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%	4.78%	3.52%	3.61%	23.47	25.18	22.66	26.08
Weekly	7.37%	9.88%	8.29%	11.44%	7.75%	7.94%	22.50	26.27	20.82	28.38
Monthly	14.72%	36.19%	23.10%	24.64%	16.13%	16.53%	20.69	28.56	17.61	33.56
Quarterly	24.29%	93.84%	38.18%	43.04%	27.93%	28.64%	18.39	32.14	13.91	42.50
Annual	—	—	—	—	55.86%	57.28%	13.91	42.50	7.95	74.30
Option Time Horizon	—	—	—	—	21.49%	22.03%	19.61	30.14	15.82	37.36

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $24.31 | Strike (K): $25.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.8550 (Bid $1.7700 / Ask $1.9400) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 55.86% (CRR binomial tree, American, n=20 steps) | BS IV: 56.30% (European Black-Scholes) | Yahoo IV (Annual): 57.28% → 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 19.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.45%	30	0.91%	0.91%
-10.45% to -7.82%	23	0.70%	1.61%
-7.82% to -5.19%	81	2.46%	4.07%
-5.19% to -2.57%	274	8.33%	12.40%
-2.57% to 0.06%	1259	38.26%	50.65%
0.06% to 2.69%	1195	36.31%	86.96%
2.69% to 5.31%	279	8.48%	95.44%
5.31% to 7.94%	93	2.83%	98.27%
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	-3.44%	3.56%	83.44%	68.27%
±2σ	-6.94%	7.06%	95.41%	95.45%
±3σ	-10.45%	10.57%	98.30%	99.73%

Descriptive Statistics

Mean	0.061%
Standard Error	0.061%
Median	0.022%
Mode	0.000%
Standard Deviation	3.502%
Sample Variance	12.263%
Kurtosis	19.26
Skewness	0.24
Range	77.987%
Minimum	-35.795%
Maximum	42.192%
Count	3291

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.198%	1653	50.23%	1.104%
Negative	-2.123%	1617	49.13%	-1.043%
Zero	0.000%	21	0.64%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.23%
20	1 Month	5.74%
60	1 Quarter	4.48%
250	1 Year	4.42%
750	3 Years	4.18%
1,250	5 Years	4.78%
2,500	10 Years	4.38%
5,000	20 Years	4.01%
12,500	50 Years	4.01%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.57. Further, an Excess Kurtosis of 36.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.69%	0	0.00%	0.00%
-5.69% to -3.32%	0	0.00%	0.00%
-3.32% to -0.95%	0	0.00%	0.00%
-0.95% to 1.43%	295	8.96%	8.96%
1.43% to 3.80%	1882	57.17%	66.13%
3.80% to 6.17%	689	20.93%	87.06%
6.17% to 8.54%	243	7.38%	94.44%
8.54% to 10.91%	97	2.95%	97.39%
10.91% to 13.28%	39	1.18%	98.57%
Greater than 13.28%	47	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.63%	6.96%	90.92%	68.27%
±2σ	-2.53%	10.12%	96.75%	95.45%
±3σ	-5.69%	13.28%	98.57%	99.73%

Descriptive Statistics

Mean	3.796%
Standard Error	0.055%
Median	2.972%
Mode	2.379%
Standard Deviation	3.161%
Sample Variance	9.993%
Kurtosis	36.03
Skewness	4.57
Range	41.470%
Minimum	0.635%
Maximum	42.105%
Count	3292

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.796%	3292	100.00%	3.796%
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 1.20. Further, an Excess Kurtosis of 11.42 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	0.43%	0.43%
-8.22% to -6.14%	44	1.34%	1.76%
-6.14% to -4.06%	86	2.61%	4.37%
-4.06% to -1.98%	352	10.69%	15.07%
-1.98% to 0.10%	1223	37.15%	52.22%
0.10% to 2.18%	1098	33.35%	85.57%
2.18% to 4.26%	315	9.57%	95.14%
4.26% to 6.34%	88	2.67%	97.81%
6.34% to 8.42%	37	1.12%	98.94%
Greater than 8.42%	35	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.68%	2.87%	79.89%	68.27%
±2σ	-5.45%	5.64%	94.93%	95.45%
±3σ	-8.22%	8.42%	98.51%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.048%
Median	0.018%
Mode	0.000%
Standard Deviation	2.773%
Sample Variance	7.690%
Kurtosis	11.42
Skewness	1.20
Range	43.980%
Minimum	-15.171%
Maximum	28.809%
Count	3292

