UPWK - 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	4.09%	3.15%	3.46%	5.15%	3.86%	3.91%	12.67	13.69	12.19	14.23
Weekly	8.73%	8.43%	8.36%	12.29%	8.49%	8.60%	12.10	14.34	11.11	15.61
Monthly	18.50%	15.97%	17.26%	26.41%	17.67%	17.90%	11.04	15.72	9.25	18.75
Quarterly	33.97%	26.20%	28.91%	47.94%	30.60%	31.01%	9.70	17.89	7.14	24.29
Annual	—	—	—	—	61.21%	62.01%	7.14	24.29	3.87	44.79
Option Time Horizon	—	—	—	—	23.54%	23.85%	10.41	16.67	8.22	21.09

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $13.17 | Strike (K): $15.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.6250 (Bid $0.5500 / Ask $0.7000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 61.21% (CRR binomial tree, American, n=20 steps) | BS IV: 61.41% (European Black-Scholes) | Yahoo IV (Annual): 62.01% → 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 1.48. Further, an Excess Kurtosis of 16.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.23%	12	0.65%	0.65%
-12.23% to -9.16%	12	0.65%	1.29%
-9.16% to -6.09%	51	2.75%	4.05%
-6.09% to -3.02%	230	12.41%	16.45%
-3.02% to 0.06%	661	35.65%	52.10%
0.06% to 3.13%	581	31.34%	83.44%
3.13% to 6.20%	211	11.38%	94.82%
6.20% to 9.27%	62	3.34%	98.17%
9.27% to 12.34%	19	1.02%	99.19%
Greater than 12.34%	15	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.04%	4.15%	79.18%	68.27%
±2σ	-8.13%	8.25%	95.69%	95.45%
±3σ	-12.23%	12.34%	98.54%	99.73%

Descriptive Statistics

Mean	0.056%
Standard Error	0.095%
Median	-0.100%
Mode	0.000%
Standard Deviation	4.095%
Sample Variance	16.770%
Kurtosis	16.68
Skewness	1.48
Range	63.286%
Minimum	-19.053%
Maximum	44.233%
Count	1854

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.948%	892	48.11%	1.418%
Negative	-2.670%	946	51.02%	-1.362%
Zero	0.000%	16	0.86%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.97%
20	1 Month	7.74%
60	1 Quarter	5.61%
250	1 Year	4.68%
750	3 Years	4.55%
1,250	5 Years	5.15%
2,500	10 Years	5.31%
5,000	20 Years	5.31%
12,500	50 Years	5.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.77. Further, an Excess Kurtosis of 13.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.24%	0	0.00%	0.00%
-4.24% to -1.88%	0	0.00%	0.00%
-1.88% to 0.48%	0	0.00%	0.00%
0.48% to 2.84%	316	17.04%	17.04%
2.84% to 5.20%	850	45.82%	62.86%
5.20% to 7.56%	419	22.59%	85.44%
7.56% to 9.92%	136	7.33%	92.78%
9.92% to 12.28%	71	3.83%	96.60%
12.28% to 14.64%	32	1.73%	98.33%
Greater than 14.64%	31	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.05%	8.35%	85.12%	68.27%
±2σ	-1.10%	11.50%	95.80%	95.45%
±3σ	-4.24%	14.64%	98.33%	99.73%

Descriptive Statistics

Mean	5.201%
Standard Error	0.073%
Median	4.447%
Mode	4.530%
Standard Deviation	3.148%
Sample Variance	9.912%
Kurtosis	13.23
Skewness	2.77
Range	31.815%
Minimum	1.126%
Maximum	32.941%
Count	1855

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.201%	1855	100.00%	5.201%
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 0.36. Further, an Excess Kurtosis of 3.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.20%	12	0.65%	0.65%
-10.20% to -7.61%	20	1.08%	1.73%
-7.61% to -5.01%	70	3.77%	5.50%
-5.01% to -2.42%	226	12.18%	17.68%
-2.42% to 0.18%	600	32.35%	50.03%
0.18% to 2.78%	599	32.29%	82.32%
2.78% to 5.38%	218	11.75%	94.07%
5.38% to 7.97%	72	3.88%	97.95%
7.97% to 10.57%	22	1.19%	99.14%
Greater than 10.57%	16	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.28%	3.64%	75.63%	68.27%
±2σ	-6.74%	7.11%	94.93%	95.45%
±3σ	-10.20%	10.57%	98.49%	99.73%

