%

Descriptive Statistics

Mean	1.233%
Standard Error	2.839%
Median	-3.560%
Mode	-52.704%
Standard Deviation	29.370%
Sample Variance	862.616%
Kurtosis	2.29
Skewness	1.16
Range	159.519%
Minimum	-52.704%
Maximum	106.815%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.213%	48	44.86%	11.311%
Negative	-18.277%	59	55.14%	-10.078%
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 4.27. Further, an Excess Kurtosis of 22.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -276.25%	0	0.00%	0.00%
-276.25% to -199.89%	0	0.00%	0.00%
-199.89% to -123.54%	0	0.00%	0.00%
-123.54% to -47.19%	3	8.33%	8.33%
-47.19% to 29.17%	19	52.78%	61.11%
29.17% to 105.52%	13	36.11%	97.22%
105.52% to 181.87%	0	0.00%	97.22%
181.87% to 258.23%	0	0.00%	97.22%
258.23% to 334.58%	0	0.00%	97.22%
Greater than 334.58%	1	2.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-72.64%	130.97%	97.22%	68.27%
±2σ	-174.44%	232.78%	97.22%	95.45%
±3σ	-276.25%	334.58%	97.22%	99.73%

Descriptive Statistics

Mean	29.167%
Standard Error	16.967%
Median	5.150%
Mode	-64.235%
Standard Deviation	101.804%
Sample Variance	10364.076%
Kurtosis	22.31
Skewness	4.27
Range	626.339%
Minimum	-64.235%
Maximum	562.104%
Count	36

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	73.284%	20	55.56%	40.714%
Negative	-25.980%	16	44.44%	-11.547%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	46.95%
12	3 Years	123.73%
20	5 Years	106.34%
40	10 Years	92.34%
80	20 Years	92.34%
200	50 Years	92.34%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.91. Further, an Excess Kurtosis of 10.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -283.80%	0	0.00%	0.00%
-283.80% to -179.04%	0	0.00%	0.00%
-179.04% to -74.29%	0	0.00%	0.00%
-74.29% to 30.47%	1	2.70%	2.70%
30.47% to 135.23%	25	67.57%	70.27%
135.23% to 239.98%	7	18.92%	89.19%
239.98% to 344.74%	0	0.00%	89.19%
344.74% to 449.50%	3	8.11%	97.30%
449.50% to 554.25%	0	0.00%	97.30%
Greater than 554.25%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.45%	274.90%	89.19%	68.27%
±2σ	-144.12%	414.58%	94.59%	95.45%
±3σ	-283.80%	554.25%	97.30%	99.73%

Descriptive Statistics

Mean	135.227%
Standard Error	22.963%
Median	95.693%
Mode	30.280%
Standard Deviation	139.675%
Sample Variance	19509.229%
Kurtosis	10.38
Skewness	2.91
Range	723.302%
Minimum	30.280%
Maximum	753.582%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	135.227%	37	100.00%	135.227%
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 1.38. Further, an Excess Kurtosis of 2.60 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -154.49%	0	0.00%	0.00%
-154.49% to -114.80%	0	0.00%	0.00%
-114.80% to -75.11%	1	2.70%	2.70%
-75.11% to -35.41%	9	24.32%	27.03%
-35.41% to 4.28%	12	32.43%	59.46%
4.28% to 43.98%	8	21.62%	81.08%
43.98% to 83.67%	3	8.11%	89.19%
83.67% to 123.36%	3	8.11%	97.30%
123.36% to 163.06%	0	0.00%	97.30%
Greater than 163.06%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-48.64%	57.21%	81.08%	68.27%
±2σ	-101.57%	110.13%	94.59%	95.45%
±3σ	-154.49%	163.06%	97.30%	99.73%

Descriptive Statistics

Mean	4.281%
Standard Error	8.701%
Median	-1.385%
Mode	-84.135%
Standard Deviation	52.925%
Sample Variance	2801.084%
Kurtosis	2.60
Skewness	1.38
Range	267.123%
Minimum	-84.135%
Maximum	182.988%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.002%	17	45.95%	21.136%
Negative	-31.182%	20	54.05%	-16.855%
Zero	0.000%	0	0.00%	0.000%

CVNA Deep Analytical Report