URBN - 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	3.16%	2.54%	2.81%	4.01%	3.54%	3.56%	65.97	70.81	63.68	73.36
Weekly	7.00%	6.87%	7.26%	9.28%	7.79%	7.83%	63.23	73.89	58.49	79.87
Monthly	13.30%	14.32%	14.58%	18.75%	16.21%	16.31%	58.12	80.38	49.42	94.53
Quarterly	22.19%	22.07%	20.42%	31.44%	28.08%	28.25%	51.61	90.51	38.98	119.86
Annual	—	—	—	—	56.17%	56.49%	38.98	119.86	22.23	210.18
Option Time Horizon	—	—	—	—	16.89%	16.99%	57.73	80.93	48.76	95.81

Calculation Notes: Computed at 2026-02-22T13:44 UTC | Reference Contract: Call option expiring 2026-03-27 (33 days) | Spot Price (S): $68.35 | Strike (K): $69.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.4000 (Bid $3.9000 / Ask $4.9000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 56.17% (CRR binomial tree, American, n=20 steps) | BS IV: 56.07% (European Black-Scholes) | Yahoo IV (Annual): 56.49% → 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 0.14. Further, an Excess Kurtosis of 8.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.39%	54	0.67%	0.67%
-9.39% to -7.01%	72	0.89%	1.56%
-7.01% to -4.64%	237	2.93%	4.49%
-4.64% to -2.27%	949	11.74%	16.23%
-2.27% to 0.10%	2962	36.64%	52.86%
0.10% to 2.47%	2502	30.95%	83.81%
2.47% to 4.84%	887	10.97%	94.78%
4.84% to 7.21%	251	3.10%	97.88%
7.21% to 9.58%	93	1.15%	99.04%
Greater than 9.58%	78	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.06%	3.26%	78.55%	68.27%
±2σ	-6.22%	6.42%	95.03%	95.45%
±3σ	-9.39%	9.58%	98.37%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.035%
Median	0.000%
Mode	0.000%
Standard Deviation	3.161%
Sample Variance	9.990%
Kurtosis	8.27
Skewness	0.14
Range	61.339%
Minimum	-38.503%
Maximum	22.836%
Count	8085

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.319%	3938	48.71%	1.130%
Negative	-2.150%	3881	48.00%	-1.032%
Zero	0.000%	266	3.29%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.44%
20	1 Month	3.67%
60	1 Quarter	4.23%
250	1 Year	4.33%
750	3 Years	3.69%
1,250	5 Years	4.01%
2,500	10 Years	4.05%
5,000	20 Years	3.84%
12,500	50 Years	4.13%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.64%	0	0.00%	0.00%
-3.64% to -1.73%	0	0.00%	0.00%
-1.73% to 0.18%	0	0.00%	0.00%
0.18% to 2.09%	1351	16.71%	16.71%
2.09% to 4.00%	3751	46.39%	63.10%
4.00% to 5.91%	1771	21.90%	85.00%
5.91% to 7.82%	657	8.13%	93.12%
7.82% to 9.72%	272	3.36%	96.49%
9.72% to 11.63%	126	1.56%	98.05%
Greater than 11.63%	158	1.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.45%	6.54%	84.08%	68.27%
±2σ	-1.09%	9.09%	95.77%	95.45%
±3σ	-3.64%	11.63%	98.05%	99.73%

Descriptive Statistics

Mean	3.998%
Standard Error	0.028%
Median	3.355%
Mode	3.614%
Standard Deviation	2.545%
Sample Variance	6.477%
Kurtosis	18.61
Skewness	2.91
Range	45.286%
Minimum	0.250%
Maximum	45.536%
Count	8086

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.998%	8086	100.00%	3.998%
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 0.48. Further, an Excess Kurtosis of 9.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.43%	64	0.79%	0.79%
-8.43% to -6.32%	88	1.09%	1.88%
-6.32% to -4.22%	285	3.52%	5.40%
-4.22% to -2.11%	957	11.84%	17.24%
-2.11% to -0.01%	2532	31.31%	48.55%
-0.01% to 2.10%	2776	34.33%	82.88%
2.10% to 4.21%	970	12.00%	94.88%
4.21% to 6.31%	281	3.48%	98.36%
6.31% to 8.42%	70	0.87%	99.22%
Greater than 8.42%	63	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.81%	2.80%	76.58%	68.27%
±2σ	-5.62%	5.61%	94.89%	95.45%
±3σ	-8.43%	8.42%	98.43%	99.73%

