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%	3.87%	2.30%	2.49%	93.42	97.81	91.30	100.08
Weekly	5.57%	5.14%	5.75%	8.83%	5.05%	5.49%	90.88	100.54	86.40	105.76
Monthly	11.72%	11.77%	11.97%	18.47%	10.52%	11.42%	86.05	106.19	77.45	117.97
Quarterly	19.34%	24.00%	18.53%	30.72%	18.22%	19.79%	79.67	114.69	66.40	137.61
Annual	—	—	—	—	36.44%	39.58%	66.40	137.61	46.12	198.11
Option Time Horizon	—	—	—	—	13.75%	14.94%	83.31	109.68	72.60	125.86

Calculation Notes: Computed at 2026-03-23T16:38 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $95.59 | Strike (K): $105.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.2000 (Bid $1.9000 / Ask $2.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 36.44% (CRR binomial tree, American, n=20 steps) | BS IV: 36.82% (European Black-Scholes) | Yahoo IV (Annual): 39.58% → 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 -0.60. Further, an Excess Kurtosis of 9.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.03%	16	0.60%	0.60%
-8.03% to -6.00%	25	0.93%	1.53%
-6.00% to -3.97%	88	3.28%	4.80%
-3.97% to -1.94%	340	12.66%	17.46%
-1.94% to 0.09%	856	31.87%	49.33%
0.09% to 2.12%	898	33.43%	82.76%
2.12% to 4.15%	325	12.10%	94.86%
4.15% to 6.18%	91	3.39%	98.25%
6.18% to 8.21%	29	1.08%	99.33%
Greater than 8.21%	18	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.61%	2.80%	76.55%	68.27%
±2σ	-5.32%	5.50%	95.90%	95.45%
±3σ	-8.03%	8.21%	98.73%	99.73%

Descriptive Statistics

Mean	0.093%
Standard Error	0.052%
Median	0.117%
Mode	0.000%
Standard Deviation	2.706%
Sample Variance	7.322%
Kurtosis	9.19
Skewness	-0.60
Range	43.189%
Minimum	-27.530%
Maximum	15.659%
Count	2686

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.927%	1396	51.97%	1.002%
Negative	-1.916%	1273	47.39%	-0.908%
Zero	0.000%	17	0.63%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.95%
20	1 Month	4.31%
60	1 Quarter	3.66%
250	1 Year	3.76%
750	3 Years	3.44%
1,250	5 Years	3.87%
2,500	10 Years	3.76%
5,000	20 Years	3.85%
12,500	50 Years	3.85%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.80. Further, an Excess Kurtosis of 33.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.83%	0	0.00%	0.00%
-2.83% to -1.18%	0	0.00%	0.00%
-1.18% to 0.47%	0	0.00%	0.00%
0.47% to 2.12%	429	15.97%	15.97%
2.12% to 3.77%	1252	46.59%	62.56%
3.77% to 5.42%	614	22.85%	85.41%
5.42% to 7.06%	227	8.45%	93.86%
7.06% to 8.71%	82	3.05%	96.91%
8.71% to 10.36%	38	1.41%	98.33%
Greater than 10.36%	45	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.57%	5.96%	85.26%	68.27%
±2σ	-0.63%	8.16%	95.94%	95.45%
±3σ	-2.83%	10.36%	98.33%	99.73%

Descriptive Statistics

Mean	3.766%
Standard Error	0.042%
Median	3.234%
Mode	2.333%
Standard Deviation	2.199%
Sample Variance	4.836%
Kurtosis	33.40
Skewness	3.80
Range	37.084%
Minimum	0.654%
Maximum	37.738%
Count	2687

