OLLI - 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	2.71%	2.20%	2.38%	3.88%	2.75%	3.14%	105.77	111.74	102.90	114.85
Weekly	5.56%	5.16%	5.74%	8.82%	6.04%	6.91%	102.34	115.48	96.33	122.68
Monthly	11.71%	11.83%	11.98%	18.45%	12.58%	14.39%	95.86	123.28	84.53	139.81
Quarterly	19.15%	24.31%	18.35%	30.16%	21.79%	24.93%	87.43	135.17	70.31	168.08
Annual	—	—	—	—	43.58%	49.85%	70.31	168.08	45.48	259.87
Option Time Horizon	—	—	—	—	16.76%	19.18%	91.93	128.55	77.75	152.00

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $108.71 | Strike (K): $110.00 (first OTM call ≥ spot) | Observed Mid-Price: $6.9500 (Bid $6.1000 / Ask $7.8000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 43.58% (CRR binomial tree, American, n=20 steps) | BS IV: 43.60% (European Black-Scholes) | Yahoo IV (Annual): 49.85% → 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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.61. Further, an Excess Kurtosis of 9.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.02%	16	0.60%	0.60%
-8.02% to -5.99%	25	0.94%	1.54%
-5.99% to -3.96%	88	3.30%	4.84%
-3.96% to -1.93%	333	12.50%	17.34%
-1.93% to 0.10%	852	31.97%	49.31%
0.10% to 2.13%	892	33.47%	82.78%
2.13% to 4.16%	325	12.20%	94.97%
4.16% to 6.19%	87	3.26%	98.24%
6.19% to 8.22%	29	1.09%	99.32%
Greater than 8.22%	18	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.61%	2.81%	76.66%	68.27%
±2σ	-5.31%	5.51%	95.87%	95.45%
±3σ	-8.02%	8.22%	98.72%	99.73%

Descriptive Statistics

Mean	0.099%
Standard Error	0.052%
Median	0.119%
Mode	0.000%
Standard Deviation	2.707%
Sample Variance	7.326%
Kurtosis	9.26
Skewness	-0.61
Range	43.189%
Minimum	-27.530%
Maximum	15.659%
Count	2665

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.928%	1387	52.05%	1.003%
Negative	-1.912%	1261	47.32%	-0.905%
Zero	0.000%	17	0.64%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.28%
20	1 Month	3.16%
60	1 Quarter	3.53%
250	1 Year	3.76%
750	3 Years	3.44%
1,250	5 Years	3.88%
2,500	10 Years	3.76%
5,000	20 Years	3.84%
12,500	50 Years	3.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.81. Further, an Excess Kurtosis of 33.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.84%	0	0.00%	0.00%
-2.84% to -1.19%	0	0.00%	0.00%
-1.19% to 0.46%	0	0.00%	0.00%
0.46% to 2.11%	422	15.83%	15.83%
2.11% to 3.77%	1246	46.74%	62.57%
3.77% to 5.42%	611	22.92%	85.48%
5.42% to 7.07%	224	8.40%	93.89%
7.07% to 8.72%	80	3.00%	96.89%
8.72% to 10.37%	38	1.43%	98.31%
Greater than 10.37%	45	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.56%	5.97%	85.30%	68.27%
±2σ	-0.64%	8.17%	95.91%	95.45%
±3σ	-2.84%	10.37%	98.31%	99.73%

Descriptive Statistics

Mean	3.765%
Standard Error	0.043%
Median	3.234%
Mode	2.333%
Standard Deviation	2.202%
Sample Variance	4.850%
Kurtosis	33.47
Skewness	3.81
Range	37.084%
Minimum	0.654%
Maximum	37.738%
Count	2666

