W - 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	4.67%	3.52%	3.80%	6.59%	5.22%	5.18%	73.12	81.17	69.40	85.52
Weekly	10.47%	10.16%	10.24%	15.63%	11.50%	11.40%	68.67	86.43	61.22	96.95
Monthly	22.83%	27.00%	20.05%	33.23%	23.93%	23.72%	60.64	97.87	47.74	124.33
Quarterly	42.77%	75.53%	37.30%	65.64%	41.45%	41.09%	50.90	116.61	33.63	176.49
Annual	—	—	—	—	82.90%	82.18%	33.63	176.49	14.68	404.33
Option Time Horizon	—	—	—	—	31.29%	31.02%	56.34	105.34	41.20	144.04

Calculation Notes: Computed at 2026-03-23T16:40 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $77.04 | Strike (K): $77.50 (first OTM call ≥ spot) | Observed Mid-Price: $9.4750 (Bid $9.2500 / Ask $9.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 82.90% (CRR binomial tree, American, n=20 steps) | BS IV: 82.19% (European Black-Scholes) | Yahoo IV (Annual): 82.18% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 9.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.87%	21	0.73%	0.73%
-13.87% to -10.37%	15	0.52%	1.25%
-10.37% to -6.87%	103	3.57%	4.82%
-6.87% to -3.37%	319	11.06%	15.89%
-3.37% to 0.13%	997	34.58%	50.47%
0.13% to 3.63%	974	33.78%	84.25%
3.63% to 7.13%	314	10.89%	95.14%
7.13% to 10.63%	86	2.98%	98.13%
10.63% to 14.13%	29	1.01%	99.13%
Greater than 14.13%	25	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.53%	4.80%	79.19%	68.27%
±2σ	-9.20%	9.47%	95.42%	95.45%
±3σ	-13.87%	14.13%	98.40%	99.73%

Descriptive Statistics

Mean	0.133%
Standard Error	0.087%
Median	0.101%
Mode	0.000%
Standard Deviation	4.667%
Sample Variance	21.780%
Kurtosis	9.34
Skewness	0.67
Range	69.521%
Minimum	-26.683%
Maximum	42.838%
Count	2883

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.214%	1479	51.30%	1.649%
Negative	-3.132%	1396	48.42%	-1.517%
Zero	0.000%	8	0.28%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.82%
20	1 Month	6.26%
60	1 Quarter	6.06%
250	1 Year	6.14%
750	3 Years	6.03%
1,250	5 Years	6.59%
2,500	10 Years	5.92%
5,000	20 Years	5.98%
12,500	50 Years	5.98%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.79%	0	0.00%	0.00%
-4.79% to -2.14%	0	0.00%	0.00%
-2.14% to 0.50%	0	0.00%	0.00%
0.50% to 3.14%	504	17.48%	17.48%
3.14% to 5.78%	1283	44.49%	61.96%
5.78% to 8.42%	658	22.82%	84.78%
8.42% to 11.06%	254	8.81%	93.59%
11.06% to 13.71%	96	3.33%	96.91%
13.71% to 16.35%	35	1.21%	98.13%
Greater than 16.35%	54	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.26%	9.30%	84.26%	68.27%
±2σ	-1.26%	12.82%	96.12%	95.45%
±3σ	-4.78%	16.35%	98.13%	99.73%

Descriptive Statistics

Mean	5.781%
Standard Error	0.066%
Median	4.957%
Mode	3.090%
Standard Deviation	3.522%
Sample Variance	12.406%
Kurtosis	13.94
Skewness	2.78
Range	39.639%
Minimum	0.897%
Maximum	40.536%
Count	2884

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.781%	2884	100.00%	5.781%
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 0.30. Further, an Excess Kurtosis of 3.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.39%	16	0.55%	0.55%
-11.39% to -8.54%	25	0.87%	1.42%
-8.54% to -5.69%	107	3.71%	5.13%
-5.69% to -2.85%	396	13.73%	18.86%
-2.85% to 0.00%	950	32.94%	51.80%
0.00% to 2.85%	880	30.51%	82.32%
2.85% to 5.70%	338	11.72%	94.04%
5.70% to 8.54%	112	3.88%	97.92%
8.54% to 11.39%	40	1.39%	99.31%
Greater than 11.39%	20	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.79%	3.80%	76.11%	68.27%
±2σ	-7.59%	7.59%	94.63%	95.45%
±3σ	-11.39%	11.39%	98.75%	99.73%