Descriptive Statistics

Mean	0.182%
Standard Error	0.080%
Median	0.181%
Mode	0.000%
Standard Deviation	3.462%
Sample Variance	11.985%
Kurtosis	3.73
Skewness	0.36
Range	41.276%
Minimum	-17.647%
Maximum	23.629%
Count	1855

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.576%	966	52.08%	1.341%
Negative	-2.488%	864	46.58%	-1.159%
Zero	0.000%	25	1.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.80. Further, an Excess Kurtosis of 3.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.94%	1	0.26%	0.26%
-25.94% to -19.39%	4	1.04%	1.30%
-19.39% to -12.84%	11	2.86%	4.16%
-12.84% to -6.29%	55	14.29%	18.44%
-6.29% to 0.26%	139	36.10%	54.55%
0.26% to 6.81%	104	27.01%	81.56%
6.81% to 13.36%	45	11.69%	93.25%
13.36% to 19.91%	17	4.42%	97.66%
19.91% to 26.46%	6	1.56%	99.22%
Greater than 26.46%	3	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.47%	8.99%	77.92%	68.27%
±2σ	-17.21%	17.73%	93.77%	95.45%
±3σ	-25.94%	26.46%	98.96%	99.73%

Descriptive Statistics

Mean	0.260%
Standard Error	0.445%
Median	-0.414%
Mode	0.000%
Standard Deviation	8.733%
Sample Variance	76.262%
Kurtosis	3.78
Skewness	0.80
Range	78.104%
Minimum	-29.590%
Maximum	48.514%
Count	385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.829%	184	47.79%	3.264%
Negative	-5.810%	199	51.69%	-3.003%
Zero	0.000%	2	0.52%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	19.41%
12	1 Quarter	13.03%
52	1 Year	11.11%
156	3 Years	11.00%
260	5 Years	12.29%
520	10 Years	12.61%
1,040	20 Years	12.61%
2,600	50 Years	12.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.28. 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 -11.74%	0	0.00%	0.00%
-11.74% to -5.42%	0	0.00%	0.00%
-5.42% to 0.91%	0	0.00%	0.00%
0.91% to 7.22%	73	18.91%	18.91%
7.22% to 13.54%	167	43.26%	62.18%
13.54% to 19.86%	87	22.54%	84.72%
19.86% to 26.18%	30	7.77%	92.49%
26.18% to 32.51%	15	3.89%	96.37%
32.51% to 38.83%	7	1.81%	98.19%
Greater than 38.83%	7	1.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.12%	21.97%	84.72%	68.27%
±2σ	-3.31%	30.40%	94.04%	95.45%
±3σ	-11.74%	38.83%	98.19%	99.73%

Descriptive Statistics

Mean	13.545%
Standard Error	0.429%
Median	11.288%
Mode	8.389%
Standard Deviation	8.427%
Sample Variance	71.007%
Kurtosis	8.07
Skewness	2.28
Range	62.611%
Minimum	2.897%
Maximum	65.508%
Count	386

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.545%	386	100.00%	13.545%
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 0.15. Further, an Excess Kurtosis of 1.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.40%	2	0.52%	0.52%
-24.40% to -18.13%	2	0.52%	1.04%
-18.13% to -11.86%	20	5.18%	6.22%
-11.86% to -5.59%	52	13.47%	19.69%
-5.59% to 0.69%	120	31.09%	50.78%
0.69% to 6.96%	119	30.83%	81.61%
6.96% to 13.23%	47	12.18%	93.78%
13.23% to 19.50%	15	3.89%	97.67%
19.50% to 25.77%	7	1.81%	99.48%
Greater than 25.77%	2	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.68%	9.05%	74.09%	68.27%
±2σ	-16.04%	17.41%	95.08%	95.45%
±3σ	-24.40%	25.77%	98.96%	99.73%

