NIO - 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	5.50%	4.56%	4.41%	6.19%	3.84%	3.88%	5.53	5.98	5.33	6.21
Weekly	12.12%	13.17%	11.46%	15.03%	8.44%	8.53%	5.28	6.26	4.86	6.81
Monthly	28.29%	27.76%	27.24%	32.22%	17.58%	17.76%	4.82	6.86	4.05	8.17
Quarterly	70.97%	79.61%	50.90%	57.04%	30.44%	30.76%	4.24	7.80	3.13	10.57
Annual	—	—	—	—	60.88%	61.52%	3.13	10.57	1.70	19.43
Option Time Horizon	—	—	—	—	22.98%	23.22%	4.57	7.24	3.63	9.11

Calculation Notes: Computed at 2026-03-23T16:42 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $5.75 | Strike (K): $6.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.4400 (Bid $0.4200 / Ask $0.4600) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 60.88% (CRR binomial tree, American, n=20 steps) | BS IV: 61.58% (European Black-Scholes) | Yahoo IV (Annual): 61.52% → 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 2.40. Further, an Excess Kurtosis of 25.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.36%	3	0.16%	0.16%
-16.36% to -12.24%	12	0.63%	0.79%
-12.24% to -8.11%	50	2.65%	3.44%
-8.11% to -3.99%	273	14.44%	17.88%
-3.99% to 0.14%	662	35.03%	52.91%
0.14% to 4.26%	578	30.58%	83.49%
4.26% to 8.38%	211	11.16%	94.66%
8.38% to 12.51%	68	3.60%	98.25%
12.51% to 16.63%	15	0.79%	99.05%
Greater than 16.63%	18	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.36%	5.63%	76.93%	68.27%
±2σ	-10.86%	11.13%	96.08%	95.45%
±3σ	-16.36%	16.63%	98.89%	99.73%

Descriptive Statistics

Mean	0.135%
Standard Error	0.126%
Median	-0.224%
Mode	0.000%
Standard Deviation	5.498%
Sample Variance	30.232%
Kurtosis	25.37
Skewness	2.40
Range	96.919%
Minimum	-21.161%
Maximum	75.758%
Count	1890

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.117%	901	47.67%	1.963%
Negative	-3.572%	967	51.16%	-1.828%
Zero	0.000%	22	1.16%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.92%
20	1 Month	5.69%
60	1 Quarter	5.11%
250	1 Year	5.32%
750	3 Years	5.76%
1,250	5 Years	6.19%
2,500	10 Years	7.04%
5,000	20 Years	7.04%
12,500	50 Years	7.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.83. Further, an Excess Kurtosis of 99.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.05%	0	0.00%	0.00%
-7.05% to -3.63%	0	0.00%	0.00%
-3.63% to -0.21%	0	0.00%	0.00%
-0.21% to 3.21%	203	10.74%	10.74%
3.21% to 6.62%	976	51.61%	62.35%
6.62% to 10.04%	472	24.96%	87.31%
10.04% to 13.46%	149	7.88%	95.19%
13.46% to 16.88%	46	2.43%	97.62%
16.88% to 20.30%	24	1.27%	98.89%
Greater than 20.30%	21	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.07%	11.18%	89.32%	68.27%
±2σ	-2.49%	15.74%	97.14%	95.45%
±3σ	-7.05%	20.30%	98.89%	99.73%

Descriptive Statistics

Mean	6.623%
Standard Error	0.105%
Median	5.605%
Mode	4.000%
Standard Deviation	4.558%
Sample Variance	20.774%
Kurtosis	99.21
Skewness	6.83
Range	93.628%
Minimum	1.004%
Maximum	94.632%
Count	1891

