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	6.30%	5.85%	5.31%	8.41%	5.35%	5.29%	283.59	315.63	268.81	332.98
Weekly	13.85%	16.81%	14.07%	20.36%	11.78%	11.65%	265.92	336.59	236.37	378.69
Monthly	30.66%	43.04%	29.24%	44.75%	24.53%	24.25%	234.10	382.35	183.18	488.64
Quarterly	101.93%	139.32%	53.06%	106.85%	42.48%	42.01%	195.62	457.55	127.91	699.76
Annual	—	—	—	—	84.97%	84.02%	127.91	699.76	54.69	1636.71
Option Time Horizon	—	—	—	—	32.07%	31.71%	217.09	412.30	157.53	568.20

Calculation Notes: Computed at 2026-03-23T16:37 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $299.18 | Strike (K): $300.00 (first OTM call ≥ spot) | Observed Mid-Price: $38.0500 (Bid $37.1000 / Ask $39.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 84.97% (CRR binomial tree, American, n=20 steps) | BS IV: 84.06% (European Black-Scholes) | Yahoo IV (Annual): 84.02% → 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 10.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.57%	9	0.40%	0.40%
-18.57% to -13.84%	19	0.85%	1.25%
-13.84% to -9.11%	63	2.82%	4.07%
-9.11% to -4.39%	249	11.14%	15.21%
-4.39% to 0.34%	848	37.92%	53.13%
0.34% to 5.07%	743	33.23%	86.36%
5.07% to 9.79%	201	8.99%	95.35%
9.79% to 14.52%	53	2.37%	97.72%
14.52% to 19.25%	20	0.89%	98.61%
Greater than 19.25%	31	1.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.96%	6.64%	81.48%	68.27%
±2σ	-12.27%	12.95%	95.26%	95.45%
±3σ	-18.57%	19.25%	98.21%	99.73%

Descriptive Statistics

Mean	0.340%
Standard Error	0.133%
Median	0.106%
Mode	-0.071%
Standard Deviation	6.303%
Sample Variance	39.725%
Kurtosis	10.89
Skewness	1.21
Range	98.942%
Minimum	-42.921%
Maximum	56.021%
Count	2236

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.284%	1149	51.39%	2.201%
Negative	-3.839%	1084	48.48%	-1.861%
Zero	0.000%	3	0.13%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.92%
20	1 Month	6.35%
60	1 Quarter	6.27%
250	1 Year	5.82%
750	3 Years	7.33%
1,250	5 Years	8.41%
2,500	10 Years	7.78%
5,000	20 Years	7.78%
12,500	50 Years	7.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.32. Further, an Excess Kurtosis of 18.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.83%	0	0.00%	0.00%
-9.83% to -5.44%	0	0.00%	0.00%
-5.44% to -1.05%	0	0.00%	0.00%
-1.05% to 3.34%	307	13.72%	13.72%
3.34% to 7.73%	1119	50.02%	63.75%
7.73% to 12.12%	515	23.02%	86.77%
12.12% to 16.50%	160	7.15%	93.92%
16.50% to 20.89%	71	3.17%	97.09%
20.89% to 25.28%	25	1.12%	98.21%
Greater than 25.28%	40	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.88%	13.58%	88.60%	68.27%
±2σ	-3.97%	19.43%	96.24%	95.45%
±3σ	-9.83%	25.28%	98.21%	99.73%

Descriptive Statistics

Mean	7.727%
Standard Error	0.124%
Median	6.126%
Mode	2.987%
Standard Deviation	5.851%
Sample Variance	34.238%
Kurtosis	18.26
Skewness	3.32
Range	60.154%
Minimum	1.136%
Maximum	61.290%
Count	2237