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.765%	2666	100.00%	3.765%
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 0.22. Further, an Excess Kurtosis of 2.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.16%	14	0.53%	0.53%
-7.16% to -5.37%	28	1.05%	1.58%
-5.37% to -3.58%	112	4.20%	5.78%
-3.58% to -1.80%	357	13.39%	19.17%
-1.80% to -0.01%	847	31.77%	50.94%
-0.01% to 1.78%	795	29.82%	80.76%
1.78% to 3.57%	347	13.02%	93.77%
3.57% to 5.36%	117	4.39%	98.16%
5.36% to 7.14%	29	1.09%	99.25%
Greater than 7.14%	20	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.39%	2.38%	74.27%	68.27%
±2σ	-4.78%	4.76%	94.71%	95.45%
±3σ	-7.16%	7.14%	98.72%	99.73%

Descriptive Statistics

Mean	-0.008%
Standard Error	0.046%
Median	-0.068%
Mode	0.000%
Standard Deviation	2.384%
Sample Variance	5.684%
Kurtosis	2.19
Skewness	0.22
Range	24.837%
Minimum	-11.114%
Maximum	13.723%
Count	2666

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.835%	1282	48.09%	0.882%
Negative	-1.746%	1359	50.98%	-0.890%
Zero	0.000%	25	0.94%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.29. Further, an Excess Kurtosis of 2.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.21%	3	0.54%	0.54%
-16.21% to -12.04%	3	0.54%	1.08%
-12.04% to -7.87%	27	4.88%	5.97%
-7.87% to -3.71%	87	15.73%	21.70%
-3.71% to 0.46%	145	26.22%	47.92%
0.46% to 4.63%	180	32.55%	80.47%
4.63% to 8.79%	75	13.56%	94.03%
8.79% to 12.96%	22	3.98%	98.01%
12.96% to 17.13%	10	1.81%	99.82%
Greater than 17.13%	1	0.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.09%	6.02%	72.15%	68.27%
±2σ	-10.65%	11.57%	95.30%	95.45%
±3σ	-16.21%	17.13%	99.28%	99.73%

Descriptive Statistics

Mean	0.461%
Standard Error	0.236%
Median	0.662%
Mode	0.000%
Standard Deviation	5.556%
Sample Variance	30.868%
Kurtosis	2.24
Skewness	-0.29
Range	46.986%
Minimum	-29.462%
Maximum	17.524%
Count	553

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.243%	305	55.15%	2.340%
Negative	-4.242%	245	44.30%	-1.879%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.47%
12	1 Quarter	6.70%
52	1 Year	8.45%
156	3 Years	7.88%
260	5 Years	8.82%
520	10 Years	8.61%
1,040	20 Years	8.70%
2,600	50 Years	8.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.82. Further, an Excess Kurtosis of 13.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.29%	0	0.00%	0.00%
-6.29% to -2.43%	0	0.00%	0.00%
-2.43% to 1.44%	0	0.00%	0.00%
1.44% to 5.31%	97	17.51%	17.51%
5.31% to 9.18%	255	46.03%	63.54%
9.18% to 13.04%	120	21.66%	85.20%
13.04% to 16.91%	45	8.12%	93.32%
16.91% to 20.78%	20	3.61%	96.93%
20.78% to 24.65%	8	1.44%	98.38%
Greater than 24.65%	9	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.02%	14.33%	84.30%	68.27%
±2σ	-1.14%	19.49%	96.39%	95.45%
±3σ	-6.29%	24.65%	98.38%	99.73%

Descriptive Statistics

Mean	9.177%
Standard Error	0.219%
Median	8.044%
Mode	4.144%
Standard Deviation	5.157%
Sample Variance	26.596%
Kurtosis	13.53
Skewness	2.82
Range	44.091%
Minimum	2.436%
Maximum	46.527%
Count	554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.177%	554	100.00%	9.177%
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 1.33. Further, an Excess Kurtosis of 7.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.25%	0	0.00%	0.00%
-17.25% to -12.94%	5	0.90%	0.90%
-12.94% to -8.64%	19	3.43%	4.33%
-8.64% to -4.34%	90	16.25%	20.58%
-4.34% to -0.04%	197	35.56%	56.14%
-0.04% to 4.26%	141	25.45%	81.59%
4.26% to 8.57%	69	12.45%	94.04%
8.57% to 12.87%	26	4.69%	98.74%
12.87% to 17.17%	3	0.54%	99.28%
Greater than 17.17%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.77%	5.70%	74.55%	68.27%
±2σ	-11.51%	11.43%	95.85%	95.45%
±3σ	-17.25%	17.17%	99.28%	99.73%