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.766%	2687	100.00%	3.766%
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 2.17 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	0.52%	0.52%
-7.16% to -5.37%	28	1.04%	1.56%
-5.37% to -3.58%	113	4.21%	5.77%
-3.58% to -1.79%	358	13.32%	19.09%
-1.79% to -0.01%	857	31.89%	50.99%
-0.01% to 1.78%	797	29.66%	80.65%
1.78% to 3.57%	354	13.17%	93.82%
3.57% to 5.36%	116	4.32%	98.14%
5.36% to 7.15%	30	1.12%	99.26%
Greater than 7.15%	20	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.39%	2.38%	74.25%	68.27%
±2σ	-4.77%	4.76%	94.75%	95.45%
±3σ	-7.16%	7.15%	98.73%	99.73%

Descriptive Statistics

Mean	-0.005%
Standard Error	0.046%
Median	-0.073%
Mode	0.000%
Standard Deviation	2.384%
Sample Variance	5.681%
Kurtosis	2.17
Skewness	0.22
Range	24.837%
Minimum	-11.114%
Maximum	13.723%
Count	2687

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.839%	1292	48.08%	0.884%
Negative	-1.743%	1370	50.99%	-0.889%
Zero	0.000%	25	0.93%	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 2.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.26%	3	0.54%	0.54%
-16.26% to -12.09%	3	0.54%	1.08%
-12.09% to -7.91%	28	5.03%	6.10%
-7.91% to -3.74%	88	15.80%	21.90%
-3.74% to 0.44%	146	26.21%	48.11%
0.44% to 4.61%	179	32.14%	80.25%
4.61% to 8.79%	77	13.82%	94.08%
8.79% to 12.96%	22	3.95%	98.03%
12.96% to 17.13%	10	1.80%	99.82%
Greater than 17.13%	1	0.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.13%	6.00%	71.63%	68.27%
±2σ	-10.70%	11.57%	95.33%	95.45%
±3σ	-16.26%	17.13%	99.28%	99.73%

Descriptive Statistics

Mean	0.436%
Standard Error	0.236%
Median	0.643%
Mode	0.000%
Standard Deviation	5.566%
Sample Variance	30.979%
Kurtosis	2.19
Skewness	-0.29
Range	46.986%
Minimum	-29.462%
Maximum	17.524%
Count	557

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.232%	307	55.12%	2.333%
Negative	-4.277%	247	44.34%	-1.897%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.99%
12	1 Quarter	7.94%
52	1 Year	8.51%
156	3 Years	7.88%
260	5 Years	8.83%
520	10 Years	8.61%
1,040	20 Years	8.71%
2,600	50 Years	8.71%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.24%	0	0.00%	0.00%
-6.24% to -2.38%	0	0.00%	0.00%
-2.38% to 1.48%	0	0.00%	0.00%
1.48% to 5.34%	98	17.56%	17.56%
5.34% to 9.19%	255	45.70%	63.26%
9.19% to 13.05%	122	21.86%	85.13%
13.05% to 16.91%	46	8.24%	93.37%
16.91% to 20.77%	20	3.58%	96.95%
20.77% to 24.62%	8	1.43%	98.39%
Greater than 24.62%	9	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.05%	14.34%	84.05%	68.27%
±2σ	-1.09%	19.48%	96.42%	95.45%
±3σ	-6.24%	24.62%	98.39%	99.73%

Descriptive Statistics

Mean	9.193%
Standard Error	0.218%
Median	8.059%
Mode	4.144%
Standard Deviation	5.143%
Sample Variance	26.453%
Kurtosis	13.55
Skewness	2.82
Range	44.091%
Minimum	2.436%
Maximum	46.527%
Count	558

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.193%	558	100.00%	9.193%
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 1.32. Further, an Excess Kurtosis of 7.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.27%	0	0.00%	0.00%
-17.27% to -12.95%	5	0.90%	0.90%
-12.95% to -8.64%	19	3.41%	4.30%
-8.64% to -4.33%	92	16.49%	20.79%
-4.33% to -0.02%	197	35.30%	56.09%
-0.02% to 4.29%	141	25.27%	81.36%
4.29% to 8.60%	71	12.72%	94.09%
8.60% to 12.92%	26	4.66%	98.75%
12.92% to 17.23%	3	0.54%	99.28%
Greater than 17.23%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.77%	5.73%	74.01%	68.27%
±2σ	-11.52%	11.48%	95.88%	95.45%
±3σ	-17.27%	17.23%	99.28%	99.73%