Descriptive Statistics

Mean	0.685%
Standard Error	0.426%
Median	0.574%
Mode	0.000%
Standard Deviation	8.363%
Sample Variance	69.941%
Kurtosis	1.82
Skewness	0.15
Range	66.246%
Minimum	-32.773%
Maximum	33.473%
Count	386

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.437%	206	53.37%	3.435%
Negative	-5.999%	177	45.85%	-2.751%
Zero	0.000%	3	0.78%	0.000%

Close-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 2.46 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.40%	0	0.00%	0.00%
-54.40% to -40.52%	0	0.00%	0.00%
-40.52% to -26.65%	1	1.14%	1.14%
-26.65% to -12.77%	19	21.59%	22.73%
-12.77% to 1.11%	31	35.23%	57.95%
1.11% to 14.99%	20	22.73%	80.68%
14.99% to 28.86%	10	11.36%	92.05%
28.86% to 42.74%	5	5.68%	97.73%
42.74% to 56.62%	1	1.14%	98.86%
Greater than 56.62%	1	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.39%	19.61%	70.45%	68.27%
±2σ	-35.90%	38.12%	96.59%	95.45%
±3σ	-54.40%	56.62%	98.86%	99.73%

Descriptive Statistics

Mean	1.109%
Standard Error	1.972%
Median	-2.019%
Mode	-34.249%
Standard Deviation	18.503%
Sample Variance	342.370%
Kurtosis	2.46
Skewness	1.16
Range	111.593%
Minimum	-34.249%
Maximum	77.344%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.743%	42	47.73%	7.514%
Negative	-12.253%	46	52.27%	-6.405%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	26.19%
12	1 Year	25.47%
36	3 Years	24.66%
60	5 Years	26.41%
120	10 Years	28.13%
240	20 Years	28.13%
600	50 Years	28.13%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.46. Further, an Excess Kurtosis of 3.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.93%	0	0.00%	0.00%
-14.93% to -2.96%	0	0.00%	0.00%
-2.96% to 9.02%	1	1.12%	1.12%
9.02% to 21.00%	23	25.84%	26.97%
21.00% to 32.97%	22	24.72%	51.69%
32.97% to 44.95%	31	34.83%	86.52%
44.95% to 56.92%	5	5.62%	92.13%
56.92% to 68.90%	3	3.37%	95.51%
68.90% to 80.88%	3	3.37%	98.88%
Greater than 80.88%	1	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.00%	48.94%	78.65%	68.27%
±2σ	1.04%	64.91%	95.51%	95.45%
±3σ	-14.93%	80.88%	98.88%	99.73%

Descriptive Statistics

Mean	32.973%
Standard Error	1.693%
Median	30.624%
Mode	8.416%
Standard Deviation	15.968%
Sample Variance	254.968%
Kurtosis	3.26
Skewness	1.46
Range	91.584%
Minimum	8.416%
Maximum	100.000%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.973%	89	100.00%	32.973%
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 -0.04. Further, an Excess Kurtosis of 0.14 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -49.40%	0	0.00%	0.00%
-49.40% to -36.46%	1	1.12%	1.12%
-36.46% to -23.51%	5	5.62%	6.74%
-23.51% to -10.57%	16	17.98%	24.72%
-10.57% to 2.37%	22	24.72%	49.44%
2.37% to 15.31%	27	30.34%	79.78%
15.31% to 28.26%	12	13.48%	93.26%
28.26% to 41.20%	5	5.62%	98.88%
41.20% to 54.14%	1	1.12%	100.00%
Greater than 54.14%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.89%	19.63%	68.54%	68.27%
±2σ	-32.14%	36.89%	96.63%	95.45%
±3σ	-49.40%	54.14%	100.00%	99.73%