Descriptive Statistics

Mean	-0.038%
Standard Error	0.244%
Median	-0.564%
Mode	-2.756%
Standard Deviation	5.736%
Sample Variance	32.902%
Kurtosis	7.44
Skewness	1.33
Range	57.206%
Minimum	-14.483%
Maximum	42.723%
Count	554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.722%	243	43.86%	2.071%
Negative	-3.758%	311	56.14%	-2.110%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. Further, an Excess Kurtosis of 1.90 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.09%	1	0.79%	0.79%
-33.09% to -24.31%	1	0.79%	1.57%
-24.31% to -15.53%	5	3.94%	5.51%
-15.53% to -6.75%	18	14.17%	19.69%
-6.75% to 2.02%	40	31.50%	51.18%
2.02% to 10.80%	35	27.56%	78.74%
10.80% to 19.58%	21	16.54%	95.28%
19.58% to 28.36%	3	2.36%	97.64%
28.36% to 37.14%	2	1.57%	99.21%
Greater than 37.14%	1	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.68%	13.73%	80.31%	68.27%
±2σ	-21.39%	25.43%	93.70%	95.45%
±3σ	-33.09%	37.14%	98.43%	99.73%

Descriptive Statistics

Mean	2.024%
Standard Error	1.039%
Median	1.622%
Mode	-34.526%
Standard Deviation	11.705%
Sample Variance	137.009%
Kurtosis	1.90
Skewness	0.35
Range	81.073%
Minimum	-34.526%
Maximum	46.547%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.629%	72	56.69%	5.459%
Negative	-7.932%	55	43.31%	-3.435%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	12.83%
12	1 Year	16.03%
36	3 Years	16.35%
60	5 Years	18.45%
120	10 Years	18.76%
240	20 Years	18.89%
600	50 Years	18.89%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.57. Further, an Excess Kurtosis of 8.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.36%	0	0.00%	0.00%
-14.36% to -5.49%	0	0.00%	0.00%
-5.49% to 3.39%	0	0.00%	0.00%
3.39% to 12.26%	19	14.84%	14.84%
12.26% to 21.13%	67	52.34%	67.19%
21.13% to 30.01%	27	21.09%	88.28%
30.01% to 38.88%	5	3.91%	92.19%
38.88% to 47.75%	4	3.12%	95.31%
47.75% to 56.63%	3	2.34%	97.66%
Greater than 56.63%	3	2.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.30%	32.96%	87.50%	68.27%
±2σ	-2.53%	44.80%	94.53%	95.45%
±3σ	-14.36%	56.63%	97.66%	99.73%

Descriptive Statistics

Mean	21.133%
Standard Error	1.046%
Median	18.187%
Mode	11.548%
Standard Deviation	11.831%
Sample Variance	139.981%
Kurtosis	8.95
Skewness	2.57
Range	79.717%
Minimum	6.582%
Maximum	86.299%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.133%	128	100.00%	21.133%
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 3.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.48%	0	0.00%	0.00%
-36.48% to -27.49%	1	0.78%	0.78%
-27.49% to -18.50%	5	3.91%	4.69%
-18.50% to -9.51%	19	14.84%	19.53%
-9.51% to -0.53%	45	35.16%	54.69%
-0.53% to 8.46%	35	27.34%	82.03%
8.46% to 17.45%	15	11.72%	93.75%
17.45% to 26.44%	4	3.12%	96.88%
26.44% to 35.42%	2	1.56%	98.44%
Greater than 35.42%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.51%	11.46%	81.25%	68.27%
±2σ	-24.49%	23.44%	93.75%	95.45%
±3σ	-36.48%	35.42%	98.44%	99.73%