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.933%	1648	50.06%	0.968%
Negative	-1.766%	1623	49.30%	-0.871%
Zero	0.000%	21	0.64%	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 9.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.82%	4	0.59%	0.59%
-21.82% to -16.30%	10	1.46%	2.05%
-16.30% to -10.77%	21	3.07%	5.12%
-10.77% to -5.25%	70	10.25%	15.37%
-5.25% to 0.28%	233	34.11%	49.49%
0.28% to 5.80%	240	35.14%	84.63%
5.80% to 11.33%	68	9.96%	94.58%
11.33% to 16.85%	28	4.10%	98.68%
16.85% to 22.38%	5	0.73%	99.41%
Greater than 22.38%	4	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.09%	7.64%	78.92%	68.27%
±2σ	-14.46%	15.01%	94.73%	95.45%
±3σ	-21.82%	22.38%	98.83%	99.73%

Descriptive Statistics

Mean	0.277%
Standard Error	0.282%
Median	0.337%
Mode	-2.597%
Standard Deviation	7.366%
Sample Variance	54.257%
Kurtosis	9.39
Skewness	-0.01
Range	100.125%
Minimum	-44.775%
Maximum	55.350%
Count	683

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.820%	366	53.59%	2.583%
Negative	-5.001%	315	46.12%	-2.306%
Zero	0.000%	2	0.29%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.50%
12	1 Quarter	11.16%
52	1 Year	10.63%
156	3 Years	10.06%
260	5 Years	11.44%
520	10 Years	10.47%
1,040	20 Years	9.54%
2,600	50 Years	9.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.87. Further, an Excess Kurtosis of 53.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.46%	0	0.00%	0.00%
-19.46% to -12.05%	0	0.00%	0.00%
-12.05% to -4.65%	0	0.00%	0.00%
-4.65% to 2.76%	17	2.49%	2.49%
2.76% to 10.16%	450	65.79%	68.27%
10.16% to 17.57%	139	20.32%	88.60%
17.57% to 24.98%	50	7.31%	95.91%
24.98% to 32.38%	12	1.75%	97.66%
32.38% to 39.79%	6	0.88%	98.54%
Greater than 39.79%	10	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.29%	20.04%	92.11%	68.27%
±2σ	-9.59%	29.91%	97.66%	95.45%
±3σ	-19.46%	39.79%	98.54%	99.73%

Descriptive Statistics

Mean	10.164%
Standard Error	0.378%
Median	7.692%
Mode	2.877%
Standard Deviation	9.875%
Sample Variance	97.513%
Kurtosis	53.64
Skewness	5.87
Range	129.797%
Minimum	1.974%
Maximum	131.771%
Count	684

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.164%	684	100.00%	10.164%
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 4.35. Further, an Excess Kurtosis of 46.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.38%	2	0.29%	0.29%
-24.38% to -18.16%	1	0.15%	0.44%
-18.16% to -11.95%	11	1.61%	2.05%
-11.95% to -5.73%	77	11.26%	13.30%
-5.73% to 0.49%	296	43.27%	56.58%
0.49% to 6.71%	216	31.58%	88.16%
6.71% to 12.93%	51	7.46%	95.61%
12.93% to 19.15%	15	2.19%	97.81%
19.15% to 25.37%	11	1.61%	99.42%
Greater than 25.37%	4	0.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.80%	8.79%	83.92%	68.27%
±2σ	-16.09%	17.08%	96.20%	95.45%
±3σ	-24.38%	25.37%	99.12%	99.73%