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.623%	1891	100.00%	6.623%
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 -0.46. Further, an Excess Kurtosis of 7.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.96%	9	0.48%	0.48%
-12.96% to -9.66%	21	1.11%	1.59%
-9.66% to -6.36%	75	3.97%	5.55%
-6.36% to -3.05%	243	12.85%	18.40%
-3.05% to 0.25%	575	30.41%	48.81%
0.25% to 3.56%	617	32.63%	81.44%
3.56% to 6.86%	245	12.96%	94.39%
6.86% to 10.17%	75	3.97%	98.36%
10.17% to 13.47%	20	1.06%	99.42%
Greater than 13.47%	11	0.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.15%	4.66%	75.52%	68.27%
±2σ	-8.56%	9.07%	95.61%	95.45%
±3σ	-12.96%	13.47%	98.94%	99.73%

Descriptive Statistics

Mean	0.254%
Standard Error	0.101%
Median	0.358%
Mode	0.000%
Standard Deviation	4.406%
Sample Variance	19.410%
Kurtosis	7.44
Skewness	-0.46
Range	70.810%
Minimum	-42.931%
Maximum	27.879%
Count	1891

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.244%	1003	53.04%	1.721%
Negative	-3.271%	848	44.84%	-1.467%
Zero	0.000%	40	2.12%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.79. 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 -35.76%	1	0.26%	0.26%
-35.76% to -26.66%	2	0.51%	0.77%
-26.66% to -17.57%	10	2.55%	3.32%
-17.57% to -8.48%	71	18.11%	21.43%
-8.48% to 0.60%	138	35.20%	56.63%
0.60% to 9.70%	104	26.53%	83.16%
9.70% to 18.79%	34	8.67%	91.84%
18.79% to 27.88%	20	5.10%	96.94%
27.88% to 36.97%	7	1.79%	98.72%
Greater than 36.97%	5	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.51%	12.72%	75.00%	68.27%
±2σ	-23.63%	24.84%	94.39%	95.45%
±3σ	-35.76%	36.96%	98.47%	99.73%

Descriptive Statistics

Mean	0.605%
Standard Error	0.612%
Median	-0.516%
Mode	0.000%
Standard Deviation	12.120%
Sample Variance	146.904%
Kurtosis	2.32
Skewness	0.79
Range	101.845%
Minimum	-42.647%
Maximum	59.198%
Count	392

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.403%	177	45.15%	4.697%
Negative	-7.639%	210	53.57%	-4.092%
Zero	0.000%	5	1.28%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.18%
12	1 Quarter	12.70%
52	1 Year	13.04%
156	3 Years	14.22%
260	5 Years	15.03%
520	10 Years	17.09%
1,040	20 Years	17.09%
2,600	50 Years	17.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.56. Further, an Excess Kurtosis of 36.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.67%	0	0.00%	0.00%
-20.67% to -10.79%	0	0.00%	0.00%
-10.79% to -0.91%	0	0.00%	0.00%
-0.91% to 8.97%	42	10.69%	10.69%
8.97% to 18.84%	214	54.45%	65.14%
18.84% to 28.72%	81	20.61%	85.75%
28.72% to 38.60%	34	8.65%	94.40%
38.60% to 48.48%	13	3.31%	97.71%
48.48% to 58.36%	4	1.02%	98.73%
Greater than 58.36%	5	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.67%	32.02%	87.79%	68.27%
±2σ	-7.50%	45.19%	96.69%	95.45%
±3σ	-20.67%	58.36%	98.73%	99.73%

Descriptive Statistics

Mean	18.845%
Standard Error	0.664%
Median	15.318%
Mode	7.928%
Standard Deviation	13.171%
Sample Variance	173.467%
Kurtosis	36.99
Skewness	4.56
Range	153.614%
Minimum	4.330%
Maximum	157.944%
Count	393

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.845%	393	100.00%	18.845%
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 0.22. Further, an Excess Kurtosis of 1.59 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.28%	2	0.51%	0.51%
-33.28% to -24.68%	5	1.27%	1.78%
-24.68% to -16.09%	19	4.83%	6.62%
-16.09% to -7.49%	36	9.16%	15.78%
-7.49% to 1.11%	141	35.88%	51.65%
1.11% to 9.71%	113	28.75%	80.41%
9.71% to 18.31%	53	13.49%	93.89%
18.31% to 26.91%	17	4.33%	98.22%
26.91% to 35.51%	3	0.76%	98.98%
Greater than 35.51%	4	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.35%	12.58%	73.03%	68.27%
±2σ	-21.82%	24.04%	95.17%	95.45%
±3σ	-33.28%	35.51%	98.47%	99.73%