Descriptive Statistics

Mean	-0.526%
Standard Error	1.059%
Median	-1.674%
Mode	-6.804%
Standard Deviation	11.983%
Sample Variance	143.603%
Kurtosis	3.33
Skewness	0.88
Range	87.621%
Minimum	-34.546%
Maximum	53.075%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.209%	58	45.31%	4.173%
Negative	-8.591%	70	54.69%	-4.698%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.30. Further, an Excess Kurtosis of -0.25 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.70%	0	0.00%	0.00%
-51.70% to -37.34%	0	0.00%	0.00%
-37.34% to -22.98%	3	6.98%	6.98%
-22.98% to -8.61%	7	16.28%	23.26%
-8.61% to 5.75%	13	30.23%	53.49%
5.75% to 20.11%	9	20.93%	74.42%
20.11% to 34.48%	9	20.93%	95.35%
34.48% to 48.84%	1	2.33%	97.67%
48.84% to 63.20%	1	2.33%	100.00%
Greater than 63.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.40%	24.90%	67.44%	68.27%
±2σ	-32.55%	44.05%	97.67%	95.45%
±3σ	-51.70%	63.21%	100.00%	99.73%

Descriptive Statistics

Mean	5.752%
Standard Error	2.921%
Median	1.682%
Mode	-29.146%
Standard Deviation	19.151%
Sample Variance	366.770%
Kurtosis	-0.25
Skewness	0.30
Range	83.910%
Minimum	-29.146%
Maximum	54.764%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.145%	24	55.81%	10.686%
Negative	-11.166%	19	44.19%	-4.934%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	22.05%
12	3 Years	25.00%
20	5 Years	30.16%
40	10 Years	31.61%
80	20 Years	32.22%
200	50 Years	32.22%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.62. Further, an Excess Kurtosis of 10.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.96%	0	0.00%	0.00%
-33.96% to -15.73%	0	0.00%	0.00%
-15.73% to 2.50%	0	0.00%	0.00%
2.50% to 20.73%	6	13.64%	13.64%
20.73% to 38.97%	22	50.00%	63.64%
38.97% to 57.20%	8	18.18%	81.82%
57.20% to 75.43%	5	11.36%	93.18%
75.43% to 93.66%	2	4.55%	97.73%
93.66% to 111.90%	0	0.00%	97.73%
Greater than 111.90%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.66%	63.28%	84.09%	68.27%
±2σ	-9.65%	87.59%	97.73%	95.45%
±3σ	-33.96%	111.90%	97.73%	99.73%

Descriptive Statistics

Mean	38.966%
Standard Error	3.665%
Median	32.323%
Mode	9.848%
Standard Deviation	24.310%
Sample Variance	590.956%
Kurtosis	10.17
Skewness	2.62
Range	142.563%
Minimum	9.848%
Maximum	152.411%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.966%	44	100.00%	38.966%
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 0.50. Further, an Excess Kurtosis of -0.14 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -57.08%	0	0.00%	0.00%
-57.08% to -43.31%	0	0.00%	0.00%
-43.31% to -29.55%	1	2.27%	2.27%
-29.55% to -15.79%	12	27.27%	29.55%
-15.79% to -2.02%	8	18.18%	47.73%
-2.02% to 11.74%	14	31.82%	79.55%
11.74% to 25.51%	6	13.64%	93.18%
25.51% to 39.27%	2	4.55%	97.73%
39.27% to 53.03%	1	2.27%	100.00%
Greater than 53.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.37%	16.33%	70.45%	68.27%
±2σ	-38.73%	34.68%	95.45%	95.45%
±3σ	-57.08%	53.03%	100.00%	99.73%

Descriptive Statistics

Mean	-2.021%
Standard Error	2.767%
Median	-1.282%
Mode	-36.803%
Standard Deviation	18.352%
Sample Variance	336.809%
Kurtosis	-0.14
Skewness	0.50
Range	79.356%
Minimum	-36.803%
Maximum	42.553%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.848%	19	43.18%	6.412%
Negative	-14.841%	25	56.82%	-8.432%
Zero	0.000%	0	0.00%	0.000%

OLLI Deep Analytical Report