EXAS - 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	4.44%	5.19%	4.01%	4.55%	—	0.03%	—	—	—	—
Weekly	10.44%	13.05%	10.04%	10.44%	—	0.07%	—	—	—	—
Monthly	21.27%	30.70%	20.29%	22.13%	—	0.16%	—	—	—	—
Quarterly	38.49%	83.45%	40.00%	41.05%	—	0.27%	—	—	—	—
Annual	—	—	—	—	—	0.54%	—	—	—	—
Option Time Horizon	—	—	—	—	—	0.21%	—	—	—	—

Calculation Notes: Computed at 2026-03-22T12:18 UTC | Reference Contract: Call option expiring 2026-05-15 (54 days) | Spot Price (S): $104.91 | Strike (K): $105.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0250 (Bid $0.0000 / Ask $0.0500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 0.00% (CRR binomial tree, American, n=20 steps) | BS IV: — (European Black-Scholes) | Yahoo IV (Annual): 0.54% → 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 1.55. Further, an Excess Kurtosis of 22.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.20%	27	0.43%	0.43%
-13.20% to -9.87%	41	0.65%	1.08%
-9.87% to -6.53%	176	2.79%	3.86%
-6.53% to -3.20%	685	10.84%	14.70%
-3.20% to 0.13%	2418	38.27%	52.98%
0.13% to 3.46%	2110	33.40%	86.37%
3.46% to 6.79%	591	9.35%	95.73%
6.79% to 10.12%	161	2.55%	98.27%
10.12% to 13.45%	53	0.84%	99.11%
Greater than 13.45%	56	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.31%	4.57%	82.24%	68.27%
±2σ	-8.75%	9.01%	96.07%	95.45%
±3σ	-13.20%	13.45%	98.69%	99.73%

Descriptive Statistics

Mean	0.127%
Standard Error	0.056%
Median	0.000%
Mode	0.000%
Standard Deviation	4.441%
Sample Variance	19.720%
Kurtosis	22.19
Skewness	1.55
Range	99.809%
Minimum	-46.141%
Maximum	53.668%
Count	6318

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.018%	3071	48.61%	1.467%
Negative	-2.744%	3086	48.84%	-1.340%
Zero	0.000%	161	2.55%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	0.42%
20	1 Month	0.33%
60	1 Quarter	0.33%
250	1 Year	2.97%
750	3 Years	3.85%
1,250	5 Years	4.55%
2,500	10 Years	4.79%
5,000	20 Years	5.59%
12,500	50 Years	5.69%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.32. Further, an Excess Kurtosis of 97.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.87%	0	0.00%	0.00%
-9.87% to -5.97%	0	0.00%	0.00%
-5.97% to -2.08%	0	0.00%	0.00%
-2.08% to 1.82%	249	3.94%	3.94%
1.82% to 5.71%	3919	62.02%	65.96%
5.71% to 9.61%	1488	23.55%	89.51%
9.61% to 13.50%	387	6.12%	95.63%
13.50% to 17.39%	128	2.03%	97.66%
17.39% to 21.29%	65	1.03%	98.69%
Greater than 21.29%	83	1.31%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.52%	10.90%	90.93%	68.27%
±2σ	-4.67%	16.09%	97.23%	95.45%
±3σ	-9.87%	21.29%	98.69%	99.73%

Descriptive Statistics

Mean	5.711%
Standard Error	0.065%
Median	4.514%
Mode	6.667%
Standard Deviation	5.192%
Sample Variance	26.962%
Kurtosis	97.56
Skewness	7.32
Range	113.560%
Minimum	0.076%
Maximum	113.636%
Count	6319

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.711%	6319	100.00%	5.711%
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 0.88. Further, an Excess Kurtosis of 18.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.86%	38	0.60%	0.60%
-11.86% to -8.86%	66	1.04%	1.65%
-8.86% to -5.85%	166	2.63%	4.27%
-5.85% to -2.84%	698	11.05%	15.32%
-2.84% to 0.17%	2271	35.94%	51.26%
0.17% to 3.17%	2127	33.66%	84.92%
3.17% to 6.18%	653	10.33%	95.25%
6.18% to 9.19%	202	3.20%	98.45%
9.19% to 12.20%	51	0.81%	99.26%
Greater than 12.20%	47	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.84%	4.18%	79.82%	68.27%
±2σ	-7.85%	8.19%	95.55%	95.45%
±3σ	-11.86%	12.20%	98.65%	99.73%