Descriptive Statistics

Mean	0.493%
Standard Error	0.317%
Median	-0.281%
Mode	-4.424%
Standard Deviation	8.292%
Sample Variance	68.750%
Kurtosis	46.37
Skewness	4.35
Range	136.351%
Minimum	-33.060%
Maximum	103.291%
Count	684

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.586%	329	48.10%	2.687%
Negative	-4.250%	353	51.61%	-2.193%
Zero	0.000%	2	0.29%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.18. Further, an Excess Kurtosis of 4.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.99%	1	0.64%	0.64%
-42.99% to -31.95%	0	0.00%	0.64%
-31.95% to -20.92%	7	4.46%	5.10%
-20.92% to -9.88%	17	10.83%	15.92%
-9.88% to 1.16%	52	33.12%	49.04%
1.16% to 12.19%	55	35.03%	84.08%
12.19% to 23.23%	15	9.55%	93.63%
23.23% to 34.27%	6	3.82%	97.45%
34.27% to 45.30%	1	0.64%	98.09%
Greater than 45.30%	3	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.56%	15.87%	78.98%	68.27%
±2σ	-28.27%	30.59%	94.90%	95.45%
±3σ	-42.99%	45.30%	97.45%	99.73%

Descriptive Statistics

Mean	1.157%
Standard Error	1.174%
Median	1.437%
Mode	0.000%
Standard Deviation	14.716%
Sample Variance	216.560%
Kurtosis	4.40
Skewness	-0.18
Range	120.220%
Minimum	-70.585%
Maximum	49.635%
Count	157

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.890%	83	52.87%	5.757%
Negative	-10.030%	72	45.86%	-4.600%
Zero	0.000%	2	1.27%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.13%
12	1 Year	21.66%
36	3 Years	21.93%
60	5 Years	24.64%
120	10 Years	22.79%
240	20 Years	20.70%
600	50 Years	20.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.03. Further, an Excess Kurtosis of 98.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -82.87%	0	0.00%	0.00%
-82.87% to -55.73%	0	0.00%	0.00%
-55.73% to -28.59%	0	0.00%	0.00%
-28.59% to -1.45%	0	0.00%	0.00%
-1.45% to 25.69%	109	68.99%	68.99%
25.69% to 52.83%	39	24.68%	93.67%
52.83% to 79.97%	6	3.80%	97.47%
79.97% to 107.11%	2	1.27%	98.73%
107.11% to 134.25%	1	0.63%	99.37%
Greater than 134.25%	1	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.50%	61.88%	96.84%	68.27%
±2σ	-46.68%	98.06%	98.73%	95.45%
±3σ	-82.87%	134.25%	99.37%	99.73%

Descriptive Statistics

Mean	25.691%
Standard Error	2.879%
Median	17.706%
Mode	6.020%
Standard Deviation	36.187%
Sample Variance	1309.463%
Kurtosis	98.22
Skewness	9.03
Range	421.718%
Minimum	6.020%
Maximum	427.738%
Count	158

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.691%	158	100.00%	25.691%
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 70.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.57%	0	0.00%	0.00%
-67.57% to -50.24%	0	0.00%	0.00%
-50.24% to -32.91%	1	0.63%	0.63%
-32.91% to -15.59%	11	6.96%	7.59%
-15.59% to 1.74%	83	52.53%	60.13%
1.74% to 19.07%	48	30.38%	90.51%
19.07% to 36.39%	12	7.59%	98.10%
36.39% to 53.72%	2	1.27%	99.37%
53.72% to 71.05%	0	0.00%	99.37%
Greater than 71.05%	1	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.36%	24.84%	90.51%	68.27%
±2σ	-44.47%	47.94%	99.37%	95.45%
±3σ	-67.57%	71.05%	99.37%	99.73%

Descriptive Statistics

Mean	1.739%
Standard Error	1.838%
Median	-1.695%
Mode	-35.976%
Standard Deviation	23.102%
Sample Variance	533.710%
Kurtosis	70.43
Skewness	6.97
Range	274.480%
Minimum	-35.976%
Maximum	238.504%
Count	158