Descriptive Statistics

Mean	0.001%
Standard Error	0.071%
Median	-0.147%
Mode	-1.245%
Standard Deviation	3.796%
Sample Variance	14.406%
Kurtosis	3.75
Skewness	0.30
Range	48.684%
Minimum	-21.987%
Maximum	26.697%
Count	2884

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.867%	1390	48.20%	1.382%
Negative	-2.672%	1490	51.66%	-1.380%
Zero	0.000%	4	0.14%	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 4.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.75%	1	0.17%	0.17%
-30.75% to -22.89%	4	0.67%	0.84%
-22.89% to -15.04%	28	4.68%	5.52%
-15.04% to -7.18%	85	14.21%	19.73%
-7.18% to 0.67%	190	31.77%	51.51%
0.67% to 8.53%	187	31.27%	82.78%
8.53% to 16.38%	66	11.04%	93.81%
16.38% to 24.24%	24	4.01%	97.83%
24.24% to 32.09%	7	1.17%	99.00%
Greater than 32.09%	6	1.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.80%	11.15%	75.25%	68.27%
±2σ	-20.27%	21.62%	95.48%	95.45%
±3σ	-30.75%	32.09%	98.83%	99.73%

Descriptive Statistics

Mean	0.673%
Standard Error	0.428%
Median	0.256%
Mode	-5.627%
Standard Deviation	10.473%
Sample Variance	109.684%
Kurtosis	4.25
Skewness	0.81
Range	109.721%
Minimum	-38.860%
Maximum	70.861%
Count	598

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.180%	306	51.17%	4.186%
Negative	-7.194%	292	48.83%	-3.513%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.21%
12	1 Quarter	13.44%
52	1 Year	14.50%
156	3 Years	14.40%
260	5 Years	15.63%
520	10 Years	14.09%
1,040	20 Years	14.27%
2,600	50 Years	14.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.40. Further, an Excess Kurtosis of 8.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.99%	0	0.00%	0.00%
-14.99% to -7.37%	0	0.00%	0.00%
-7.37% to 0.26%	0	0.00%	0.00%
0.26% to 7.88%	95	15.86%	15.86%
7.88% to 15.50%	290	48.41%	64.27%
15.50% to 23.12%	131	21.87%	86.14%
23.12% to 30.74%	36	6.01%	92.15%
30.74% to 38.36%	24	4.01%	96.16%
38.36% to 45.98%	13	2.17%	98.33%
Greater than 45.98%	10	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.34%	25.66%	82.64%	68.27%
±2σ	-4.83%	35.82%	95.49%	95.45%
±3σ	-14.99%	45.98%	98.33%	99.73%

Descriptive Statistics

Mean	15.496%
Standard Error	0.415%
Median	12.663%
Mode	7.932%
Standard Deviation	10.161%
Sample Variance	103.236%
Kurtosis	8.66
Skewness	2.40
Range	80.511%
Minimum	3.598%
Maximum	84.109%
Count	599

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.496%	599	100.00%	15.496%
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 0.73. Further, an Excess Kurtosis of 3.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.23%	1	0.17%	0.17%
-30.23% to -22.55%	8	1.34%	1.50%
-22.55% to -14.87%	23	3.84%	5.34%
-14.87% to -7.19%	81	13.52%	18.86%
-7.19% to 0.49%	212	35.39%	54.26%
0.49% to 8.17%	162	27.05%	81.30%
8.17% to 15.85%	71	11.85%	93.16%
15.85% to 23.52%	26	4.34%	97.50%
23.52% to 31.20%	13	2.17%	99.67%
Greater than 31.20%	2	0.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.75%	10.73%	74.29%	68.27%
±2σ	-19.99%	20.96%	94.16%	95.45%
±3σ	-30.23%	31.20%	99.50%	99.73%

