GH - 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	4.30%	3.16%	3.76%	5.78%	4.12%	4.10%	82.36	89.44	79.03	93.20
Weekly	9.71%	9.45%	10.55%	13.70%	9.07%	9.03%	78.38	93.98	71.58	102.90
Monthly	20.78%	20.29%	20.52%	29.85%	18.89%	18.79%	71.05	103.67	58.82	125.22
Quarterly	45.35%	35.70%	35.38%	55.67%	32.72%	32.54%	61.88	119.04	44.61	165.11
Annual	—	—	—	—	65.43%	65.09%	44.61	165.11	23.19	317.65
Option Time Horizon	—	—	—	—	24.70%	24.57%	67.04	109.87	52.37	140.65

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $85.82 | Strike (K): $110.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.0500 (Bid $1.6000 / Ask $2.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 65.43% (CRR binomial tree, American, n=20 steps) | BS IV: 65.45% (European Black-Scholes) | Yahoo IV (Annual): 65.09% → 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 0.61. Further, an Excess Kurtosis of 6.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.75%	6	0.32%	0.32%
-12.75% to -9.52%	19	1.01%	1.33%
-9.52% to -6.30%	70	3.74%	5.07%
-6.30% to -3.08%	233	12.44%	17.51%
-3.08% to 0.14%	662	35.34%	52.86%
0.14% to 3.37%	573	30.59%	83.45%
3.37% to 6.59%	209	11.16%	94.61%
6.59% to 9.81%	64	3.42%	98.02%
9.81% to 13.04%	18	0.96%	98.99%
Greater than 13.04%	19	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.15%	4.44%	76.83%	68.27%
±2σ	-8.45%	8.74%	95.73%	95.45%
±3σ	-12.75%	13.03%	98.67%	99.73%

Descriptive Statistics

Mean	0.144%
Standard Error	0.099%
Median	-0.016%
Mode	0.000%
Standard Deviation	4.297%
Sample Variance	18.466%
Kurtosis	6.05
Skewness	0.61
Range	55.720%
Minimum	-27.145%
Maximum	28.575%
Count	1873

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.209%	923	49.28%	1.581%
Negative	-2.862%	941	50.24%	-1.438%
Zero	0.000%	9	0.48%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.21%
20	1 Month	4.68%
60	1 Quarter	5.08%
250	1 Year	5.23%
750	3 Years	5.38%
1,250	5 Years	5.78%
2,500	10 Years	5.83%
5,000	20 Years	5.83%
12,500	50 Years	5.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.51. Further, an Excess Kurtosis of 11.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.74%	0	0.00%	0.00%
-3.74% to -1.37%	0	0.00%	0.00%
-1.37% to 1.00%	0	0.00%	0.00%
1.00% to 3.37%	334	17.82%	17.82%
3.37% to 5.74%	836	44.61%	62.43%
5.74% to 8.11%	408	21.77%	84.20%
8.11% to 10.48%	168	8.96%	93.17%
10.48% to 12.85%	69	3.68%	96.85%
12.85% to 15.22%	25	1.33%	98.19%
Greater than 15.22%	34	1.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.58%	8.90%	81.43%	68.27%
±2σ	-0.58%	12.06%	96.21%	95.45%
±3σ	-3.74%	15.22%	98.19%	99.73%

Descriptive Statistics

Mean	5.739%
Standard Error	0.073%
Median	4.936%
Mode	2.522%
Standard Deviation	3.160%
Sample Variance	9.986%
Kurtosis	11.36
Skewness	2.51
Range	29.797%
Minimum	1.490%
Maximum	31.287%
Count	1874