Descriptive Statistics

Mean	0.167%
Standard Error	0.050%
Median	0.083%
Mode	0.000%
Standard Deviation	4.010%
Sample Variance	16.078%
Kurtosis	18.20
Skewness	0.88
Range	85.756%
Minimum	-31.910%
Maximum	53.846%
Count	6319

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.780%	3208	50.77%	1.411%
Negative	-2.656%	2961	46.86%	-1.245%
Zero	0.000%	150	2.37%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.01. Further, an Excess Kurtosis of 22.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.67%	6	0.46%	0.46%
-30.67% to -22.83%	8	0.61%	1.07%
-22.83% to -15.00%	39	2.97%	4.04%
-15.00% to -7.17%	138	10.53%	14.57%
-7.17% to 0.67%	510	38.90%	53.47%
0.67% to 8.50%	423	32.27%	85.74%
8.50% to 16.33%	118	9.00%	94.74%
16.33% to 24.16%	42	3.20%	97.94%
24.16% to 32.00%	10	0.76%	98.70%
Greater than 32.00%	17	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.78%	11.11%	80.93%	68.27%
±2σ	-20.22%	21.55%	95.58%	95.45%
±3σ	-30.67%	32.00%	98.25%	99.73%

Descriptive Statistics

Mean	0.665%
Standard Error	0.288%
Median	0.098%
Mode	0.000%
Standard Deviation	10.444%
Sample Variance	109.074%
Kurtosis	22.42
Skewness	2.01
Range	186.301%
Minimum	-55.532%
Maximum	130.769%
Count	1311

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.320%	662	50.50%	3.696%
Negative	-6.200%	641	48.89%	-3.031%
Zero	0.000%	8	0.61%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	0.81%
12	1 Quarter	0.69%
52	1 Year	7.06%
156	3 Years	8.80%
260	5 Years	10.44%
520	10 Years	11.26%
1,040	20 Years	13.15%
2,600	50 Years	13.39%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.92. Further, an Excess Kurtosis of 36.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.51%	0	0.00%	0.00%
-24.51% to -14.72%	0	0.00%	0.00%
-14.72% to -4.94%	0	0.00%	0.00%
-4.94% to 4.85%	60	4.57%	4.57%
4.85% to 14.64%	820	62.50%	67.07%
14.64% to 24.42%	289	22.03%	89.10%
24.42% to 34.21%	83	6.33%	95.43%
34.21% to 44.00%	22	1.68%	97.10%
44.00% to 53.78%	18	1.37%	98.48%
Greater than 53.78%	20	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.59%	27.68%	90.85%	68.27%
±2σ	-11.46%	40.73%	96.34%	95.45%
±3σ	-24.51%	53.78%	98.48%	99.73%

Descriptive Statistics

Mean	14.636%
Standard Error	0.360%
Median	11.478%
Mode	12.500%
Standard Deviation	13.049%
Sample Variance	170.280%
Kurtosis	36.87
Skewness	4.92
Range	158.713%
Minimum	0.378%
Maximum	159.091%
Count	1312

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.636%	1312	100.00%	14.636%
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 1.46. 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 -29.69%	6	0.46%	0.46%
-29.69% to -22.16%	13	0.99%	1.45%
-22.16% to -14.62%	40	3.05%	4.50%
-14.62% to -7.09%	149	11.36%	15.85%
-7.09% to 0.45%	497	37.88%	53.73%
0.45% to 7.98%	411	31.33%	85.06%
7.98% to 15.51%	127	9.68%	94.74%
15.51% to 23.05%	46	3.51%	98.25%
23.05% to 30.58%	10	0.76%	99.01%
Greater than 30.58%	13	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.60%	10.49%	80.41%	68.27%
±2σ	-19.64%	20.54%	95.58%	95.45%
±3σ	-29.69%	30.58%	98.55%	99.73%