Descriptive Statistics

Mean	-0.005%
Standard Error	0.031%
Median	0.000%
Mode	0.000%
Standard Deviation	2.807%
Sample Variance	7.879%
Kurtosis	9.55
Skewness	0.48
Range	58.008%
Minimum	-18.878%
Maximum	39.130%
Count	8086

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.033%	3901	48.24%	0.981%
Negative	-2.031%	3926	48.55%	-0.986%
Zero	0.000%	259	3.20%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 5.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.53%	9	0.53%	0.53%
-20.53% to -15.28%	17	1.01%	1.54%
-15.28% to -10.03%	50	2.97%	4.51%
-10.03% to -4.78%	207	12.29%	16.81%
-4.78% to 0.47%	627	37.23%	54.04%
0.47% to 5.72%	490	29.10%	83.14%
5.72% to 10.97%	186	11.05%	94.18%
10.97% to 16.22%	61	3.62%	97.80%
16.22% to 21.47%	18	1.07%	98.87%
Greater than 21.47%	19	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.53%	7.47%	77.73%	68.27%
±2σ	-13.53%	14.47%	94.77%	95.45%
±3σ	-20.53%	21.47%	98.34%	99.73%

Descriptive Statistics

Mean	0.474%
Standard Error	0.171%
Median	0.000%
Mode	0.000%
Standard Deviation	7.000%
Sample Variance	49.005%
Kurtosis	5.27
Skewness	0.25
Range	97.925%
Minimum	-51.136%
Maximum	46.789%
Count	1684

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.477%	826	49.05%	2.686%
Negative	-4.523%	824	48.93%	-2.213%
Zero	0.000%	34	2.02%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.95%
12	1 Quarter	8.40%
52	1 Year	10.00%
156	3 Years	8.60%
260	5 Years	9.28%
520	10 Years	9.42%
1,040	20 Years	8.80%
2,600	50 Years	9.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.77. Further, an Excess Kurtosis of 34.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.48%	0	0.00%	0.00%
-10.48% to -5.32%	0	0.00%	0.00%
-5.32% to -0.17%	0	0.00%	0.00%
-0.17% to 4.98%	238	14.12%	14.12%
4.98% to 10.13%	863	51.22%	65.34%
10.13% to 15.29%	334	19.82%	85.16%
15.29% to 20.44%	139	8.25%	93.41%
20.44% to 25.59%	51	3.03%	96.44%
25.59% to 30.74%	25	1.48%	97.92%
Greater than 30.74%	35	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.26%	17.00%	85.93%	68.27%
±2σ	-3.61%	23.87%	95.73%	95.45%
±3σ	-10.48%	30.74%	97.92%	99.73%

Descriptive Statistics

Mean	10.133%
Standard Error	0.167%
Median	8.285%
Mode	7.143%
Standard Deviation	6.870%
Sample Variance	47.199%
Kurtosis	34.85
Skewness	3.77
Range	112.416%
Minimum	1.176%
Maximum	113.592%
Count	1685

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.133%	1685	100.00%	10.133%
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 2.23. Further, an Excess Kurtosis of 26.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.75%	9	0.53%	0.53%
-21.75% to -16.31%	16	0.95%	1.48%
-16.31% to -10.87%	50	2.97%	4.45%
-10.87% to -5.43%	210	12.46%	16.91%
-5.43% to 0.01%	558	33.12%	50.03%
0.01% to 5.46%	594	35.25%	85.28%
5.46% to 10.90%	172	10.21%	95.49%
10.90% to 16.34%	43	2.55%	98.04%
16.34% to 21.78%	16	0.95%	98.99%
Greater than 21.78%	17	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.24%	7.27%	80.71%	68.27%
±2σ	-14.50%	14.53%	95.49%	95.45%
±3σ	-21.75%	21.78%	98.46%	99.73%

