NCLH - 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	3.50%	3.16%	2.77%	4.77%	4.07%	4.12%	19.45	21.10	18.68	21.98
Weekly	7.35%	9.85%	8.27%	11.38%	8.95%	9.07%	18.52	22.16	16.94	24.23
Monthly	14.76%	36.07%	23.05%	24.55%	18.64%	18.87%	16.81	24.41	13.96	29.41
Quarterly	24.32%	93.74%	38.14%	43.68%	32.28%	32.69%	14.67	27.98	10.62	38.64
Annual	—	—	—	—	64.57%	65.38%	10.62	38.64	5.57	73.70
Option Time Horizon	—	—	—	—	24.37%	24.68%	15.88	25.85	12.44	32.99

Calculation Notes: Computed at 2026-03-23T16:42 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $20.26 | Strike (K): $21.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.7150 (Bid $1.5900 / Ask $1.8400) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 64.57% (CRR binomial tree, American, n=20 steps) | BS IV: 65.17% (European Black-Scholes) | Yahoo IV (Annual): 65.38% → 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 0.24. Further, an Excess Kurtosis of 19.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.46%	31	0.94%	0.94%
-10.46% to -7.83%	23	0.69%	1.63%
-7.83% to -5.20%	81	2.45%	4.08%
-5.20% to -2.57%	280	8.45%	12.53%
-2.57% to 0.06%	1262	38.10%	50.63%
0.06% to 2.69%	1201	36.26%	86.90%
2.69% to 5.31%	283	8.54%	95.44%
5.31% to 7.94%	94	2.84%	98.28%
7.94% to 10.57%	31	0.94%	99.21%
Greater than 10.57%	26	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.45%	3.56%	83.30%	68.27%
±2σ	-6.95%	7.07%	95.47%	95.45%
±3σ	-10.46%	10.57%	98.28%	99.73%

Descriptive Statistics

Mean	0.056%
Standard Error	0.061%
Median	0.020%
Mode	0.000%
Standard Deviation	3.505%
Sample Variance	12.286%
Kurtosis	19.07
Skewness	0.24
Range	77.987%
Minimum	-35.795%
Maximum	42.192%
Count	3312

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.204%	1660	50.12%	1.105%
Negative	-2.130%	1631	49.24%	-1.049%
Zero	0.000%	21	0.63%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.97%
20	1 Month	5.94%
60	1 Quarter	5.21%
250	1 Year	4.45%
750	3 Years	4.20%
1,250	5 Years	4.77%
2,500	10 Years	4.41%
5,000	20 Years	4.02%
12,500	50 Years	4.02%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.67%	0	0.00%	0.00%
-5.67% to -3.30%	0	0.00%	0.00%
-3.30% to -0.93%	0	0.00%	0.00%
-0.93% to 1.44%	304	9.18%	9.18%
1.44% to 3.80%	1882	56.81%	65.98%
3.80% to 6.17%	700	21.13%	87.11%
6.17% to 8.54%	243	7.33%	94.45%
8.54% to 10.91%	97	2.93%	97.37%
10.91% to 13.27%	40	1.21%	98.58%
Greater than 13.27%	47	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.65%	6.96%	90.88%	68.27%
±2σ	-2.51%	10.12%	96.74%	95.45%
±3σ	-5.67%	13.27%	98.58%	99.73%

Descriptive Statistics

Mean	3.803%
Standard Error	0.055%
Median	2.984%
Mode	2.379%
Standard Deviation	3.157%
Sample Variance	9.966%
Kurtosis	35.96
Skewness	4.56
Range	41.470%
Minimum	0.635%
Maximum	42.105%
Count	3313

