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	4.45%	5.19%	4.02%	4.63%	0.14%	0.22%	103.29	103.57	103.14	103.72
Weekly	10.46%	13.05%	10.06%	10.65%	0.31%	0.49%	103.11	103.75	102.80	104.06
Monthly	21.30%	30.69%	20.32%	22.47%	0.64%	1.02%	102.77	104.09	102.12	104.75
Quarterly	38.49%	83.46%	39.99%	40.98%	1.10%	1.77%	102.30	104.58	101.18	105.73
Annual	—	—	—	—	2.20%	3.54%	101.18	105.73	98.97	108.09
Option Time Horizon	—	—	—	—	0.85%	1.36%	102.56	104.31	101.69	105.20

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $103.43 | Strike (K): $105.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0500 (Bid $0.0000 / Ask $0.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 2.20% (CRR binomial tree, American, n=20 steps) | BS IV: 2.12% (European Black-Scholes) | Yahoo IV (Annual): 3.54% → 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 1.54. Further, an Excess Kurtosis of 22.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.22%	26	0.41%	0.41%
-13.22% to -9.88%	41	0.65%	1.06%
-9.88% to -6.54%	177	2.81%	3.87%
-6.54% to -3.21%	684	10.86%	14.73%
-3.21% to 0.13%	2405	38.19%	52.92%
0.13% to 3.46%	2105	33.42%	86.34%
3.46% to 6.80%	591	9.38%	95.73%
6.80% to 10.13%	160	2.54%	98.27%
10.13% to 13.47%	53	0.84%	99.11%
Greater than 13.47%	56	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.32%	4.58%	82.22%	68.27%
±2σ	-8.77%	9.02%	96.06%	95.45%
±3σ	-13.22%	13.47%	98.70%	99.73%

Descriptive Statistics

Mean	0.127%
Standard Error	0.056%
Median	0.000%
Mode	0.000%
Standard Deviation	4.448%
Sample Variance	19.783%
Kurtosis	22.11
Skewness	1.54
Range	99.809%
Minimum	-46.141%
Maximum	53.668%
Count	6298

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.029%	3059	48.57%	1.471%
Negative	-2.750%	3078	48.87%	-1.344%
Zero	0.000%	161	2.56%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	0.23%
20	1 Month	0.32%
60	1 Quarter	0.35%
250	1 Year	3.33%
750	3 Years	3.95%
1,250	5 Years	4.63%
2,500	10 Years	4.83%
5,000	20 Years	5.61%
12,500	50 Years	5.71%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.34. Further, an Excess Kurtosis of 97.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.85%	0	0.00%	0.00%
-9.85% to -5.95%	0	0.00%	0.00%
-5.95% to -2.06%	0	0.00%	0.00%
-2.06% to 1.83%	234	3.71%	3.71%
1.83% to 5.73%	3934	62.45%	66.17%
5.73% to 9.62%	1471	23.35%	89.52%
9.62% to 13.52%	388	6.16%	95.68%
13.52% to 17.41%	124	1.97%	97.65%
17.41% to 21.30%	65	1.03%	98.68%
Greater than 21.30%	83	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.54%	10.92%	91.24%	68.27%
±2σ	-4.66%	16.11%	97.22%	95.45%
±3σ	-9.85%	21.30%	98.68%	99.73%

Descriptive Statistics

Mean	5.728%
Standard Error	0.065%
Median	4.522%
Mode	6.667%
Standard Deviation	5.192%
Sample Variance	26.953%
Kurtosis	97.84
Skewness	7.34
Range	113.491%
Minimum	0.145%
Maximum	113.636%
Count	6299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.728%	6299	100.00%	5.728%
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 18.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.88%	38	0.60%	0.60%
-11.88% to -8.87%	66	1.05%	1.65%
-8.87% to -5.86%	164	2.60%	4.25%
-5.86% to -2.85%	699	11.10%	15.35%
-2.85% to 0.17%	2254	35.78%	51.14%
0.17% to 3.18%	2128	33.78%	84.92%
3.18% to 6.19%	650	10.32%	95.24%
6.19% to 9.20%	203	3.22%	98.46%
9.20% to 12.21%	50	0.79%	99.25%
Greater than 12.21%	47	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.85%	4.18%	79.82%	68.27%
±2σ	-7.87%	8.20%	95.57%	95.45%
±3σ	-11.88%	12.21%	98.65%	99.73%