Descriptive Statistics

Mean	-0.019%
Standard Error	0.243%
Median	-0.564%
Mode	-2.756%
Standard Deviation	5.749%
Sample Variance	33.048%
Kurtosis	7.29
Skewness	1.32
Range	57.206%
Minimum	-14.483%
Maximum	42.723%
Count	558

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.756%	245	43.91%	2.088%
Negative	-3.757%	313	56.09%	-2.107%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.37. Further, an Excess Kurtosis of 1.86 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.24%	1	0.78%	0.78%
-33.24% to -24.45%	1	0.78%	1.56%
-24.45% to -15.66%	5	3.91%	5.47%
-15.66% to -6.88%	19	14.84%	20.31%
-6.88% to 1.91%	40	31.25%	51.56%
1.91% to 10.70%	35	27.34%	78.91%
10.70% to 19.49%	21	16.41%	95.31%
19.49% to 28.28%	3	2.34%	97.66%
28.28% to 37.07%	2	1.56%	99.22%
Greater than 37.07%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.81%	13.63%	78.91%	68.27%
±2σ	-21.52%	25.35%	93.75%	95.45%
±3σ	-33.24%	37.07%	98.44%	99.73%

Descriptive Statistics

Mean	1.912%
Standard Error	1.036%
Median	1.611%
Mode	-34.526%
Standard Deviation	11.718%
Sample Variance	137.309%
Kurtosis	1.86
Skewness	0.37
Range	81.073%
Minimum	-34.526%
Maximum	46.547%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.629%	72	56.25%	5.416%
Negative	-8.010%	56	43.75%	-3.504%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	14.54%
12	1 Year	16.06%
36	3 Years	16.27%
60	5 Years	18.47%
120	10 Years	18.75%
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 2.59. Further, an Excess Kurtosis of 9.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.18%	0	0.00%	0.00%
-14.18% to -5.35%	0	0.00%	0.00%
-5.35% to 3.48%	0	0.00%	0.00%
3.48% to 12.31%	18	13.95%	13.95%
12.31% to 21.13%	69	53.49%	67.44%
21.13% to 29.96%	27	20.93%	88.37%
29.96% to 38.79%	5	3.88%	92.25%
38.79% to 47.62%	4	3.10%	95.35%
47.62% to 56.44%	3	2.33%	97.67%
Greater than 56.44%	3	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.36%	32.90%	87.60%	68.27%
±2σ	-2.41%	44.67%	94.57%	95.45%
±3σ	-14.18%	56.44%	97.67%	99.73%

Descriptive Statistics

Mean	21.134%
Standard Error	1.036%
Median	18.227%
Mode	11.548%
Standard Deviation	11.770%
Sample Variance	138.543%
Kurtosis	9.10
Skewness	2.59
Range	79.717%
Minimum	6.582%
Maximum	86.299%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.134%	129	100.00%	21.134%
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 0.86. Further, an Excess Kurtosis of 3.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.34%	0	0.00%	0.00%
-36.34% to -27.37%	2	1.55%	1.55%
-27.37% to -18.39%	4	3.10%	4.65%
-18.39% to -9.42%	20	15.50%	20.16%
-9.42% to -0.44%	44	34.11%	54.26%
-0.44% to 8.54%	36	27.91%	82.17%
8.54% to 17.51%	15	11.63%	93.80%
17.51% to 26.49%	4	3.10%	96.90%
26.49% to 35.46%	2	1.55%	98.45%
Greater than 35.46%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.41%	11.53%	81.40%	68.27%
±2σ	-24.38%	23.50%	93.80%	95.45%
±3σ	-36.34%	35.46%	98.45%	99.73%