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.803%	3313	100.00%	3.803%
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 1.19. Further, an Excess Kurtosis of 11.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.22%	14	0.42%	0.42%
-8.22% to -6.14%	45	1.36%	1.78%
-6.14% to -4.06%	87	2.63%	4.41%
-4.06% to -1.98%	355	10.72%	15.12%
-1.98% to 0.10%	1228	37.07%	52.19%
0.10% to 2.17%	1103	33.29%	85.48%
2.17% to 4.25%	319	9.63%	95.11%
4.25% to 6.33%	89	2.69%	97.80%
6.33% to 8.41%	38	1.15%	98.94%
Greater than 8.41%	35	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.67%	2.87%	79.84%	68.27%
±2σ	-5.44%	5.64%	94.90%	95.45%
±3σ	-8.22%	8.41%	98.52%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.048%
Median	0.018%
Mode	0.000%
Standard Deviation	2.771%
Sample Variance	7.680%
Kurtosis	11.38
Skewness	1.19
Range	43.980%
Minimum	-15.171%
Maximum	28.809%
Count	3313

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.933%	1659	50.08%	0.968%
Negative	-1.767%	1633	49.29%	-0.871%
Zero	0.000%	21	0.63%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.01. Further, an Excess Kurtosis of 9.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.79%	4	0.58%	0.58%
-21.79% to -16.28%	10	1.46%	2.04%
-16.28% to -10.77%	21	3.06%	5.09%
-10.77% to -5.26%	72	10.48%	15.57%
-5.26% to 0.25%	230	33.48%	49.05%
0.25% to 5.76%	244	35.52%	84.57%
5.76% to 11.27%	69	10.04%	94.61%
11.27% to 16.78%	28	4.08%	98.69%
16.78% to 22.29%	5	0.73%	99.42%
Greater than 22.29%	4	0.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.10%	7.60%	78.89%	68.27%
±2σ	-14.45%	14.94%	94.76%	95.45%
±3σ	-21.79%	22.29%	98.84%	99.73%

Descriptive Statistics

Mean	0.249%
Standard Error	0.280%
Median	0.327%
Mode	-2.597%
Standard Deviation	7.347%
Sample Variance	53.971%
Kurtosis	9.44
Skewness	-0.01
Range	100.125%
Minimum	-44.775%
Maximum	55.350%
Count	687

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.802%	367	53.42%	2.565%
Negative	-5.005%	318	46.29%	-2.317%
Zero	0.000%	2	0.29%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.19%
12	1 Quarter	11.86%
52	1 Year	10.52%
156	3 Years	10.04%
260	5 Years	11.38%
520	10 Years	10.51%
1,040	20 Years	9.56%
2,600	50 Years	9.56%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.86. Further, an Excess Kurtosis of 53.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.37%	0	0.00%	0.00%
-19.37% to -11.98%	0	0.00%	0.00%
-11.98% to -4.59%	0	0.00%	0.00%
-4.59% to 2.80%	20	2.91%	2.91%
2.80% to 10.19%	448	65.12%	68.02%
10.19% to 17.58%	141	20.49%	88.52%
17.58% to 24.97%	51	7.41%	95.93%
24.97% to 32.36%	12	1.74%	97.67%
32.36% to 39.75%	6	0.87%	98.55%
Greater than 39.75%	10	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.33%	20.04%	92.15%	68.27%
±2σ	-9.52%	29.90%	97.67%	95.45%
±3σ	-19.37%	39.75%	98.55%	99.73%

Descriptive Statistics

Mean	10.188%
Standard Error	0.376%
Median	7.720%
Mode	2.877%
Standard Deviation	9.854%
Sample Variance	97.098%
Kurtosis	53.74
Skewness	5.86
Range	129.797%
Minimum	1.974%
Maximum	131.771%
Count	688

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.188%	688	100.00%	10.188%
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 4.36. Further, an Excess Kurtosis of 46.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.29%	2	0.29%	0.29%
-24.29% to -18.09%	1	0.15%	0.44%
-18.09% to -11.89%	12	1.74%	2.18%
-11.89% to -5.69%	76	11.05%	13.23%
-5.69% to 0.51%	298	43.31%	56.54%
0.51% to 6.71%	218	31.69%	88.23%
6.71% to 12.91%	50	7.27%	95.49%
12.91% to 19.11%	16	2.33%	97.82%
19.11% to 25.32%	11	1.60%	99.42%
Greater than 25.32%	4	0.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.76%	8.78%	84.01%	68.27%
±2σ	-16.02%	17.05%	96.22%	95.45%
±3σ	-24.29%	25.32%	99.13%	99.73%