Descriptive Statistics

Mean	0.446%
Standard Error	0.277%
Median	-0.081%
Mode	0.000%
Standard Deviation	10.045%
Sample Variance	100.905%
Kurtosis	13.94
Skewness	1.46
Range	162.410%
Minimum	-56.000%
Maximum	106.410%
Count	1312

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.312%	636	48.48%	3.545%
Negative	-6.131%	663	50.53%	-3.098%
Zero	0.000%	13	0.99%	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 10.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.08%	0	0.00%	0.00%
-61.08% to -45.13%	2	0.66%	0.66%
-45.13% to -29.18%	5	1.66%	2.33%
-29.18% to -13.22%	53	17.61%	19.93%
-13.22% to 2.73%	113	37.54%	57.48%
2.73% to 18.68%	73	24.25%	81.73%
18.68% to 34.63%	34	11.30%	93.02%
34.63% to 50.58%	15	4.98%	98.01%
50.58% to 66.53%	4	1.33%	99.34%
Greater than 66.53%	2	0.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.54%	23.99%	75.08%	68.27%
±2σ	-39.81%	45.26%	95.35%	95.45%
±3σ	-61.08%	66.53%	99.34%	99.73%

Descriptive Statistics

Mean	2.726%
Standard Error	1.226%
Median	-0.249%
Mode	-53.696%
Standard Deviation	21.268%
Sample Variance	452.331%
Kurtosis	10.30
Skewness	1.80
Range	215.100%
Minimum	-53.696%
Maximum	161.404%
Count	301

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.100%	147	48.84%	8.839%
Negative	-12.027%	153	50.83%	-6.113%
Zero	0.000%	1	0.33%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	1.49%
12	1 Year	16.71%
36	3 Years	19.89%
60	5 Years	22.13%
120	10 Years	24.90%
240	20 Years	28.86%
600	50 Years	29.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.34. Further, an Excess Kurtosis of 26.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.88%	0	0.00%	0.00%
-55.88% to -32.85%	0	0.00%	0.00%
-32.85% to -9.83%	0	0.00%	0.00%
-9.83% to 13.20%	20	6.62%	6.62%
13.20% to 36.23%	178	58.94%	65.56%
36.23% to 59.26%	80	26.49%	92.05%
59.26% to 82.28%	8	2.65%	94.70%
82.28% to 105.31%	7	2.32%	97.02%
105.31% to 128.34%	3	0.99%	98.01%
Greater than 128.34%	6	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.52%	66.93%	92.38%	68.27%
±2σ	-25.18%	97.64%	96.36%	95.45%
±3σ	-55.88%	128.34%	98.01%	99.73%

Descriptive Statistics

Mean	36.229%
Standard Error	1.767%
Median	28.733%
Mode	22.755%
Standard Deviation	30.704%
Sample Variance	942.752%
Kurtosis	26.50
Skewness	4.34
Range	294.322%
Minimum	1.133%
Maximum	295.455%
Count	302

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.229%	302	100.00%	36.229%
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 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 -59.28%	1	0.33%	0.33%
-59.28% to -44.07%	1	0.33%	0.66%
-44.07% to -28.85%	12	3.97%	4.64%
-28.85% to -13.64%	46	15.23%	19.87%
-13.64% to 1.58%	99	32.78%	52.65%
1.58% to 16.79%	89	29.47%	82.12%
16.79% to 32.01%	41	13.58%	95.70%
32.01% to 47.22%	6	1.99%	97.68%
47.22% to 62.43%	2	0.66%	98.34%
Greater than 62.43%	5	1.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.71%	21.86%	73.18%	68.27%
±2σ	-39.00%	42.15%	97.02%	95.45%
±3σ	-59.28%	62.43%	98.01%	99.73%

Descriptive Statistics

Mean	1.576%
Standard Error	1.167%
Median	0.989%
Mode	0.000%
Standard Deviation	20.286%
Sample Variance	411.539%
Kurtosis	5.27
Skewness	1.20
Range	183.594%
Minimum	-61.745%
Maximum	121.849%
Count	302