Descriptive Statistics

Mean	-0.441%
Standard Error	1.054%
Median	-1.658%
Mode	-6.804%
Standard Deviation	11.968%
Sample Variance	143.227%
Kurtosis	3.29
Skewness	0.86
Range	87.621%
Minimum	-34.546%
Maximum	53.075%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.229%	59	45.74%	4.221%
Negative	-8.591%	70	54.26%	-4.662%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.31. Further, an Excess Kurtosis of -0.32 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.56%	0	0.00%	0.00%
-52.56% to -38.05%	0	0.00%	0.00%
-38.05% to -23.54%	3	6.98%	6.98%
-23.54% to -9.03%	7	16.28%	23.26%
-9.03% to 5.47%	13	30.23%	53.49%
5.47% to 19.98%	9	20.93%	74.42%
19.98% to 34.49%	9	20.93%	95.35%
34.49% to 49.00%	1	2.33%	97.67%
49.00% to 63.51%	1	2.33%	100.00%
Greater than 63.51%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.87%	24.82%	67.44%	68.27%
±2σ	-33.21%	44.16%	97.67%	95.45%
±3σ	-52.56%	63.51%	100.00%	99.73%

Descriptive Statistics

Mean	5.474%
Standard Error	2.950%
Median	1.682%
Mode	-29.146%
Standard Deviation	19.344%
Sample Variance	374.184%
Kurtosis	-0.32
Skewness	0.31
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	-11.795%	19	44.19%	-5.212%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	24.83%
12	3 Years	25.93%
20	5 Years	30.72%
40	10 Years	31.88%
80	20 Years	32.48%
200	50 Years	32.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.71. Further, an Excess Kurtosis of 10.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.72%	0	0.00%	0.00%
-32.72% to -14.72%	0	0.00%	0.00%
-14.72% to 3.28%	0	0.00%	0.00%
3.28% to 21.29%	5	11.36%	11.36%
21.29% to 39.29%	24	54.55%	65.91%
39.29% to 57.30%	7	15.91%	81.82%
57.30% to 75.30%	5	11.36%	93.18%
75.30% to 93.30%	2	4.55%	97.73%
93.30% to 111.31%	0	0.00%	97.73%
Greater than 111.31%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.29%	63.30%	86.36%	68.27%
±2σ	-8.72%	87.30%	97.73%	95.45%
±3σ	-32.72%	111.31%	97.73%	99.73%

Descriptive Statistics

Mean	39.291%
Standard Error	3.619%
Median	32.323%
Mode	13.546%
Standard Deviation	24.005%
Sample Variance	576.264%
Kurtosis	10.64
Skewness	2.71
Range	138.865%
Minimum	13.546%
Maximum	152.411%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.291%	44	100.00%	39.291%
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 0.45. Further, an Excess Kurtosis of -0.28 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -57.29%	0	0.00%	0.00%
-57.29% to -43.40%	0	0.00%	0.00%
-43.40% to -29.50%	1	2.27%	2.27%
-29.50% to -15.60%	12	27.27%	29.55%
-15.60% to -1.70%	8	18.18%	47.73%
-1.70% to 12.20%	13	29.55%	77.27%
12.20% to 26.09%	7	15.91%	93.18%
26.09% to 39.99%	2	4.55%	97.73%
39.99% to 53.89%	1	2.27%	100.00%
Greater than 53.89%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.23%	16.83%	68.18%	68.27%
±2σ	-38.76%	35.36%	95.45%	95.45%
±3σ	-57.29%	53.89%	100.00%	99.73%

Descriptive Statistics

Mean	-1.703%
Standard Error	2.794%
Median	-1.282%
Mode	-36.803%
Standard Deviation	18.530%
Sample Variance	343.379%
Kurtosis	-0.28
Skewness	0.45
Range	79.356%
Minimum	-36.803%
Maximum	42.553%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.583%	19	43.18%	6.729%
Negative	-14.841%	25	56.82%	-8.432%
Zero	0.000%	0	0.00%	0.000%

OLLI Deep Analytical Report