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.727%	2237	100.00%	7.727%
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 6.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.84%	19	0.85%	0.85%
-15.84% to -11.86%	27	1.21%	2.06%
-11.86% to -7.88%	56	2.50%	4.56%
-7.88% to -3.90%	258	11.53%	16.09%
-3.90% to 0.08%	789	35.27%	51.36%
0.08% to 4.07%	729	32.59%	83.95%
4.07% to 8.05%	238	10.64%	94.59%
8.05% to 12.03%	74	3.31%	97.90%
12.03% to 16.01%	29	1.30%	99.20%
Greater than 16.01%	18	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.22%	5.39%	78.95%	68.27%
±2σ	-10.53%	10.70%	94.55%	95.45%
±3σ	-15.84%	16.01%	98.35%	99.73%

Descriptive Statistics

Mean	0.084%
Standard Error	0.112%
Median	-0.030%
Mode	0.000%
Standard Deviation	5.308%
Sample Variance	28.174%
Kurtosis	6.95
Skewness	0.29
Range	78.746%
Minimum	-29.888%
Maximum	48.858%
Count	2237

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.750%	1106	49.44%	1.854%
Negative	-3.526%	1123	50.20%	-1.770%
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 0.76. Further, an Excess Kurtosis of 2.77 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.90%	1	0.22%	0.22%
-39.90% to -29.52%	4	0.86%	1.08%
-29.52% to -19.13%	20	4.31%	5.39%
-19.13% to -8.75%	51	10.99%	16.38%
-8.75% to 1.64%	180	38.79%	55.17%
1.64% to 12.02%	134	28.88%	84.05%
12.02% to 22.40%	41	8.84%	92.89%
22.40% to 32.79%	18	3.88%	96.77%
32.79% to 43.17%	9	1.94%	98.71%
Greater than 43.17%	6	1.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.21%	15.48%	77.59%	68.27%
±2σ	-26.05%	29.33%	93.53%	95.45%
±3σ	-39.90%	43.17%	98.49%	99.73%

Descriptive Statistics

Mean	1.636%
Standard Error	0.643%
Median	0.586%
Mode	-4.867%
Standard Deviation	13.845%
Sample Variance	191.690%
Kurtosis	2.77
Skewness	0.76
Range	108.440%
Minimum	-45.381%
Maximum	63.059%
Count	464

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.620%	247	53.23%	5.653%
Negative	-8.591%	217	46.77%	-4.018%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.43%
12	1 Quarter	13.69%
52	1 Year	13.16%
156	3 Years	17.71%
260	5 Years	20.36%
520	10 Years	18.62%
1,040	20 Years	18.62%
2,600	50 Years	18.62%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.76. Further, an Excess Kurtosis of 11.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.52%	0	0.00%	0.00%
-29.52% to -16.92%	0	0.00%	0.00%
-16.92% to -4.31%	0	0.00%	0.00%
-4.31% to 8.29%	63	13.55%	13.55%
8.29% to 20.90%	244	52.47%	66.02%
20.90% to 33.50%	84	18.06%	84.09%
33.50% to 46.11%	45	9.68%	93.76%
46.11% to 58.71%	11	2.37%	96.13%
58.71% to 71.32%	7	1.51%	97.63%
Greater than 71.32%	11	2.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.09%	37.70%	87.96%	68.27%
±2σ	-12.71%	54.51%	95.05%	95.45%
±3σ	-29.52%	71.32%	97.63%	99.73%

Descriptive Statistics

Mean	20.898%
Standard Error	0.779%
Median	15.781%
Mode	8.664%
Standard Deviation	16.806%
Sample Variance	282.447%
Kurtosis	11.03
Skewness	2.76
Range	136.512%
Minimum	4.057%
Maximum	140.569%
Count	465

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.898%	465	100.00%	20.898%
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 8.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.71%	0	0.00%	0.00%
-41.71% to -31.16%	5	1.08%	1.08%
-31.16% to -20.60%	17	3.66%	4.73%
-20.60% to -10.05%	55	11.83%	16.56%
-10.05% to 0.51%	182	39.14%	55.70%
0.51% to 11.06%	138	29.68%	85.38%
11.06% to 21.61%	38	8.17%	93.55%
21.61% to 32.17%	16	3.44%	96.99%
32.17% to 42.72%	9	1.94%	98.92%
Greater than 42.72%	5	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.57%	14.58%	78.49%	68.27%
±2σ	-27.64%	28.65%	94.41%	95.45%
±3σ	-41.71%	42.72%	98.92%	99.73%