Descriptive Statistics

Mean	2.372%
Standard Error	1.829%
Median	4.026%
Mode	-43.643%
Standard Deviation	17.257%
Sample Variance	297.816%
Kurtosis	0.14
Skewness	-0.04
Range	95.655%
Minimum	-43.643%
Maximum	52.012%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.992%	48	53.93%	8.086%
Negative	-12.403%	41	46.07%	-5.714%
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 1.89. Further, an Excess Kurtosis of 5.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -98.75%	0	0.00%	0.00%
-98.75% to -73.28%	0	0.00%	0.00%
-73.28% to -47.80%	0	0.00%	0.00%
-47.80% to -22.33%	6	20.00%	20.00%
-22.33% to 3.15%	11	36.67%	56.67%
3.15% to 28.62%	9	30.00%	86.67%
28.62% to 54.10%	2	6.67%	93.33%
54.10% to 79.57%	0	0.00%	93.33%
79.57% to 105.05%	1	3.33%	96.67%
Greater than 105.05%	1	3.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.82%	37.12%	83.33%	68.27%
±2σ	-64.79%	71.08%	93.33%	95.45%
±3σ	-98.75%	105.05%	96.67%	99.73%

Descriptive Statistics

Mean	3.148%
Standard Error	6.202%
Median	-1.725%
Mode	-42.275%
Standard Deviation	33.967%
Sample Variance	1153.769%
Kurtosis	5.18
Skewness	1.89
Range	166.936%
Minimum	-42.275%
Maximum	124.661%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.765%	15	50.00%	12.882%
Negative	-19.469%	15	50.00%	-9.734%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	51.80%
12	3 Years	47.11%
20	5 Years	47.94%
40	10 Years	51.88%
80	20 Years	51.88%
200	50 Years	51.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.47. Further, an Excess Kurtosis of 2.95 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.10%	0	0.00%	0.00%
-13.10% to 6.56%	0	0.00%	0.00%
6.56% to 26.21%	0	0.00%	0.00%
26.21% to 45.86%	7	22.58%	22.58%
45.86% to 65.51%	11	35.48%	58.06%
65.51% to 85.17%	8	25.81%	83.87%
85.17% to 104.82%	2	6.45%	90.32%
104.82% to 124.47%	2	6.45%	96.77%
124.47% to 144.12%	0	0.00%	96.77%
Greater than 144.12%	1	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	39.31%	91.72%	77.42%	68.27%
±2σ	13.11%	117.92%	93.55%	95.45%
±3σ	-13.10%	144.12%	96.77%	99.73%

Descriptive Statistics

Mean	65.513%
Standard Error	4.706%
Median	62.720%
Mode	31.683%
Standard Deviation	26.203%
Sample Variance	686.600%
Kurtosis	2.95
Skewness	1.47
Range	119.272%
Minimum	31.683%
Maximum	150.955%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	65.513%	31	100.00%	65.513%
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 0.34. Further, an Excess Kurtosis of 0.60 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.78%	0	0.00%	0.00%
-80.78% to -59.10%	0	0.00%	0.00%
-59.10% to -37.42%	2	6.45%	6.45%
-37.42% to -15.73%	4	12.90%	19.35%
-15.73% to 5.95%	9	29.03%	48.39%
5.95% to 27.63%	10	32.26%	80.65%
27.63% to 49.31%	3	9.68%	90.32%
49.31% to 71.00%	2	6.45%	96.77%
71.00% to 92.68%	1	3.23%	100.00%
Greater than 92.68%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.96%	34.86%	70.97%	68.27%
±2σ	-51.87%	63.77%	90.32%	95.45%
±3σ	-80.78%	92.68%	100.00%	99.73%

Descriptive Statistics

Mean	5.949%
Standard Error	5.192%
Median	7.253%
Mode	-55.513%
Standard Deviation	28.910%
Sample Variance	835.771%
Kurtosis	0.60
Skewness	0.34
Range	131.506%
Minimum	-55.513%
Maximum	75.993%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.460%	17	54.84%	13.962%
Negative	-17.743%	14	45.16%	-8.013%
Zero	0.000%	0	0.00%	0.000%

UPWK Deep Analytical Report