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%	3.14%	3.46%	5.11%	4.71%	4.71%	10.79	11.86	10.30	12.43
Weekly	8.72%	8.38%	8.35%	12.19%	10.36%	10.37%	10.20	12.55	9.20	13.92
Monthly	18.45%	16.00%	17.11%	26.30%	21.56%	21.59%	9.12	14.04	7.35	17.42
Quarterly	34.35%	26.51%	30.48%	48.35%	37.35%	37.40%	7.79	16.44	5.36	23.88
Annual	—	—	—	—	74.70%	74.80%	5.36	23.88	2.54	50.41
Option Time Horizon	—	—	—	—	28.20%	28.23%	8.53	15.00	6.44	19.89

Calculation Notes: Computed at 2026-03-23T16:36 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $11.31 | Strike (K): $12.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.8500 (Bid $0.8000 / Ask $0.9000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 74.70% (CRR binomial tree, American, n=20 steps) | BS IV: 74.99% (European Black-Scholes) | Yahoo IV (Annual): 74.80% → 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 16.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.22%	12	0.64%	0.64%
-12.22% to -9.15%	12	0.64%	1.28%
-9.15% to -6.08%	53	2.83%	4.11%
-6.08% to -3.02%	233	12.43%	16.53%
-3.02% to 0.05%	665	35.47%	52.00%
0.05% to 3.11%	584	31.15%	83.15%
3.11% to 6.18%	219	11.68%	94.83%
6.18% to 9.25%	63	3.36%	98.19%
9.25% to 12.31%	19	1.01%	99.20%
Greater than 12.31%	15	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.04%	4.14%	79.09%	68.27%
±2σ	-8.13%	8.22%	95.68%	95.45%
±3σ	-12.22%	12.31%	98.56%	99.73%

Descriptive Statistics

Mean	0.048%
Standard Error	0.094%
Median	-0.125%
Mode	0.000%
Standard Deviation	4.088%
Sample Variance	16.714%
Kurtosis	16.62
Skewness	1.48
Range	63.286%
Minimum	-19.053%
Maximum	44.233%
Count	1875

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.942%	901	48.05%	1.414%
Negative	-2.673%	958	51.09%	-1.366%
Zero	0.000%	16	0.85%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.43%
20	1 Month	4.79%
60	1 Quarter	5.65%
250	1 Year	4.69%
750	3 Years	4.55%
1,250	5 Years	5.11%
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 2.78. Further, an Excess Kurtosis of 13.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.21%	0	0.00%	0.00%
-4.21% to -1.86%	0	0.00%	0.00%
-1.86% to 0.49%	0	0.00%	0.00%
0.49% to 2.85%	321	17.11%	17.11%
2.85% to 5.20%	859	45.79%	62.90%
5.20% to 7.55%	420	22.39%	85.29%
7.55% to 9.90%	142	7.57%	92.86%
9.90% to 12.25%	71	3.78%	96.64%
12.25% to 14.61%	32	1.71%	98.35%
Greater than 14.61%	31	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.06%	8.33%	85.13%	68.27%
±2σ	-1.08%	11.47%	95.84%	95.45%
±3σ	-4.21%	14.61%	98.35%	99.73%

Descriptive Statistics

Mean	5.197%
Standard Error	0.072%
Median	4.447%
Mode	4.530%
Standard Deviation	3.136%
Sample Variance	9.835%
Kurtosis	13.31
Skewness	2.78
Range	31.815%
Minimum	1.126%
Maximum	32.941%
Count	1876

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.197%	1876	100.00%	5.197%
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 0.35. Further, an Excess Kurtosis of 3.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.19%	12	0.64%	0.64%
-10.19% to -7.60%	20	1.07%	1.71%
-7.60% to -5.00%	73	3.89%	5.60%
-5.00% to -2.41%	226	12.05%	17.64%
-2.41% to 0.18%	608	32.41%	50.05%
0.18% to 2.77%	605	32.25%	82.30%
2.77% to 5.37%	221	11.78%	94.08%
5.37% to 7.96%	73	3.89%	97.97%
7.96% to 10.55%	22	1.17%	99.15%
Greater than 10.55%	16	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.27%	3.64%	75.48%	68.27%
±2σ	-6.73%	7.10%	94.88%	95.45%
±3σ	-10.19%	10.55%	98.51%	99.73%