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.421%	159	52.65%	8.119%
Negative	-14.013%	141	46.69%	-6.543%
Zero	0.000%	2	0.66%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.60. Further, an Excess Kurtosis of 5.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -106.66%	0	0.00%	0.00%
-106.66% to -77.79%	0	0.00%	0.00%
-77.79% to -48.92%	2	2.00%	2.00%
-48.92% to -20.05%	16	16.00%	18.00%
-20.05% to 8.82%	38	38.00%	56.00%
8.82% to 37.69%	25	25.00%	81.00%
37.69% to 66.56%	15	15.00%	96.00%
66.56% to 95.43%	2	2.00%	98.00%
95.43% to 124.30%	0	0.00%	98.00%
Greater than 124.30%	2	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.67%	47.31%	77.00%	68.27%
±2σ	-68.16%	85.80%	97.00%	95.45%
±3σ	-106.66%	124.30%	98.00%	99.73%

Descriptive Statistics

Mean	8.820%
Standard Error	3.849%
Median	5.168%
Mode	-65.393%
Standard Deviation	38.492%
Sample Variance	1481.663%
Kurtosis	5.47
Skewness	1.60
Range	257.550%
Minimum	-65.393%
Maximum	192.157%
Count	100

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.610%	56	56.00%	18.262%
Negative	-21.458%	44	44.00%	-9.442%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	37.28%
12	3 Years	39.22%
20	5 Years	41.05%
40	10 Years	46.48%
80	20 Years	54.06%
200	50 Years	55.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.00. Further, an Excess Kurtosis of 34.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -169.75%	0	0.00%	0.00%
-169.75% to -107.17%	0	0.00%	0.00%
-107.17% to -44.58%	0	0.00%	0.00%
-44.58% to 18.01%	1	0.99%	0.99%
18.01% to 80.59%	75	74.26%	75.25%
80.59% to 143.18%	13	12.87%	88.12%
143.18% to 205.77%	6	5.94%	94.06%
205.77% to 268.35%	4	3.96%	98.02%
268.35% to 330.94%	1	0.99%	99.01%
Greater than 330.94%	1	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.86%	164.04%	92.08%	68.27%
±2σ	-86.30%	247.49%	96.04%	95.45%
±3σ	-169.75%	330.94%	99.01%	99.73%

Descriptive Statistics

Mean	80.593%
Standard Error	8.304%
Median	58.527%
Mode	2.791%
Standard Deviation	83.449%
Sample Variance	6963.770%
Kurtosis	34.18
Skewness	5.00
Range	715.391%
Minimum	2.791%
Maximum	718.182%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	80.593%	101	100.00%	80.593%
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 1.80. Further, an Excess Kurtosis of 5.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.19%	0	0.00%	0.00%
-115.19% to -85.20%	0	0.00%	0.00%
-85.20% to -55.20%	2	1.98%	1.98%
-55.20% to -25.20%	17	16.83%	18.81%
-25.20% to 4.79%	40	39.60%	58.42%
4.79% to 34.79%	28	27.72%	86.14%
34.79% to 64.79%	8	7.92%	94.06%
64.79% to 94.78%	3	2.97%	97.03%
94.78% to 124.78%	0	0.00%	97.03%
Greater than 124.78%	3	2.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.20%	44.79%	78.22%	68.27%
±2σ	-75.20%	84.79%	96.04%	95.45%
±3σ	-115.19%	124.78%	97.03%	99.73%

Descriptive Statistics

Mean	4.793%
Standard Error	3.980%
Median	-4.228%
Mode	-63.087%
Standard Deviation	39.996%
Sample Variance	1599.707%
Kurtosis	5.22
Skewness	1.80
Range	251.322%
Minimum	-63.087%
Maximum	188.235%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.934%	46	45.55%	16.366%
Negative	-21.252%	55	54.45%	-11.573%
Zero	0.000%	0	0.00%	0.000%

EXAS Deep Analytical Report