Descriptive Statistics

Mean	0.167%
Standard Error	0.051%
Median	0.089%
Mode	0.000%
Standard Deviation	4.016%
Sample Variance	16.129%
Kurtosis	18.13
Skewness	0.88
Range	85.756%
Minimum	-31.910%
Maximum	53.846%
Count	6299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.786%	3200	50.80%	1.415%
Negative	-2.665%	2950	46.83%	-1.248%
Zero	0.000%	149	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 22.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.71%	6	0.46%	0.46%
-30.71% to -22.87%	8	0.61%	1.07%
-22.87% to -15.02%	38	2.91%	3.98%
-15.02% to -7.18%	139	10.64%	14.61%
-7.18% to 0.67%	507	38.79%	53.40%
0.67% to 8.51%	422	32.29%	85.69%
8.51% to 16.36%	118	9.03%	94.72%
16.36% to 24.20%	42	3.21%	97.93%
24.20% to 32.05%	10	0.77%	98.70%
Greater than 32.05%	17	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.79%	11.13%	80.87%	68.27%
±2σ	-20.25%	21.59%	95.56%	95.45%
±3σ	-30.71%	32.05%	98.24%	99.73%

Descriptive Statistics

Mean	0.666%
Standard Error	0.289%
Median	0.097%
Mode	0.000%
Standard Deviation	10.460%
Sample Variance	109.407%
Kurtosis	22.35
Skewness	2.01
Range	186.301%
Minimum	-55.532%
Maximum	130.769%
Count	1307

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.351%	659	50.42%	3.706%
Negative	-6.209%	640	48.97%	-3.040%
Zero	0.000%	8	0.61%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	0.61%
12	1 Quarter	0.69%
52	1 Year	7.74%
156	3 Years	9.04%
260	5 Years	10.65%
520	10 Years	11.36%
1,040	20 Years	13.22%
2,600	50 Years	13.42%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.94. Further, an Excess Kurtosis of 36.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.46%	0	0.00%	0.00%
-24.46% to -14.68%	0	0.00%	0.00%
-14.68% to -4.89%	0	0.00%	0.00%
-4.89% to 4.89%	56	4.28%	4.28%
4.89% to 14.68%	822	62.84%	67.13%
14.68% to 24.46%	288	22.02%	89.14%
24.46% to 34.25%	82	6.27%	95.41%
34.25% to 44.03%	22	1.68%	97.09%
44.03% to 53.82%	18	1.38%	98.47%
Greater than 53.82%	20	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.63%	27.73%	91.21%	68.27%
±2σ	-11.42%	40.77%	96.33%	95.45%
±3σ	-24.46%	53.82%	98.47%	99.73%

Descriptive Statistics

Mean	14.678%
Standard Error	0.361%
Median	11.495%
Mode	12.500%
Standard Deviation	13.047%
Sample Variance	170.217%
Kurtosis	36.95
Skewness	4.94
Range	158.742%
Minimum	0.349%
Maximum	159.091%
Count	1308

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.678%	1308	100.00%	14.678%
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 13.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.73%	6	0.46%	0.46%
-29.73% to -22.19%	13	0.99%	1.45%
-22.19% to -14.64%	39	2.98%	4.43%
-14.64% to -7.10%	150	11.47%	15.90%
-7.10% to 0.45%	493	37.69%	53.59%
0.45% to 7.99%	412	31.50%	85.09%
7.99% to 15.54%	126	9.63%	94.72%
15.54% to 23.08%	46	3.52%	98.24%
23.08% to 30.63%	10	0.76%	99.01%
Greater than 30.63%	13	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.61%	10.51%	80.43%	68.27%
±2σ	-19.67%	20.57%	95.57%	95.45%
±3σ	-29.73%	30.63%	98.55%	99.73%