Descriptive Statistics

Mean	0.182%
Standard Error	0.080%
Median	0.177%
Mode	0.000%
Standard Deviation	3.457%
Sample Variance	11.953%
Kurtosis	3.71
Skewness	0.35
Range	41.276%
Minimum	-17.647%
Maximum	23.629%
Count	1876

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.577%	976	52.03%	1.341%
Negative	-2.490%	873	46.53%	-1.159%
Zero	0.000%	27	1.44%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.81. 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 -25.93%	1	0.26%	0.26%
-25.93% to -19.39%	4	1.03%	1.29%
-19.39% to -12.85%	10	2.57%	3.86%
-12.85% to -6.32%	57	14.65%	18.51%
-6.32% to 0.22%	139	35.73%	54.24%
0.22% to 6.76%	106	27.25%	81.49%
6.76% to 13.30%	46	11.83%	93.32%
13.30% to 19.83%	17	4.37%	97.69%
19.83% to 26.37%	6	1.54%	99.23%
Greater than 26.37%	3	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.49%	8.94%	78.15%	68.27%
±2σ	-17.21%	17.65%	93.83%	95.45%
±3σ	-25.93%	26.37%	98.97%	99.73%

Descriptive Statistics

Mean	0.222%
Standard Error	0.442%
Median	-0.414%
Mode	0.000%
Standard Deviation	8.716%
Sample Variance	75.977%
Kurtosis	3.78
Skewness	0.81
Range	78.104%
Minimum	-29.590%
Maximum	48.514%
Count	389

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.790%	186	47.81%	3.247%
Negative	-5.853%	201	51.67%	-3.024%
Zero	0.000%	2	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.40%
12	1 Quarter	13.99%
52	1 Year	11.21%
156	3 Years	10.96%
260	5 Years	12.19%
520	10 Years	12.60%
1,040	20 Years	12.60%
2,600	50 Years	12.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.29. 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 -11.62%	0	0.00%	0.00%
-11.62% to -5.33%	0	0.00%	0.00%
-5.33% to 0.96%	0	0.00%	0.00%
0.96% to 7.25%	74	18.97%	18.97%
7.25% to 13.54%	168	43.08%	62.05%
13.54% to 19.83%	89	22.82%	84.87%
19.83% to 26.11%	30	7.69%	92.56%
26.11% to 32.40%	15	3.85%	96.41%
32.40% to 38.69%	7	1.79%	98.21%
Greater than 38.69%	7	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.15%	21.92%	84.62%	68.27%
±2σ	-3.23%	30.31%	94.10%	95.45%
±3σ	-11.62%	38.69%	98.21%	99.73%

Descriptive Statistics

Mean	13.537%
Standard Error	0.425%
Median	11.342%
Mode	8.389%
Standard Deviation	8.385%
Sample Variance	70.313%
Kurtosis	8.18
Skewness	2.29
Range	62.611%
Minimum	2.897%
Maximum	65.508%
Count	390

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.537%	390	100.00%	13.537%
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 0.14. Further, an Excess Kurtosis of 1.80 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.34%	2	0.51%	0.51%
-24.34% to -18.07%	2	0.51%	1.03%
-18.07% to -11.81%	20	5.13%	6.15%
-11.81% to -5.55%	52	13.33%	19.49%
-5.55% to 0.71%	121	31.03%	50.51%
0.71% to 6.98%	121	31.03%	81.54%
6.98% to 13.24%	48	12.31%	93.85%
13.24% to 19.50%	15	3.85%	97.69%
19.50% to 25.76%	7	1.79%	99.49%
Greater than 25.76%	2	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.64%	9.06%	73.85%	68.27%
±2σ	-15.99%	17.41%	95.13%	95.45%
±3σ	-24.34%	25.76%	98.97%	99.73%