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.739%	1874	100.00%	5.739%
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 0.09. Further, an Excess Kurtosis of 3.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.19%	11	0.59%	0.59%
-11.19% to -8.38%	21	1.12%	1.71%
-8.38% to -5.56%	74	3.95%	5.66%
-5.56% to -2.74%	225	12.01%	17.66%
-2.74% to 0.08%	610	32.55%	50.21%
0.08% to 2.90%	601	32.07%	82.28%
2.90% to 5.72%	208	11.10%	93.38%
5.72% to 8.54%	91	4.86%	98.24%
8.54% to 11.35%	22	1.17%	99.41%
Greater than 11.35%	11	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.68%	3.84%	74.65%	68.27%
±2σ	-7.44%	7.60%	94.77%	95.45%
±3σ	-11.19%	11.35%	98.83%	99.73%

Descriptive Statistics

Mean	0.080%
Standard Error	0.087%
Median	0.066%
Mode	0.000%
Standard Deviation	3.758%
Sample Variance	14.121%
Kurtosis	3.13
Skewness	0.09
Range	45.611%
Minimum	-20.113%
Maximum	25.498%
Count	1874

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.774%	953	50.85%	1.411%
Negative	-2.722%	916	48.88%	-1.330%
Zero	0.000%	5	0.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.19. Further, an Excess Kurtosis of 3.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.38%	2	0.51%	0.51%
-28.38% to -21.10%	0	0.00%	0.51%
-21.10% to -13.82%	14	3.60%	4.11%
-13.82% to -6.53%	60	15.42%	19.54%
-6.53% to 0.75%	137	35.22%	54.76%
0.75% to 8.03%	103	26.48%	81.23%
8.03% to 15.32%	46	11.83%	93.06%
15.32% to 22.60%	17	4.37%	97.43%
22.60% to 29.88%	8	2.06%	99.49%
Greater than 29.88%	2	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.96%	10.46%	75.84%	68.27%
±2σ	-18.67%	20.17%	95.89%	95.45%
±3σ	-28.38%	29.88%	98.97%	99.73%

Descriptive Statistics

Mean	0.750%
Standard Error	0.492%
Median	-0.116%
Mode	0.464%
Standard Deviation	9.711%
Sample Variance	94.295%
Kurtosis	3.11
Skewness	0.19
Range	90.692%
Minimum	-50.764%
Maximum	39.928%
Count	389

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.043%	191	49.10%	3.949%
Negative	-6.285%	198	50.90%	-3.199%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.07%
12	1 Quarter	10.85%
52	1 Year	11.99%
156	3 Years	12.69%
260	5 Years	13.70%
520	10 Years	13.67%
1,040	20 Years	13.67%
2,600	50 Years	13.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.45. Further, an Excess Kurtosis of 36.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.46%	0	0.00%	0.00%
-13.46% to -6.37%	0	0.00%	0.00%
-6.37% to 0.71%	0	0.00%	0.00%
0.71% to 7.79%	52	13.33%	13.33%
7.79% to 14.88%	185	47.44%	60.77%
14.88% to 21.96%	92	23.59%	84.36%
21.96% to 29.05%	40	10.26%	94.62%
29.05% to 36.13%	15	3.85%	98.46%
36.13% to 43.21%	1	0.26%	98.72%
Greater than 43.21%	5	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.43%	24.32%	87.69%	68.27%
±2σ	-4.01%	33.77%	98.21%	95.45%
±3σ	-13.46%	43.21%	98.72%	99.73%

Descriptive Statistics

Mean	14.878%
Standard Error	0.478%
Median	12.470%
Mode	9.165%
Standard Deviation	9.445%
Sample Variance	89.206%
Kurtosis	36.53
Skewness	4.45
Range	109.274%
Minimum	4.296%
Maximum	113.570%
Count	390

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.878%	390	100.00%	14.878%
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 2.74. Further, an Excess Kurtosis of 23.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.34%	0	0.00%	0.00%
-31.34% to -23.42%	2	0.51%	0.51%
-23.42% to -15.51%	11	2.82%	3.33%
-15.51% to -7.59%	58	14.87%	18.21%
-7.59% to 0.33%	129	33.08%	51.28%
0.33% to 8.24%	123	31.54%	82.82%
8.24% to 16.16%	49	12.56%	95.38%
16.16% to 24.07%	16	4.10%	99.49%
24.07% to 31.99%	0	0.00%	99.49%
Greater than 31.99%	2	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.23%	10.88%	79.49%	68.27%
±2σ	-20.78%	21.44%	97.44%	95.45%
±3σ	-31.34%	31.99%	99.49%	99.73%

