ORLY - 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	2.07%	1.93%	1.92%	2.00%	1.87%	2.15%	91.77	95.27	90.07	97.06
Weekly	4.51%	4.53%	4.42%	4.60%	4.12%	4.74%	89.73	97.43	86.11	101.53
Monthly	8.41%	9.89%	8.31%	9.96%	8.57%	9.86%	85.82	101.87	78.77	110.98
Quarterly	13.42%	15.72%	13.01%	15.71%	14.84%	17.08%	80.60	108.46	69.48	125.82
Annual	—	—	—	—	29.69%	34.17%	69.48	125.82	51.63	169.31
Option Time Horizon	—	—	—	—	14.07%	16.20%	81.23	107.63	70.56	123.89

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $93.50 | Strike (K): $95.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.9500 (Bid $4.5000 / Ask $5.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 29.69% (CRR binomial tree, American, n=20 steps) | BS IV: 29.87% (European Black-Scholes) | Yahoo IV (Annual): 34.17% → 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 Fairly Symmetrical with a Skewness factor of 0.41. Further, an Excess Kurtosis of 10.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.11%	57	0.69%	0.69%
-6.11% to -4.56%	76	0.93%	1.62%
-4.56% to -3.01%	226	2.76%	4.38%
-3.01% to -1.45%	911	11.11%	15.48%
-1.45% to 0.10%	2994	36.50%	51.99%
0.10% to 1.65%	2691	32.81%	84.80%
1.65% to 3.21%	865	10.55%	95.34%
3.21% to 4.76%	221	2.69%	98.04%
4.76% to 6.31%	78	0.95%	98.99%
Greater than 6.31%	83	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.97%	2.17%	80.50%	68.27%
±2σ	-4.04%	4.24%	95.35%	95.45%
±3σ	-6.11%	6.31%	98.29%	99.73%

Descriptive Statistics

Mean	0.099%
Standard Error	0.023%
Median	0.029%
Mode	0.000%
Standard Deviation	2.071%
Sample Variance	4.291%
Kurtosis	10.02
Skewness	0.41
Range	39.094%
Minimum	-18.892%
Maximum	20.202%
Count	8202

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.450%	4151	50.61%	0.734%
Negative	-1.395%	3732	45.50%	-0.635%
Zero	0.000%	319	3.89%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.96%
20	1 Month	2.59%
60	1 Quarter	2.10%
250	1 Year	2.10%
750	3 Years	1.89%
1,250	5 Years	2.00%
2,500	10 Years	2.17%
5,000	20 Years	2.31%
12,500	50 Years	2.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.72. Further, an Excess Kurtosis of 32.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.13%	0	0.00%	0.00%
-3.13% to -1.68%	0	0.00%	0.00%
-1.68% to -0.23%	0	0.00%	0.00%
-0.23% to 1.22%	1026	12.51%	12.51%
1.22% to 2.67%	4413	53.80%	66.31%
2.67% to 4.12%	1617	19.71%	86.02%
4.12% to 5.57%	607	7.40%	93.42%
5.57% to 7.01%	262	3.19%	96.61%
7.01% to 8.46%	99	1.21%	97.82%
Greater than 8.46%	179	2.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.74%	4.60%	88.27%	68.27%
±2σ	-1.20%	6.53%	95.87%	95.45%
±3σ	-3.13%	8.46%	97.82%	99.73%

Descriptive Statistics

Mean	2.668%
Standard Error	0.021%
Median	2.146%
Mode	2.632%
Standard Deviation	1.932%
Sample Variance	3.732%
Kurtosis	32.56
Skewness	3.72
Range	41.650%
Minimum	0.285%
Maximum	41.935%
Count	8203