Descriptive Statistics

Mean	0.714%
Standard Error	0.423%
Median	0.574%
Mode	0.000%
Standard Deviation	8.350%
Sample Variance	69.725%
Kurtosis	1.80
Skewness	0.14
Range	66.246%
Minimum	-32.773%
Maximum	33.473%
Count	390

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.482%	208	53.33%	3.457%
Negative	-5.977%	179	45.90%	-2.743%
Zero	0.000%	3	0.77%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.18. Further, an Excess Kurtosis of 2.48 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.42%	0	0.00%	0.00%
-54.42% to -40.58%	0	0.00%	0.00%
-40.58% to -26.74%	1	1.12%	1.12%
-26.74% to -12.90%	20	22.47%	23.60%
-12.90% to 0.94%	29	32.58%	56.18%
0.94% to 14.78%	22	24.72%	80.90%
14.78% to 28.62%	9	10.11%	91.01%
28.62% to 42.46%	6	6.74%	97.75%
42.46% to 56.30%	1	1.12%	98.88%
Greater than 56.30%	1	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.52%	19.39%	70.79%	68.27%
±2σ	-35.97%	37.85%	96.63%	95.45%
±3σ	-54.42%	56.30%	98.88%	99.73%

Descriptive Statistics

Mean	0.938%
Standard Error	1.956%
Median	-2.791%
Mode	-33.001%
Standard Deviation	18.454%
Sample Variance	340.543%
Kurtosis	2.48
Skewness	1.18
Range	110.345%
Minimum	-33.001%
Maximum	77.344%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.743%	42	47.19%	7.429%
Negative	-12.292%	47	52.81%	-6.491%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.16%
12	1 Year	25.49%
36	3 Years	24.70%
60	5 Years	26.30%
120	10 Years	28.07%
240	20 Years	28.07%
600	50 Years	28.07%

High-to-Low 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 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 -15.06%	0	0.00%	0.00%
-15.06% to -3.06%	0	0.00%	0.00%
-3.06% to 8.93%	1	1.11%	1.11%
8.93% to 20.93%	22	24.44%	25.56%
20.93% to 32.93%	24	26.67%	52.22%
32.93% to 44.93%	31	34.44%	86.67%
44.93% to 56.93%	5	5.56%	92.22%
56.93% to 68.93%	3	3.33%	95.56%
68.93% to 80.92%	3	3.33%	98.89%
Greater than 80.92%	1	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.93%	48.93%	78.89%	68.27%
±2σ	0.93%	64.93%	94.44%	95.45%
±3σ	-15.06%	80.92%	98.89%	99.73%

Descriptive Statistics

Mean	32.931%
Standard Error	1.686%
Median	30.427%
Mode	8.416%
Standard Deviation	15.998%
Sample Variance	255.945%
Kurtosis	3.26
Skewness	1.48
Range	91.584%
Minimum	8.416%
Maximum	100.000%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.931%	90	100.00%	32.931%
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 -0.10. Further, an Excess Kurtosis of 0.04 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.87%	0	0.00%	0.00%
-48.87% to -36.04%	1	1.11%	1.11%
-36.04% to -23.20%	5	5.56%	6.67%
-23.20% to -10.37%	16	17.78%	24.44%
-10.37% to 2.47%	22	24.44%	48.89%
2.47% to 15.30%	28	31.11%	80.00%
15.30% to 28.14%	12	13.33%	93.33%
28.14% to 40.97%	5	5.56%	98.89%
40.97% to 53.81%	1	1.11%	100.00%
Greater than 53.81%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.65%	19.58%	68.89%	68.27%
±2σ	-31.76%	36.69%	96.67%	95.45%
±3σ	-48.87%	53.81%	100.00%	99.73%