Descriptive Statistics

Mean	1.111%
Standard Error	0.578%
Median	0.841%
Mode	0.000%
Standard Deviation	11.465%
Sample Variance	131.453%
Kurtosis	1.59
Skewness	0.22
Range	86.069%
Minimum	-37.359%
Maximum	48.710%
Count	393

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.037%	210	53.44%	4.829%
Negative	-8.162%	179	45.55%	-3.718%
Zero	0.000%	4	1.02%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.89. Further, an Excess Kurtosis of 0.69 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.53%	0	0.00%	0.00%
-81.53% to -60.31%	0	0.00%	0.00%
-60.31% to -39.10%	2	2.22%	2.22%
-39.10% to -17.88%	18	20.00%	22.22%
-17.88% to 3.34%	33	36.67%	58.89%
3.34% to 24.56%	19	21.11%	80.00%
24.56% to 45.78%	10	11.11%	91.11%
45.78% to 67.00%	6	6.67%	97.78%
67.00% to 88.22%	1	1.11%	98.89%
Greater than 88.22%	1	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.95%	31.63%	76.67%	68.27%
±2σ	-53.24%	59.93%	95.56%	95.45%
±3σ	-81.53%	88.22%	98.89%	99.73%

Descriptive Statistics

Mean	3.342%
Standard Error	2.982%
Median	-3.085%
Mode	-46.708%
Standard Deviation	28.292%
Sample Variance	800.419%
Kurtosis	0.69
Skewness	0.89
Range	140.678%
Minimum	-46.708%
Maximum	93.970%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.020%	40	44.44%	12.453%
Negative	-16.400%	50	55.56%	-9.111%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.66%
12	1 Year	30.04%
36	3 Years	31.79%
60	5 Years	32.22%
120	10 Years	38.69%
240	20 Years	38.69%
600	50 Years	38.69%

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 2.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.39%	0	0.00%	0.00%
-34.39% to -13.57%	0	0.00%	0.00%
-13.57% to 7.24%	0	0.00%	0.00%
7.24% to 28.06%	23	25.27%	25.27%
28.06% to 48.88%	35	38.46%	63.74%
48.88% to 69.69%	17	18.68%	82.42%
69.69% to 90.51%	7	7.69%	90.11%
90.51% to 111.33%	4	4.40%	94.51%
111.33% to 132.15%	4	4.40%	98.90%
Greater than 132.15%	1	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.12%	76.63%	80.22%	68.27%
±2σ	-6.63%	104.39%	94.51%	95.45%
±3σ	-34.39%	132.15%	98.90%	99.73%

Descriptive Statistics

Mean	48.877%
Standard Error	2.910%
Median	42.264%
Mode	17.365%
Standard Deviation	27.756%
Sample Variance	770.398%
Kurtosis	2.73
Skewness	1.59
Range	140.579%
Minimum	17.365%
Maximum	157.944%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.877%	91	100.00%	48.877%
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 0.64. Further, an Excess Kurtosis of 0.68 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -77.38%	0	0.00%	0.00%
-77.38% to -56.95%	0	0.00%	0.00%
-56.95% to -36.53%	3	3.30%	3.30%
-36.53% to -16.10%	21	23.08%	26.37%
-16.10% to 4.33%	24	26.37%	52.75%
4.33% to 24.76%	24	26.37%	79.12%
24.76% to 45.19%	13	14.29%	93.41%
45.19% to 65.61%	4	4.40%	97.80%
65.61% to 86.04%	1	1.10%	98.90%
Greater than 86.04%	1	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.91%	31.57%	70.33%	68.27%
±2σ	-50.14%	58.80%	95.60%	95.45%
±3σ	-77.38%	86.04%	98.90%	99.73%