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.201%	72	45.57%	6.471%
Negative	-8.695%	86	54.43%	-4.733%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.12. Further, an Excess Kurtosis of 1.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.76%	0	0.00%	0.00%
-69.76% to -51.54%	1	1.89%	1.89%
-51.54% to -33.32%	3	5.66%	7.55%
-33.32% to -15.10%	4	7.55%	15.09%
-15.10% to 3.12%	19	35.85%	50.94%
3.12% to 21.35%	17	32.08%	83.02%
21.35% to 39.57%	7	13.21%	96.23%
39.57% to 57.79%	0	0.00%	96.23%
57.79% to 76.01%	2	3.77%	100.00%
Greater than 76.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.17%	27.42%	73.58%	68.27%
±2σ	-45.46%	51.71%	94.34%	95.45%
±3σ	-69.76%	76.01%	100.00%	99.73%

Descriptive Statistics

Mean	3.125%
Standard Error	3.337%
Median	2.670%
Mode	-69.545%
Standard Deviation	24.294%
Sample Variance	590.221%
Kurtosis	1.35
Skewness	-0.12
Range	134.863%
Minimum	-69.545%
Maximum	65.318%
Count	53

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.044%	31	58.49%	10.554%
Negative	-17.898%	22	41.51%	-7.429%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	35.36%
12	3 Years	43.40%
20	5 Years	43.04%
40	10 Years	39.57%
80	20 Years	35.87%
200	50 Years	35.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.25. Further, an Excess Kurtosis of 42.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -226.92%	0	0.00%	0.00%
-226.92% to -156.54%	0	0.00%	0.00%
-156.54% to -86.16%	0	0.00%	0.00%
-86.16% to -15.79%	0	0.00%	0.00%
-15.79% to 54.59%	39	72.22%	72.22%
54.59% to 124.97%	13	24.07%	96.30%
124.97% to 195.35%	1	1.85%	98.15%
195.35% to 265.72%	0	0.00%	98.15%
265.72% to 336.10%	0	0.00%	98.15%
Greater than 336.10%	1	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-39.24%	148.43%	96.30%	68.27%
±2σ	-133.08%	242.26%	98.15%	95.45%
±3σ	-226.92%	336.10%	98.15%	99.73%

Descriptive Statistics

Mean	54.592%
Standard Error	12.769%
Median	31.816%
Mode	10.599%
Standard Deviation	93.836%
Sample Variance	8805.204%
Kurtosis	42.61
Skewness	6.25
Range	683.853%
Minimum	10.599%
Maximum	694.452%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.592%	54	100.00%	54.592%
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 4.18. Further, an Excess Kurtosis of 23.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -110.51%	0	0.00%	0.00%
-110.51% to -81.88%	0	0.00%	0.00%
-81.88% to -53.24%	0	0.00%	0.00%
-53.24% to -24.61%	6	11.11%	11.11%
-24.61% to 4.02%	29	53.70%	64.81%
4.02% to 32.66%	14	25.93%	90.74%
32.66% to 61.29%	2	3.70%	94.44%
61.29% to 89.92%	2	3.70%	98.15%
89.92% to 118.55%	0	0.00%	98.15%
Greater than 118.55%	1	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.15%	42.20%	88.89%	68.27%
±2σ	-72.33%	80.38%	98.15%	95.45%
±3σ	-110.51%	118.55%	98.15%	99.73%

Descriptive Statistics

Mean	4.023%
Standard Error	5.195%
Median	-3.428%
Mode	-39.012%
Standard Deviation	38.177%
Sample Variance	1457.456%
Kurtosis	23.44
Skewness	4.18
Range	269.439%
Minimum	-39.012%
Maximum	230.427%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.442%	22	40.74%	11.995%
Negative	-13.886%	31	57.41%	-7.972%
Zero	0.000%	1	1.85%	0.000%

NCLH Deep Analytical Report