Descriptive Statistics

Mean	0.512%
Standard Error	0.315%
Median	-0.268%
Mode	-4.424%
Standard Deviation	8.268%
Sample Variance	68.363%
Kurtosis	46.60
Skewness	4.36
Range	136.351%
Minimum	-33.060%
Maximum	103.291%
Count	688

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.553%	333	48.40%	2.688%
Negative	-4.241%	353	51.31%	-2.176%
Zero	0.000%	2	0.29%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.17. Further, an Excess Kurtosis of 4.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.23%	1	0.63%	0.63%
-43.23% to -32.16%	0	0.00%	0.63%
-32.16% to -21.09%	7	4.43%	5.06%
-21.09% to -10.02%	18	11.39%	16.46%
-10.02% to 1.05%	52	32.91%	49.37%
1.05% to 12.12%	54	34.18%	83.54%
12.12% to 23.19%	16	10.13%	93.67%
23.19% to 34.26%	6	3.80%	97.47%
34.26% to 45.33%	1	0.63%	98.10%
Greater than 45.33%	3	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.71%	15.81%	78.48%	68.27%
±2σ	-28.47%	30.57%	94.94%	95.45%
±3σ	-43.23%	45.33%	97.47%	99.73%

Descriptive Statistics

Mean	1.048%
Standard Error	1.174%
Median	1.407%
Mode	0.000%
Standard Deviation	14.761%
Sample Variance	217.879%
Kurtosis	4.28
Skewness	-0.17
Range	120.220%
Minimum	-70.585%
Maximum	49.635%
Count	158

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.917%	83	52.53%	5.735%
Negative	-10.144%	73	46.20%	-4.687%
Zero	0.000%	2	1.27%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.44%
12	1 Year	22.05%
36	3 Years	21.84%
60	5 Years	24.55%
120	10 Years	22.88%
240	20 Years	20.75%
600	50 Years	20.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.06. Further, an Excess Kurtosis of 98.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -82.53%	0	0.00%	0.00%
-82.53% to -55.47%	0	0.00%	0.00%
-55.47% to -28.42%	0	0.00%	0.00%
-28.42% to -1.37%	0	0.00%	0.00%
-1.37% to 25.69%	110	69.18%	69.18%
25.69% to 52.74%	39	24.53%	93.71%
52.74% to 79.79%	6	3.77%	97.48%
79.79% to 106.85%	2	1.26%	98.74%
106.85% to 133.90%	1	0.63%	99.37%
Greater than 133.90%	1	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.38%	61.76%	96.86%	68.27%
±2σ	-46.46%	97.83%	98.74%	95.45%
±3σ	-82.53%	133.90%	99.37%	99.73%

Descriptive Statistics

Mean	25.686%
Standard Error	2.861%
Median	17.720%
Mode	6.020%
Standard Deviation	36.071%
Sample Variance	1301.091%
Kurtosis	98.86
Skewness	9.06
Range	421.718%
Minimum	6.020%
Maximum	427.738%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.686%	159	100.00%	25.686%
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 6.97. Further, an Excess Kurtosis of 70.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.35%	0	0.00%	0.00%
-67.35% to -50.07%	0	0.00%	0.00%
-50.07% to -32.78%	1	0.63%	0.63%
-32.78% to -15.50%	11	6.92%	7.55%
-15.50% to 1.79%	84	52.83%	60.38%
1.79% to 19.08%	48	30.19%	90.57%
19.08% to 36.36%	12	7.55%	98.11%
36.36% to 53.65%	2	1.26%	99.37%
53.65% to 70.93%	0	0.00%	99.37%
Greater than 70.93%	1	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.26%	24.84%	89.94%	68.27%
±2σ	-44.31%	47.89%	99.37%	95.45%
±3σ	-67.35%	70.93%	99.37%	99.73%