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.668%	8203	100.00%	2.668%
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 9.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.81%	71	0.87%	0.87%
-5.81% to -4.37%	64	0.78%	1.65%
-4.37% to -2.93%	255	3.11%	4.75%
-2.93% to -1.49%	900	10.97%	15.73%
-1.49% to -0.05%	2734	33.33%	49.06%
-0.05% to 1.39%	2856	34.82%	83.87%
1.39% to 2.83%	936	11.41%	95.28%
2.83% to 4.28%	247	3.01%	98.29%
4.28% to 5.72%	71	0.87%	99.16%
Greater than 5.72%	69	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.97%	1.87%	78.40%	68.27%
±2σ	-3.89%	3.80%	95.49%	95.45%
±3σ	-5.81%	5.72%	98.29%	99.73%

Descriptive Statistics

Mean	-0.048%
Standard Error	0.021%
Median	-0.008%
Mode	0.000%
Standard Deviation	1.922%
Sample Variance	3.694%
Kurtosis	9.38
Skewness	0.15
Range	38.807%
Minimum	-20.625%
Maximum	18.182%
Count	8203

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.368%	3739	45.58%	0.624%
Negative	-1.339%	4116	50.18%	-0.672%
Zero	0.000%	348	4.24%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.64. Further, an Excess Kurtosis of 7.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.06%	12	0.70%	0.70%
-13.06% to -9.68%	16	0.93%	1.63%
-9.68% to -6.29%	43	2.51%	4.14%
-6.29% to -2.91%	209	12.20%	16.35%
-2.91% to 0.47%	623	36.37%	52.71%
0.47% to 3.86%	533	31.12%	83.83%
3.86% to 7.24%	190	11.09%	94.92%
7.24% to 10.63%	49	2.86%	97.78%
10.63% to 14.01%	15	0.88%	98.66%
Greater than 14.01%	23	1.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.04%	4.99%	79.33%	68.27%
±2σ	-8.55%	9.50%	94.98%	95.45%
±3σ	-13.06%	14.01%	97.96%	99.73%

Descriptive Statistics

Mean	0.474%
Standard Error	0.109%
Median	0.234%
Mode	0.000%
Standard Deviation	4.512%
Sample Variance	20.354%
Kurtosis	7.12
Skewness	0.64
Range	60.092%
Minimum	-22.222%
Maximum	37.870%
Count	1713

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.305%	919	53.65%	1.773%
Negative	-2.886%	771	45.01%	-1.299%
Zero	0.000%	23	1.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.52%
12	1 Quarter	5.28%
52	1 Year	5.04%
156	3 Years	4.34%
260	5 Years	4.60%
520	10 Years	4.98%
1,040	20 Years	5.28%
2,600	50 Years	6.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.77. Further, an Excess Kurtosis of 11.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.30%	0	0.00%	0.00%
-7.30% to -3.90%	0	0.00%	0.00%
-3.90% to -0.50%	0	0.00%	0.00%
-0.50% to 2.90%	243	14.18%	14.18%
2.90% to 6.30%	886	51.69%	65.87%
6.30% to 9.70%	334	19.49%	85.36%
9.70% to 13.10%	126	7.35%	92.71%
13.10% to 16.50%	58	3.38%	96.09%
16.50% to 19.89%	33	1.93%	98.02%
Greater than 19.89%	34	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.76%	10.83%	87.11%	68.27%
±2σ	-2.77%	15.36%	95.57%	95.45%
±3σ	-7.30%	19.89%	98.02%	99.73%

Descriptive Statistics

Mean	6.296%
Standard Error	0.109%
Median	4.966%
Mode	2.632%
Standard Deviation	4.533%
Sample Variance	20.551%
Kurtosis	11.85
Skewness	2.77
Range	42.217%
Minimum	1.331%
Maximum	43.548%
Count	1714