Descriptive Statistics

Mean	0.449%
Standard Error	0.278%
Median	-0.074%
Mode	0.000%
Standard Deviation	10.060%
Sample Variance	101.211%
Kurtosis	13.89
Skewness	1.46
Range	162.410%
Minimum	-56.000%
Maximum	106.410%
Count	1308

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.323%	635	48.55%	3.555%
Negative	-6.156%	660	50.46%	-3.106%
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 1.79. Further, an Excess Kurtosis of 10.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.18%	0	0.00%	0.00%
-61.18% to -45.20%	2	0.67%	0.67%
-45.20% to -29.23%	5	1.67%	2.33%
-29.23% to -13.25%	53	17.67%	20.00%
-13.25% to 2.73%	112	37.33%	57.33%
2.73% to 18.71%	73	24.33%	81.67%
18.71% to 34.68%	34	11.33%	93.00%
34.68% to 50.66%	15	5.00%	98.00%
50.66% to 66.64%	4	1.33%	99.33%
Greater than 66.64%	2	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.57%	24.03%	75.33%	68.27%
±2σ	-39.88%	45.34%	95.33%	95.45%
±3σ	-61.18%	66.64%	99.33%	99.73%

Descriptive Statistics

Mean	2.730%
Standard Error	1.230%
Median	-0.332%
Mode	-53.696%
Standard Deviation	21.303%
Sample Variance	453.838%
Kurtosis	10.26
Skewness	1.79
Range	215.100%
Minimum	-53.696%
Maximum	161.404%
Count	300

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.214%	146	48.67%	8.864%
Negative	-12.027%	153	51.00%	-6.134%
Zero	0.000%	1	0.33%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	1.40%
12	1 Year	17.97%
36	3 Years	20.22%
60	5 Years	22.47%
120	10 Years	25.24%
240	20 Years	29.06%
600	50 Years	29.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.35. Further, an Excess Kurtosis of 26.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.73%	0	0.00%	0.00%
-55.73% to -32.71%	0	0.00%	0.00%
-32.71% to -9.69%	0	0.00%	0.00%
-9.69% to 13.32%	19	6.31%	6.31%
13.32% to 36.34%	181	60.13%	66.45%
36.34% to 59.36%	77	25.58%	92.03%
59.36% to 82.38%	8	2.66%	94.68%
82.38% to 105.40%	7	2.33%	97.01%
105.40% to 128.42%	3	1.00%	98.01%
Greater than 128.42%	6	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.65%	67.03%	92.69%	68.27%
±2σ	-25.04%	97.72%	96.35%	95.45%
±3σ	-55.73%	128.42%	98.01%	99.73%

Descriptive Statistics

Mean	36.343%
Standard Error	1.769%
Median	28.767%
Mode	22.755%
Standard Deviation	30.691%
Sample Variance	941.965%
Kurtosis	26.58
Skewness	4.35
Range	294.322%
Minimum	1.133%
Maximum	295.455%
Count	301

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.343%	301	100.00%	36.343%
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 5.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.37%	1	0.33%	0.33%
-59.37% to -44.13%	1	0.33%	0.66%
-44.13% to -28.89%	12	3.99%	4.65%
-28.89% to -13.65%	46	15.28%	19.93%
-13.65% to 1.59%	98	32.56%	52.49%
1.59% to 16.82%	89	29.57%	82.06%
16.82% to 32.06%	41	13.62%	95.68%
32.06% to 47.30%	6	1.99%	97.67%
47.30% to 62.54%	2	0.66%	98.34%
Greater than 62.54%	5	1.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.73%	21.90%	73.42%	68.27%
±2σ	-39.05%	42.22%	97.01%	95.45%
±3σ	-59.37%	62.54%	98.01%	99.73%