Descriptive Statistics

Mean	1.790%
Standard Error	1.828%
Median	-1.631%
Mode	-35.976%
Standard Deviation	23.048%
Sample Variance	531.211%
Kurtosis	70.57
Skewness	6.97
Range	274.480%
Minimum	-35.976%
Maximum	238.504%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.166%	73	45.91%	6.504%
Negative	-8.715%	86	54.09%	-4.714%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.07. Further, an Excess Kurtosis of 1.33 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.17%	0	0.00%	0.00%
-70.17% to -51.94%	1	1.89%	1.89%
-51.94% to -33.70%	3	5.66%	7.55%
-33.70% to -15.46%	4	7.55%	15.09%
-15.46% to 2.78%	20	37.74%	52.83%
2.78% to 21.01%	16	30.19%	83.02%
21.01% to 39.25%	7	13.21%	96.23%
39.25% to 57.49%	0	0.00%	96.23%
57.49% to 75.72%	2	3.77%	100.00%
Greater than 75.72%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.54%	27.09%	73.58%	68.27%
±2σ	-45.86%	51.41%	94.34%	95.45%
±3σ	-70.17%	75.72%	100.00%	99.73%

Descriptive Statistics

Mean	2.776%
Standard Error	3.340%
Median	2.114%
Mode	-69.545%
Standard Deviation	24.316%
Sample Variance	591.283%
Kurtosis	1.33
Skewness	-0.07
Range	134.863%
Minimum	-69.545%
Maximum	65.318%
Count	53

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.289%	30	56.60%	10.352%
Negative	-17.458%	23	43.40%	-7.576%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	38.55%
12	3 Years	44.46%
20	5 Years	43.68%
40	10 Years	39.89%
80	20 Years	36.11%
200	50 Years	36.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.27. Further, an Excess Kurtosis of 42.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -226.29%	0	0.00%	0.00%
-226.29% to -155.99%	0	0.00%	0.00%
-155.99% to -85.68%	0	0.00%	0.00%
-85.68% to -15.38%	0	0.00%	0.00%
-15.38% to 54.92%	39	72.22%	72.22%
54.92% to 125.22%	13	24.07%	96.30%
125.22% to 195.52%	1	1.85%	98.15%
195.52% to 265.83%	0	0.00%	98.15%
265.83% to 336.13%	0	0.00%	98.15%
Greater than 336.13%	1	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-38.82%	148.66%	96.30%	68.27%
±2σ	-132.55%	242.39%	98.15%	95.45%
±3σ	-226.29%	336.13%	98.15%	99.73%

Descriptive Statistics

Mean	54.920%
Standard Error	12.756%
Median	32.655%
Mode	10.599%
Standard Deviation	93.736%
Sample Variance	8786.487%
Kurtosis	42.71
Skewness	6.27
Range	683.853%
Minimum	10.599%
Maximum	694.452%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.920%	54	100.00%	54.920%
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 4.16. Further, an Excess Kurtosis of 23.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -110.06%	0	0.00%	0.00%
-110.06% to -81.45%	0	0.00%	0.00%
-81.45% to -52.85%	0	0.00%	0.00%
-52.85% to -24.24%	6	11.11%	11.11%
-24.24% to 4.36%	28	51.85%	62.96%
4.36% to 32.97%	15	27.78%	90.74%
32.97% to 61.57%	2	3.70%	94.44%
61.57% to 90.18%	2	3.70%	98.15%
90.18% to 118.78%	0	0.00%	98.15%
Greater than 118.78%	1	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.78%	42.50%	88.89%	68.27%
±2σ	-71.92%	80.64%	98.15%	95.45%
±3σ	-110.06%	118.78%	98.15%	99.73%

Descriptive Statistics

Mean	4.361%
Standard Error	5.190%
Median	-2.428%
Mode	-39.012%
Standard Deviation	38.140%
Sample Variance	1454.647%
Kurtosis	23.39
Skewness	4.16
Range	269.439%
Minimum	-39.012%
Maximum	230.427%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.563%	23	42.59%	12.166%
Negative	-14.049%	30	55.56%	-7.805%
Zero	0.000%	1	1.85%	0.000%

NCLH Deep Analytical Report