Descriptive Statistics

Mean	0.326%
Standard Error	0.534%
Median	0.026%
Mode	-0.321%
Standard Deviation	10.555%
Sample Variance	111.401%
Kurtosis	23.80
Skewness	2.74
Range	130.204%
Minimum	-28.376%
Maximum	101.828%
Count	390

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.322%	196	50.26%	3.680%
Negative	-6.742%	194	49.74%	-3.354%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.88. Further, an Excess Kurtosis of 1.76 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.31%	0	0.00%	0.00%
-59.31% to -43.72%	1	1.12%	1.12%
-43.72% to -28.13%	2	2.25%	3.37%
-28.13% to -12.55%	15	16.85%	20.22%
-12.55% to 3.04%	29	32.58%	52.81%
3.04% to 18.63%	30	33.71%	86.52%
18.63% to 34.21%	6	6.74%	93.26%
34.21% to 49.80%	1	1.12%	94.38%
49.80% to 65.39%	5	5.62%	100.00%
Greater than 65.39%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.74%	23.82%	77.53%	68.27%
±2σ	-38.52%	44.60%	92.13%	95.45%
±3σ	-59.31%	65.39%	100.00%	99.73%

Descriptive Statistics

Mean	3.040%
Standard Error	2.203%
Median	0.118%
Mode	-48.032%
Standard Deviation	20.782%
Sample Variance	431.885%
Kurtosis	1.76
Skewness	0.88
Range	113.228%
Minimum	-48.032%
Maximum	65.196%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.538%	46	51.69%	9.065%
Negative	-12.469%	43	48.31%	-6.024%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.40%
12	1 Year	30.22%
36	3 Years	29.97%
60	5 Years	29.85%
120	10 Years	29.50%
240	20 Years	29.50%
600	50 Years	29.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.33. Further, an Excess Kurtosis of 7.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.21%	0	0.00%	0.00%
-25.21% to -10.00%	0	0.00%	0.00%
-10.00% to 5.22%	0	0.00%	0.00%
5.22% to 20.43%	16	17.78%	17.78%
20.43% to 35.65%	43	47.78%	65.56%
35.65% to 50.87%	17	18.89%	84.44%
50.87% to 66.08%	8	8.89%	93.33%
66.08% to 81.30%	3	3.33%	96.67%
81.30% to 96.51%	1	1.11%	97.78%
Greater than 96.51%	2	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.36%	55.94%	82.22%	68.27%
±2σ	-4.93%	76.23%	96.67%	95.45%
±3σ	-25.21%	96.51%	97.78%	99.73%

Descriptive Statistics

Mean	35.650%
Standard Error	2.139%
Median	29.712%
Mode	13.324%
Standard Deviation	20.288%
Sample Variance	411.598%
Kurtosis	7.51
Skewness	2.33
Range	118.068%
Minimum	13.324%
Maximum	131.392%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.650%	90	100.00%	35.650%
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 1.15. Further, an Excess Kurtosis of 3.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.81%	0	0.00%	0.00%
-60.81% to -45.42%	0	0.00%	0.00%
-45.42% to -30.03%	6	6.67%	6.67%
-30.03% to -14.64%	9	10.00%	16.67%
-14.64% to 0.76%	34	37.78%	54.44%
0.76% to 16.15%	26	28.89%	83.33%
16.15% to 31.54%	9	10.00%	93.33%
31.54% to 46.93%	4	4.44%	97.78%
46.93% to 62.32%	1	1.11%	98.89%
Greater than 62.32%	1	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.77%	21.28%	77.78%	68.27%
±2σ	-40.29%	41.80%	96.67%	95.45%
±3σ	-60.81%	62.32%	98.89%	99.73%