Descriptive Statistics

Mean	4.330%
Standard Error	2.855%
Median	4.082%
Mode	-48.187%
Standard Deviation	27.237%
Sample Variance	741.871%
Kurtosis	0.68
Skewness	0.64
Range	140.736%
Minimum	-48.187%
Maximum	92.549%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.966%	51	56.04%	12.871%
Negative	-19.431%	40	43.96%	-8.541%
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 1.83. Further, an Excess Kurtosis of 3.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -197.70%	0	0.00%	0.00%
-197.70% to -144.47%	0	0.00%	0.00%
-144.47% to -91.24%	0	0.00%	0.00%
-91.24% to -38.01%	4	13.33%	13.33%
-38.01% to 15.22%	15	50.00%	63.33%
15.22% to 68.45%	6	20.00%	83.33%
68.45% to 121.67%	2	6.67%	90.00%
121.67% to 174.90%	2	6.67%	96.67%
174.90% to 228.13%	0	0.00%	96.67%
Greater than 228.13%	1	3.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-55.75%	86.19%	80.00%	68.27%
±2σ	-126.73%	157.16%	93.33%	95.45%
±3σ	-197.70%	228.13%	96.67%	99.73%

Descriptive Statistics

Mean	15.217%
Standard Error	12.958%
Median	-8.019%
Mode	-58.213%
Standard Deviation	70.972%
Sample Variance	5037.001%
Kurtosis	3.47
Skewness	1.83
Range	308.360%
Minimum	-58.213%
Maximum	250.147%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	72.519%	13	43.33%	31.425%
Negative	-28.602%	17	56.67%	-16.208%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	51.03%
12	3 Years	57.89%
20	5 Years	57.04%
40	10 Years	82.72%
80	20 Years	82.72%
200	50 Years	82.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.47. Further, an Excess Kurtosis of 8.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -124.10%	0	0.00%	0.00%
-124.10% to -64.40%	0	0.00%	0.00%
-64.40% to -4.69%	0	0.00%	0.00%
-4.69% to 55.02%	5	16.13%	16.13%
55.02% to 114.73%	14	45.16%	61.29%
114.73% to 174.43%	9	29.03%	90.32%
174.43% to 234.14%	1	3.23%	93.55%
234.14% to 293.85%	1	3.23%	96.77%
293.85% to 353.56%	0	0.00%	96.77%
Greater than 353.56%	1	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	35.12%	194.34%	87.10%	68.27%
±2σ	-44.49%	273.95%	93.55%	95.45%
±3σ	-124.10%	353.56%	96.77%	99.73%

Descriptive Statistics

Mean	114.727%
Standard Error	14.298%
Median	102.998%
Mode	34.165%
Standard Deviation	79.610%
Sample Variance	6337.707%
Kurtosis	8.18
Skewness	2.47
Range	399.601%
Minimum	34.165%
Maximum	433.766%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	114.727%	31	100.00%	114.727%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.56. Further, an Excess Kurtosis of 0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -140.20%	0	0.00%	0.00%
-140.20% to -102.03%	0	0.00%	0.00%
-102.03% to -63.86%	1	3.23%	3.23%
-63.86% to -25.69%	5	16.13%	19.35%
-25.69% to 12.49%	11	35.48%	54.84%
12.49% to 50.66%	7	22.58%	77.42%
50.66% to 88.83%	4	12.90%	90.32%
88.83% to 127.00%	2	6.45%	96.77%
127.00% to 165.18%	1	3.23%	100.00%
Greater than 165.18%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-38.41%	63.38%	74.19%	68.27%
±2σ	-89.31%	114.28%	96.77%	95.45%
±3σ	-140.20%	165.18%	100.00%	99.73%

Descriptive Statistics

Mean	12.487%
Standard Error	9.141%
Median	3.812%
Mode	-72.362%
Standard Deviation	50.897%
Sample Variance	2590.476%
Kurtosis	0.08
Skewness	0.56
Range	210.293%
Minimum	-72.362%
Maximum	137.931%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	45.308%	18	58.06%	26.308%
Negative	-32.957%	13	41.94%	-13.821%
Zero	0.000%	0	0.00%	0.000%

NIO Deep Analytical Report