Descriptive Statistics

Mean	1.586%
Standard Error	1.171%
Median	1.124%
Mode	0.000%
Standard Deviation	20.319%
Sample Variance	412.879%
Kurtosis	5.25
Skewness	1.20
Range	183.594%
Minimum	-61.745%
Maximum	121.849%
Count	301

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.421%	159	52.82%	8.146%
Negative	-14.102%	140	46.51%	-6.559%
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 -106.68%	0	0.00%	0.00%
-106.68% to -77.81%	0	0.00%	0.00%
-77.81% to -48.94%	2	2.00%	2.00%
-48.94% to -20.07%	16	16.00%	18.00%
-20.07% to 8.81%	38	38.00%	56.00%
8.81% to 37.68%	25	25.00%	81.00%
37.68% to 66.55%	15	15.00%	96.00%
66.55% to 95.42%	2	2.00%	98.00%
95.42% to 124.29%	0	0.00%	98.00%
Greater than 124.29%	2	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.69%	47.30%	77.00%	68.27%
±2σ	-68.18%	85.80%	97.00%	95.45%
±3σ	-106.68%	124.29%	98.00%	99.73%

Descriptive Statistics

Mean	8.806%
Standard Error	3.850%
Median	5.168%
Mode	-65.393%
Standard Deviation	38.495%
Sample Variance	1481.868%
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	32.585%	56	56.00%	18.248%
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	36.93%
12	3 Years	39.10%
20	5 Years	40.98%
40	10 Years	46.44%
80	20 Years	54.04%
200	50 Years	55.74%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -169.81%	0	0.00%	0.00%
-169.81% to -107.21%	0	0.00%	0.00%
-107.21% to -44.61%	0	0.00%	0.00%
-44.61% to 17.98%	1	0.99%	0.99%
17.98% to 80.58%	75	74.26%	75.25%
80.58% to 143.18%	13	12.87%	88.12%
143.18% to 205.77%	6	5.94%	94.06%
205.77% to 268.37%	4	3.96%	98.02%
268.37% to 330.96%	1	0.99%	99.01%
Greater than 330.96%	1	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.88%	164.04%	92.08%	68.27%
±2σ	-86.35%	247.50%	96.04%	95.45%
±3σ	-169.81%	330.97%	99.01%	99.73%

Descriptive Statistics

Mean	80.579%
Standard Error	8.305%
Median	58.527%
Mode	1.381%
Standard Deviation	83.462%
Sample Variance	6965.983%
Kurtosis	34.16
Skewness	5.00
Range	716.801%
Minimum	1.381%
Maximum	718.182%
Count	101

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	80.579%	101	100.00%	80.579%
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 -115.17%	0	0.00%	0.00%
-115.17% to -85.18%	0	0.00%	0.00%
-85.18% to -55.18%	2	1.98%	1.98%
-55.18% to -25.19%	17	16.83%	18.81%
-25.19% to 4.81%	40	39.60%	58.42%
4.81% to 34.80%	28	27.72%	86.14%
34.80% to 64.80%	8	7.92%	94.06%
64.80% to 94.79%	3	2.97%	97.03%
94.79% to 124.79%	0	0.00%	97.03%
Greater than 124.79%	3	2.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.19%	44.80%	78.22%	68.27%
±2σ	-75.18%	84.80%	96.04%	95.45%
±3σ	-115.17%	124.79%	97.03%	99.73%

Descriptive Statistics

Mean	4.807%
Standard Error	3.980%
Median	-4.228%
Mode	-63.087%
Standard Deviation	39.994%
Sample Variance	1599.526%
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	-21.227%	55	54.45%	-11.559%
Zero	0.000%	0	0.00%	0.000%

EXAS Deep Analytical Report