Descriptive Statistics

Mean	0.755%
Standard Error	2.163%
Median	-0.665%
Mode	-39.841%
Standard Deviation	20.522%
Sample Variance	421.156%
Kurtosis	3.94
Skewness	1.15
Range	132.966%
Minimum	-39.841%
Maximum	93.125%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.802%	44	48.89%	7.725%
Negative	-13.638%	46	51.11%	-6.971%
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 1.18. Further, an Excess Kurtosis of 0.74 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -125.23%	0	0.00%	0.00%
-125.23% to -91.22%	0	0.00%	0.00%
-91.22% to -57.21%	0	0.00%	0.00%
-57.21% to -23.20%	8	26.67%	26.67%
-23.20% to 10.81%	12	40.00%	66.67%
10.81% to 44.82%	4	13.33%	80.00%
44.82% to 78.83%	3	10.00%	90.00%
78.83% to 112.84%	1	3.33%	93.33%
112.84% to 146.85%	2	6.67%	100.00%
Greater than 146.85%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.54%	56.16%	73.33%	68.27%
±2σ	-79.89%	101.50%	93.33%	95.45%
±3σ	-125.23%	146.85%	100.00%	99.73%

Descriptive Statistics

Mean	10.808%
Standard Error	8.279%
Median	0.871%
Mode	-40.449%
Standard Deviation	45.347%
Sample Variance	2056.361%
Kurtosis	0.74
Skewness	1.18
Range	167.438%
Minimum	-40.449%
Maximum	126.989%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.265%	16	53.33%	22.008%
Negative	-24.000%	14	46.67%	-11.200%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	58.50%
12	3 Years	62.01%
20	5 Years	55.67%
40	10 Years	57.08%
80	20 Years	57.08%
200	50 Years	57.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.24. Further, an Excess Kurtosis of 0.81 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.47%	0	0.00%	0.00%
-34.47% to -7.70%	0	0.00%	0.00%
-7.70% to 19.08%	0	0.00%	0.00%
19.08% to 45.85%	7	22.58%	22.58%
45.85% to 72.63%	14	45.16%	67.74%
72.63% to 99.40%	3	9.68%	77.42%
99.40% to 126.18%	3	9.68%	87.10%
126.18% to 152.95%	3	9.68%	96.77%
152.95% to 179.73%	1	3.23%	100.00%
Greater than 179.73%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	36.93%	108.33%	80.65%	68.27%
±2σ	1.23%	144.03%	96.77%	95.45%
±3σ	-34.47%	179.73%	100.00%	99.73%

Descriptive Statistics

Mean	72.627%
Standard Error	6.412%
Median	60.537%
Mode	35.846%
Standard Deviation	35.700%
Sample Variance	1274.472%
Kurtosis	0.81
Skewness	1.24
Range	138.280%
Minimum	35.846%
Maximum	174.126%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	72.627%	31	100.00%	72.627%
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 -0.91 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.21%	0	0.00%	0.00%
-103.21% to -76.68%	0	0.00%	0.00%
-76.68% to -50.15%	2	6.45%	6.45%
-50.15% to -23.61%	5	16.13%	22.58%
-23.61% to 2.92%	11	35.48%	58.06%
2.92% to 29.46%	5	16.13%	74.19%
29.46% to 55.99%	6	19.35%	93.55%
55.99% to 82.52%	2	6.45%	100.00%
82.52% to 109.06%	0	0.00%	100.00%
Greater than 109.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.46%	38.30%	64.52%	68.27%
±2σ	-67.83%	73.68%	100.00%	95.45%
±3σ	-103.21%	109.06%	100.00%	99.73%

Descriptive Statistics

Mean	2.922%
Standard Error	6.354%
Median	-2.308%
Mode	-56.192%
Standard Deviation	35.378%
Sample Variance	1251.600%
Kurtosis	-0.91
Skewness	0.15
Range	125.394%
Minimum	-56.192%
Maximum	69.202%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.256%	13	41.94%	16.043%
Negative	-22.596%	18	58.06%	-13.120%
Zero	0.000%	0	0.00%	0.000%

GH Deep Analytical Report