Descriptive Statistics

Mean	0.014%
Standard Error	0.177%
Median	0.000%
Mode	0.000%
Standard Deviation	7.256%
Sample Variance	52.655%
Kurtosis	26.52
Skewness	2.23
Range	131.235%
Minimum	-29.375%
Maximum	101.860%
Count	1685

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.847%	842	49.97%	2.422%
Negative	-4.918%	825	48.96%	-2.408%
Zero	0.000%	18	1.07%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.09. Further, an Excess Kurtosis of 1.38 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.08%	2	0.52%	0.52%
-38.08% to -28.10%	5	1.29%	1.81%
-28.10% to -18.12%	11	2.84%	4.65%
-18.12% to -8.15%	58	14.99%	19.64%
-8.15% to 1.83%	127	32.82%	52.45%
1.83% to 11.80%	110	28.42%	80.88%
11.80% to 21.78%	46	11.89%	92.76%
21.78% to 31.75%	20	5.17%	97.93%
31.75% to 41.73%	5	1.29%	99.22%
Greater than 41.73%	3	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.47%	15.13%	73.64%	68.27%
±2σ	-24.77%	28.43%	94.57%	95.45%
±3σ	-38.07%	41.73%	98.71%	99.73%

Descriptive Statistics

Mean	1.828%
Standard Error	0.676%
Median	1.087%
Mode	0.000%
Standard Deviation	13.301%
Sample Variance	176.927%
Kurtosis	1.38
Skewness	0.09
Range	101.116%
Minimum	-53.648%
Maximum	47.468%
Count	387

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.383%	202	52.20%	5.941%
Negative	-8.796%	181	46.77%	-4.114%
Zero	0.000%	4	1.03%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.16%
12	1 Year	20.60%
36	3 Years	17.66%
60	5 Years	18.75%
120	10 Years	19.95%
240	20 Years	18.45%
600	50 Years	20.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.55. Further, an Excess Kurtosis of 10.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.27%	0	0.00%	0.00%
-19.27% to -8.52%	0	0.00%	0.00%
-8.52% to 2.22%	0	0.00%	0.00%
2.22% to 12.96%	63	16.24%	16.24%
12.96% to 23.70%	175	45.10%	61.34%
23.70% to 34.44%	94	24.23%	85.57%
34.44% to 45.18%	26	6.70%	92.27%
45.18% to 55.93%	16	4.12%	96.39%
55.93% to 66.67%	7	1.80%	98.20%
Greater than 66.67%	7	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.38%	38.02%	84.28%	68.27%
±2σ	-4.94%	52.34%	95.10%	95.45%
±3σ	-19.26%	66.67%	98.20%	99.73%

Descriptive Statistics

Mean	23.701%
Standard Error	0.727%
Median	20.258%
Mode	16.667%
Standard Deviation	14.322%
Sample Variance	205.112%
Kurtosis	10.84
Skewness	2.55
Range	124.018%
Minimum	5.738%
Maximum	129.756%
Count	388

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.701%	388	100.00%	23.701%
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 1.90. Further, an Excess Kurtosis of 10.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.69%	0	0.00%	0.00%
-43.69% to -32.76%	0	0.00%	0.00%
-32.76% to -21.83%	15	3.87%	3.87%
-21.83% to -10.89%	60	15.46%	19.33%
-10.89% to 0.04%	131	33.76%	53.09%
0.04% to 10.97%	118	30.41%	83.51%
10.97% to 21.91%	44	11.34%	94.85%
21.91% to 32.84%	11	2.84%	97.68%
32.84% to 43.77%	3	0.77%	98.45%
Greater than 43.77%	6	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.54%	14.62%	77.06%	68.27%
±2σ	-29.11%	29.20%	96.65%	95.45%
±3σ	-43.69%	43.77%	98.45%	99.73%