Descriptive Statistics

Mean	0.488%
Standard Error	0.418%
Median	-0.417%
Mode	-5.149%
Standard Deviation	10.238%
Sample Variance	104.813%
Kurtosis	3.85
Skewness	0.73
Range	104.874%
Minimum	-34.782%
Maximum	70.092%
Count	599

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.403%	289	48.25%	4.054%
Negative	-6.892%	310	51.75%	-3.567%
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 1.80. Further, an Excess Kurtosis of 7.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.49%	0	0.00%	0.00%
-65.49% to -48.36%	0	0.00%	0.00%
-48.36% to -31.24%	3	2.19%	2.19%
-31.24% to -14.11%	24	17.52%	19.71%
-14.11% to 3.01%	50	36.50%	56.20%
3.01% to 20.14%	37	27.01%	83.21%
20.14% to 37.26%	15	10.95%	94.16%
37.26% to 54.39%	5	3.65%	97.81%
54.39% to 71.51%	1	0.73%	98.54%
Greater than 71.51%	2	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.82%	25.85%	77.37%	68.27%
±2σ	-42.65%	48.68%	97.08%	95.45%
±3σ	-65.49%	71.51%	98.54%	99.73%

Descriptive Statistics

Mean	3.013%
Standard Error	1.951%
Median	-0.027%
Mode	-38.247%
Standard Deviation	22.833%
Sample Variance	521.347%
Kurtosis	7.41
Skewness	1.80
Range	170.358%
Minimum	-38.247%
Maximum	132.111%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.716%	67	48.91%	9.642%
Negative	-13.163%	69	50.37%	-6.630%
Zero	0.000%	1	0.73%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.62%
12	1 Year	30.35%
36	3 Years	31.42%
60	5 Years	33.23%
120	10 Years	31.59%
240	20 Years	31.60%
600	50 Years	31.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.48. Further, an Excess Kurtosis of 16.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.62%	0	0.00%	0.00%
-42.62% to -22.36%	0	0.00%	0.00%
-22.36% to -2.11%	0	0.00%	0.00%
-2.11% to 18.14%	19	13.77%	13.77%
18.14% to 38.39%	75	54.35%	68.12%
38.39% to 58.64%	28	20.29%	88.41%
58.64% to 78.89%	10	7.25%	95.65%
78.89% to 99.14%	1	0.72%	96.38%
99.14% to 119.39%	3	2.17%	98.55%
Greater than 119.39%	2	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.39%	65.39%	91.30%	68.27%
±2σ	-15.62%	92.39%	95.65%	95.45%
±3σ	-42.62%	119.39%	98.55%	99.73%

Descriptive Statistics

Mean	38.387%
Standard Error	2.299%
Median	33.785%
Mode	10.652%
Standard Deviation	27.001%
Sample Variance	729.079%
Kurtosis	16.87
Skewness	3.48
Range	188.380%
Minimum	10.652%
Maximum	199.032%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.387%	138	100.00%	38.387%
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 0.23. Further, an Excess Kurtosis of 0.36 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.01%	1	0.72%	0.72%
-59.01% to -43.97%	1	0.72%	1.45%
-43.97% to -28.93%	4	2.90%	4.35%
-28.93% to -13.89%	27	19.57%	23.91%
-13.89% to 1.15%	41	29.71%	53.62%
1.15% to 16.19%	36	26.09%	79.71%
16.19% to 31.23%	16	11.59%	91.30%
31.23% to 46.27%	9	6.52%	97.83%
46.27% to 61.31%	3	2.17%	100.00%
Greater than 61.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.91%	21.20%	71.74%	68.27%
±2σ	-38.96%	41.26%	94.93%	95.45%
±3σ	-59.01%	61.31%	99.28%	99.73%