Descriptive Statistics

Mean	2.467%
Standard Error	1.804%
Median	4.092%
Mode	-43.643%
Standard Deviation	17.113%
Sample Variance	292.864%
Kurtosis	0.04
Skewness	-0.10
Range	92.823%
Minimum	-43.643%
Maximum	49.180%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.910%	49	54.44%	8.118%
Negative	-12.403%	41	45.56%	-5.650%
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 1.81. Further, an Excess Kurtosis of 4.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -100.20%	0	0.00%	0.00%
-100.20% to -74.44%	0	0.00%	0.00%
-74.44% to -48.67%	0	0.00%	0.00%
-48.67% to -22.91%	5	16.67%	16.67%
-22.91% to 2.85%	12	40.00%	56.67%
2.85% to 28.61%	9	30.00%	86.67%
28.61% to 54.37%	2	6.67%	93.33%
54.37% to 80.13%	0	0.00%	93.33%
80.13% to 105.89%	1	3.33%	96.67%
Greater than 105.89%	1	3.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.50%	37.20%	83.33%	68.27%
±2σ	-65.85%	71.54%	93.33%	95.45%
±3σ	-100.20%	105.89%	96.67%	99.73%

Descriptive Statistics

Mean	2.847%
Standard Error	6.271%
Median	-1.725%
Mode	-43.285%
Standard Deviation	34.348%
Sample Variance	1179.796%
Kurtosis	4.97
Skewness	1.81
Range	167.946%
Minimum	-43.285%
Maximum	124.661%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.765%	15	50.00%	12.882%
Negative	-20.072%	15	50.00%	-10.036%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	53.85%
12	3 Years	47.80%
20	5 Years	48.35%
40	10 Years	52.15%
80	20 Years	52.15%
200	50 Years	52.15%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.35. Further, an Excess Kurtosis of 2.50 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.23%	0	0.00%	0.00%
-13.23% to 6.65%	0	0.00%	0.00%
6.65% to 26.53%	0	0.00%	0.00%
26.53% to 46.41%	8	25.81%	25.81%
46.41% to 66.29%	9	29.03%	54.84%
66.29% to 86.18%	8	25.81%	80.65%
86.18% to 106.06%	3	9.68%	90.32%
106.06% to 125.94%	2	6.45%	96.77%
125.94% to 145.82%	0	0.00%	96.77%
Greater than 145.82%	1	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	39.78%	92.80%	77.42%	68.27%
±2σ	13.28%	119.31%	93.55%	95.45%
±3σ	-13.23%	145.82%	96.77%	99.73%

Descriptive Statistics

Mean	66.294%
Standard Error	4.761%
Median	62.720%
Mode	31.683%
Standard Deviation	26.509%
Sample Variance	702.737%
Kurtosis	2.50
Skewness	1.35
Range	119.272%
Minimum	31.683%
Maximum	150.955%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	66.294%	31	100.00%	66.294%
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 0.52. Further, an Excess Kurtosis of 0.72 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.71%	0	0.00%	0.00%
-84.71% to -61.85%	0	0.00%	0.00%
-61.85% to -38.99%	2	6.45%	6.45%
-38.99% to -16.13%	4	12.90%	19.35%
-16.13% to 6.73%	9	29.03%	48.39%
6.73% to 29.59%	10	32.26%	80.65%
29.59% to 52.45%	3	9.68%	90.32%
52.45% to 75.31%	1	3.23%	93.55%
75.31% to 98.17%	2	6.45%	100.00%
Greater than 98.17%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.75%	37.21%	74.19%	68.27%
±2σ	-54.23%	67.69%	90.32%	95.45%
±3σ	-84.71%	98.17%	100.00%	99.73%

Descriptive Statistics

Mean	6.730%
Standard Error	5.474%
Median	7.253%
Mode	-55.513%
Standard Deviation	30.481%
Sample Variance	929.070%
Kurtosis	0.72
Skewness	0.52
Range	131.745%
Minimum	-55.513%
Maximum	76.232%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.885%	17	54.84%	14.743%
Negative	-17.743%	14	45.16%	-8.013%
Zero	0.000%	0	0.00%	0.000%

UPWK Deep Analytical Report