Descriptive Statistics

Mean	0.041%
Standard Error	0.740%
Median	-1.118%
Mode	-5.376%
Standard Deviation	14.578%
Sample Variance	212.532%
Kurtosis	10.87
Skewness	1.90
Range	145.072%
Minimum	-30.257%
Maximum	114.815%
Count	388

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.942%	183	47.16%	5.161%
Negative	-9.737%	204	52.58%	-5.119%
Zero	0.000%	1	0.26%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 1.88 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.43%	0	0.00%	0.00%
-61.43% to -44.79%	0	0.00%	0.00%
-44.79% to -28.14%	5	3.88%	3.88%
-28.14% to -11.50%	29	22.48%	26.36%
-11.50% to 5.14%	38	29.46%	55.81%
5.14% to 21.79%	30	23.26%	79.07%
21.79% to 38.43%	19	14.73%	93.80%
38.43% to 55.07%	6	4.65%	98.45%
55.07% to 71.72%	1	0.78%	99.22%
Greater than 71.72%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.05%	27.34%	69.77%	68.27%
±2σ	-39.24%	49.53%	97.67%	95.45%
±3σ	-61.43%	71.72%	99.22%	99.73%

Descriptive Statistics

Mean	5.144%
Standard Error	1.954%
Median	2.353%
Mode	0.000%
Standard Deviation	22.191%
Sample Variance	492.443%
Kurtosis	1.88
Skewness	0.86
Range	139.713%
Minimum	-38.636%
Maximum	101.077%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.744%	70	54.26%	11.257%
Negative	-13.833%	57	44.19%	-6.112%
Zero	0.000%	2	1.55%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	30.96%
12	3 Years	33.26%
20	5 Years	31.44%
40	10 Years	34.89%
80	20 Years	32.21%
200	50 Years	36.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.70. Further, an Excess Kurtosis of 4.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.59%	0	0.00%	0.00%
-22.59% to -6.04%	0	0.00%	0.00%
-6.04% to 10.51%	0	0.00%	0.00%
10.51% to 27.06%	23	17.69%	17.69%
27.06% to 43.61%	54	41.54%	59.23%
43.61% to 60.16%	33	25.38%	84.62%
60.16% to 76.71%	10	7.69%	92.31%
76.71% to 93.26%	6	4.62%	96.92%
93.26% to 109.81%	0	0.00%	96.92%
Greater than 109.81%	4	3.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.54%	65.67%	78.46%	68.27%
±2σ	-0.53%	87.74%	96.15%	95.45%
±3σ	-22.59%	109.81%	96.92%	99.73%

Descriptive Statistics

Mean	43.606%
Standard Error	1.935%
Median	38.286%
Mode	11.221%
Standard Deviation	22.067%
Sample Variance	486.967%
Kurtosis	4.01
Skewness	1.70
Range	124.691%
Minimum	11.221%
Maximum	135.912%
Count	130

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.606%	130	100.00%	43.606%
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 0.53. Further, an Excess Kurtosis of 0.48 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -62.03%	0	0.00%	0.00%
-62.03% to -46.71%	1	0.77%	0.77%
-46.71% to -31.40%	3	2.31%	3.08%
-31.40% to -16.08%	27	20.77%	23.85%
-16.08% to -0.76%	37	28.46%	52.31%
-0.76% to 14.56%	31	23.85%	76.15%
14.56% to 29.88%	26	20.00%	96.15%
29.88% to 45.19%	0	0.00%	96.15%
45.19% to 60.51%	4	3.08%	99.23%
Greater than 60.51%	1	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.18%	19.66%	68.46%	68.27%
±2σ	-41.61%	40.09%	95.38%	95.45%
±3σ	-62.03%	60.51%	99.23%	99.73%

Descriptive Statistics

Mean	-0.760%
Standard Error	1.791%
Median	-1.949%
Mode	-11.538%
Standard Deviation	20.424%
Sample Variance	417.126%
Kurtosis	0.48
Skewness	0.53
Range	112.848%
Minimum	-49.885%
Maximum	62.963%
Count	130

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.057%	59	45.38%	7.741%
Negative	-15.788%	70	53.85%	-8.501%
Zero	0.000%	1	0.77%	0.000%

URBN Deep Analytical Report