Descriptive Statistics

Mean	0.506%
Standard Error	0.653%
Median	-0.542%
Mode	-6.565%
Standard Deviation	14.072%
Sample Variance	198.034%
Kurtosis	8.07
Skewness	1.42
Range	146.407%
Minimum	-39.912%
Maximum	106.495%
Count	465

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.734%	218	46.88%	5.032%
Negative	-8.556%	246	52.90%	-4.526%
Zero	0.000%	1	0.21%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.12. Further, an Excess Kurtosis of 2.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.85%	0	0.00%	0.00%
-84.85% to -61.85%	0	0.00%	0.00%
-61.85% to -38.86%	3	2.80%	2.80%
-38.86% to -15.86%	21	19.63%	22.43%
-15.86% to 7.13%	33	30.84%	53.27%
7.13% to 30.13%	36	33.64%	86.92%
30.13% to 53.13%	7	6.54%	93.46%
53.13% to 76.12%	1	0.93%	94.39%
76.12% to 99.12%	3	2.80%	97.20%
Greater than 99.12%	3	2.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.53%	37.80%	77.57%	68.27%
±2σ	-54.19%	68.46%	93.46%	95.45%
±3σ	-84.85%	99.12%	97.20%	99.73%

Descriptive Statistics

Mean	7.135%
Standard Error	2.964%
Median	3.928%
Mode	-51.413%
Standard Deviation	30.662%
Sample Variance	940.177%
Kurtosis	2.22
Skewness	1.12
Range	165.970%
Minimum	-51.413%
Maximum	114.557%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.848%	61	57.01%	14.736%
Negative	-17.680%	46	42.99%	-7.601%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.02%
12	1 Year	26.52%
36	3 Years	42.30%
60	5 Years	44.75%
120	10 Years	42.05%
240	20 Years	42.05%
600	50 Years	42.05%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.33%	0	0.00%	0.00%
-75.33% to -43.05%	0	0.00%	0.00%
-43.05% to -10.77%	0	0.00%	0.00%
-10.77% to 21.51%	11	10.19%	10.19%
21.51% to 53.79%	66	61.11%	71.30%
53.79% to 86.07%	15	13.89%	85.19%
86.07% to 118.35%	6	5.56%	90.74%
118.35% to 150.62%	6	5.56%	96.30%
150.62% to 182.90%	3	2.78%	99.07%
Greater than 182.90%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.75%	96.83%	84.26%	68.27%
±2σ	-32.29%	139.87%	93.52%	95.45%
±3σ	-75.32%	182.90%	99.07%	99.73%

Descriptive Statistics

Mean	53.789%
Standard Error	4.141%
Median	40.628%
Mode	10.004%
Standard Deviation	43.038%
Sample Variance	1852.263%
Kurtosis	8.26
Skewness	2.48
Range	278.899%
Minimum	10.004%
Maximum	288.903%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.789%	108	100.00%	53.789%
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 2.32 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.43%	0	0.00%	0.00%
-86.43% to -64.50%	0	0.00%	0.00%
-64.50% to -42.57%	6	5.56%	5.56%
-42.57% to -20.63%	13	12.04%	17.59%
-20.63% to 1.30%	43	39.81%	57.41%
1.30% to 23.23%	29	26.85%	84.26%
23.23% to 45.16%	8	7.41%	91.67%
45.16% to 67.09%	6	5.56%	97.22%
67.09% to 89.03%	0	0.00%	97.22%
Greater than 89.03%	3	2.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.95%	30.54%	78.70%	68.27%
±2σ	-57.19%	59.78%	96.30%	95.45%
±3σ	-86.43%	89.03%	97.22%	99.73%