Descriptive Statistics

Mean	1.148%
Standard Error	1.707%
Median	-0.081%
Mode	-59.884%
Standard Deviation	20.054%
Sample Variance	402.173%
Kurtosis	0.36
Skewness	0.23
Range	116.566%
Minimum	-59.884%
Maximum	56.682%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.224%	67	48.55%	8.362%
Negative	-14.222%	70	50.73%	-7.214%
Zero	0.000%	1	0.72%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.06. Further, an Excess Kurtosis of 0.85 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -118.54%	0	0.00%	0.00%
-118.54% to -86.47%	0	0.00%	0.00%
-86.47% to -54.39%	0	0.00%	0.00%
-54.39% to -22.32%	11	23.91%	23.91%
-22.32% to 9.76%	15	32.61%	56.52%
9.76% to 41.83%	11	23.91%	80.43%
41.83% to 73.91%	5	10.87%	91.30%
73.91% to 105.98%	1	2.17%	93.48%
105.98% to 138.05%	3	6.52%	100.00%
Greater than 138.05%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.01%	52.52%	69.57%	68.27%
±2σ	-75.78%	95.29%	93.48%	95.45%
±3σ	-118.54%	138.05%	100.00%	99.73%

Descriptive Statistics

Mean	9.756%
Standard Error	6.306%
Median	5.069%
Mode	-50.654%
Standard Deviation	42.766%
Sample Variance	1828.969%
Kurtosis	0.85
Skewness	1.06
Range	174.226%
Minimum	-50.654%
Maximum	123.572%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.143%	25	54.35%	20.730%
Negative	-24.037%	21	45.65%	-10.973%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	64.68%
12	3 Years	66.37%
20	5 Years	65.64%
40	10 Years	60.02%
80	20 Years	59.05%
200	50 Years	59.05%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.38. Further, an Excess Kurtosis of 24.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -141.09%	0	0.00%	0.00%
-141.09% to -84.44%	0	0.00%	0.00%
-84.44% to -27.80%	0	0.00%	0.00%
-27.80% to 28.84%	1	2.13%	2.13%
28.84% to 85.49%	33	70.21%	72.34%
85.49% to 142.13%	8	17.02%	89.36%
142.13% to 198.78%	4	8.51%	97.87%
198.78% to 255.42%	0	0.00%	97.87%
255.42% to 312.06%	0	0.00%	97.87%
Greater than 312.06%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.96%	161.01%	93.62%	68.27%
±2σ	-65.56%	236.54%	97.87%	95.45%
±3σ	-141.09%	312.06%	97.87%	99.73%

Descriptive Statistics

Mean	85.488%
Standard Error	11.016%
Median	65.439%
Mode	27.801%
Standard Deviation	75.525%
Sample Variance	5703.982%
Kurtosis	24.40
Skewness	4.38
Range	493.397%
Minimum	27.801%
Maximum	521.198%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	85.488%	47	100.00%	85.488%
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 0.59. Further, an Excess Kurtosis of -0.10 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -107.73%	0	0.00%	0.00%
-107.73% to -79.76%	0	0.00%	0.00%
-79.76% to -51.78%	2	4.26%	4.26%
-51.78% to -23.81%	8	17.02%	21.28%
-23.81% to 4.16%	18	38.30%	59.57%
4.16% to 32.14%	8	17.02%	76.60%
32.14% to 60.11%	8	17.02%	93.62%
60.11% to 88.09%	2	4.26%	97.87%
88.09% to 116.06%	1	2.13%	100.00%
Greater than 116.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.13%	41.46%	63.83%	68.27%
±2σ	-70.43%	78.76%	95.74%	95.45%
±3σ	-107.73%	116.06%	100.00%	99.73%

Descriptive Statistics

Mean	4.164%
Standard Error	5.441%
Median	-6.394%
Mode	-55.554%
Standard Deviation	37.299%
Sample Variance	1391.209%
Kurtosis	-0.10
Skewness	0.59
Range	159.011%
Minimum	-55.554%
Maximum	103.457%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.754%	21	44.68%	16.869%
Negative	-22.967%	26	55.32%	-12.705%
Zero	0.000%	0	0.00%	0.000%

W Deep Analytical Report