Descriptive Statistics

Mean	1.298%
Standard Error	2.814%
Median	-3.402%
Mode	-52.704%
Standard Deviation	29.243%
Sample Variance	855.151%
Kurtosis	2.32
Skewness	1.16
Range	159.519%
Minimum	-52.704%
Maximum	106.815%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.867%	49	45.37%	11.282%
Negative	-18.277%	59	54.63%	-9.985%
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 4.26. Further, an Excess Kurtosis of 22.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -276.88%	0	0.00%	0.00%
-276.88% to -200.43%	0	0.00%	0.00%
-200.43% to -123.98%	0	0.00%	0.00%
-123.98% to -47.53%	3	8.33%	8.33%
-47.53% to 28.91%	19	52.78%	61.11%
28.91% to 105.36%	13	36.11%	97.22%
105.36% to 181.81%	0	0.00%	97.22%
181.81% to 258.26%	0	0.00%	97.22%
258.26% to 334.70%	0	0.00%	97.22%
Greater than 334.70%	1	2.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-73.02%	130.84%	97.22%	68.27%
±2σ	-174.95%	232.78%	97.22%	95.45%
±3σ	-276.88%	334.71%	97.22%	99.73%

Descriptive Statistics

Mean	28.915%
Standard Error	16.988%
Median	5.150%
Mode	-64.235%
Standard Deviation	101.930%
Sample Variance	10389.786%
Kurtosis	22.23
Skewness	4.26
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	-26.546%	16	44.44%	-11.798%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	49.48%
12	3 Years	124.58%
20	5 Years	106.85%
40	10 Years	92.62%
80	20 Years	92.62%
200	50 Years	92.62%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.92. Further, an Excess Kurtosis of 10.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -282.22%	0	0.00%	0.00%
-282.22% to -177.73%	0	0.00%	0.00%
-177.73% to -73.24%	0	0.00%	0.00%
-73.24% to 31.25%	1	2.70%	2.70%
31.25% to 135.75%	25	67.57%	70.27%
135.75% to 240.24%	7	18.92%	89.19%
240.24% to 344.73%	0	0.00%	89.19%
344.73% to 449.22%	3	8.11%	97.30%
449.22% to 553.71%	0	0.00%	97.30%
Greater than 553.71%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.58%	275.07%	89.19%	68.27%
±2σ	-142.90%	414.39%	94.59%	95.45%
±3σ	-282.22%	553.71%	97.30%	99.73%

Descriptive Statistics

Mean	135.745%
Standard Error	22.904%
Median	95.693%
Mode	30.280%
Standard Deviation	139.322%
Sample Variance	19410.589%
Kurtosis	10.46
Skewness	2.92
Range	723.302%
Minimum	30.280%
Maximum	753.582%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	135.745%	37	100.00%	135.745%
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 1.35. Further, an Excess Kurtosis of 2.49 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -154.53%	0	0.00%	0.00%
-154.53% to -114.73%	0	0.00%	0.00%
-114.73% to -74.94%	1	2.70%	2.70%
-74.94% to -35.14%	9	24.32%	27.03%
-35.14% to 4.66%	12	32.43%	59.46%
4.66% to 44.46%	8	21.62%	81.08%
44.46% to 84.26%	3	8.11%	89.19%
84.26% to 124.06%	3	8.11%	97.30%
124.06% to 163.85%	0	0.00%	97.30%
Greater than 163.85%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-48.40%	57.73%	81.08%	68.27%
±2σ	-101.47%	110.79%	94.59%	95.45%
±3σ	-154.53%	163.85%	97.30%	99.73%

Descriptive Statistics

Mean	4.661%
Standard Error	8.724%
Median	-1.385%
Mode	-84.135%
Standard Deviation	53.064%
Sample Variance	2815.757%
Kurtosis	2.49
Skewness	1.35
Range	267.123%
Minimum	-84.135%
Maximum	182.988%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.829%	17	45.95%	21.516%
Negative	-31.182%	20	54.05%	-16.855%
Zero	0.000%	0	0.00%	0.000%

CVNA Deep Analytical Report