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.296%	1714	100.00%	6.296%
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 0.59. Further, an Excess Kurtosis of 5.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.49%	10	0.58%	0.58%
-13.49% to -10.18%	20	1.17%	1.75%
-10.18% to -6.87%	53	3.09%	4.84%
-6.87% to -3.55%	206	12.02%	16.86%
-3.55% to -0.24%	571	33.31%	50.18%
-0.24% to 3.07%	593	34.60%	84.77%
3.07% to 6.38%	178	10.39%	95.16%
6.38% to 9.69%	44	2.57%	97.72%
9.69% to 13.01%	23	1.34%	99.07%
Greater than 13.01%	16	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.66%	4.17%	78.88%	68.27%
±2σ	-9.07%	8.59%	94.81%	95.45%
±3σ	-13.49%	13.01%	98.48%	99.73%

Descriptive Statistics

Mean	-0.242%
Standard Error	0.107%
Median	-0.249%
Mode	0.000%
Standard Deviation	4.416%
Sample Variance	19.505%
Kurtosis	5.97
Skewness	0.59
Range	55.838%
Minimum	-25.751%
Maximum	30.087%
Count	1714

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.048%	785	45.80%	1.396%
Negative	-3.120%	900	52.51%	-1.638%
Zero	0.000%	29	1.69%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.85. Further, an Excess Kurtosis of 7.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.27%	1	0.25%	0.25%
-23.27% to -16.96%	2	0.51%	0.76%
-16.96% to -10.64%	12	3.05%	3.81%
-10.64% to -4.33%	59	14.97%	18.78%
-4.33% to 1.98%	132	33.50%	52.28%
1.98% to 8.29%	120	30.46%	82.74%
8.29% to 14.60%	47	11.93%	94.67%
14.60% to 20.91%	14	3.55%	98.22%
20.91% to 27.22%	4	1.02%	99.24%
Greater than 27.22%	3	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.44%	10.39%	74.37%	68.27%
±2σ	-14.85%	18.80%	96.45%	95.45%
±3σ	-23.27%	27.22%	98.98%	99.73%

Descriptive Statistics

Mean	1.976%
Standard Error	0.424%
Median	1.771%
Mode	0.000%
Standard Deviation	8.414%
Sample Variance	70.800%
Kurtosis	7.26
Skewness	0.85
Range	99.856%
Minimum	-38.954%
Maximum	60.902%
Count	394

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.807%	237	60.15%	4.095%
Negative	-5.384%	155	39.34%	-2.118%
Zero	0.000%	2	0.51%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.42%
12	1 Year	10.51%
36	3 Years	9.36%
60	5 Years	9.96%
120	10 Years	10.63%
240	20 Years	11.10%
600	50 Years	12.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.85. Further, an Excess Kurtosis of 24.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.77%	0	0.00%	0.00%
-15.77% to -8.35%	0	0.00%	0.00%
-8.35% to -0.93%	0	0.00%	0.00%
-0.93% to 6.49%	42	10.63%	10.63%
6.49% to 13.91%	210	53.16%	63.80%
13.91% to 21.34%	91	23.04%	86.84%
21.34% to 28.76%	29	7.34%	94.18%
28.76% to 36.18%	11	2.78%	96.96%
36.18% to 43.60%	6	1.52%	98.48%
Greater than 43.60%	6	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.02%	23.81%	90.63%	68.27%
±2σ	-5.88%	33.70%	95.95%	95.45%
±3σ	-15.77%	43.60%	98.48%	99.73%

Descriptive Statistics

Mean	13.915%
Standard Error	0.498%
Median	11.614%
Mode	5.072%
Standard Deviation	9.895%
Sample Variance	97.905%
Kurtosis	24.70
Skewness	3.85
Range	101.294%
Minimum	3.251%
Maximum	104.545%
Count	395

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.915%	395	100.00%	13.915%
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 1.40. Further, an Excess Kurtosis of 12.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.13%	1	0.25%	0.25%
-26.13% to -19.89%	3	0.76%	1.01%
-19.89% to -13.66%	12	3.04%	4.05%
-13.66% to -7.42%	61	15.44%	19.49%
-7.42% to -1.19%	132	33.42%	52.91%
-1.19% to 5.05%	116	29.37%	82.28%
5.05% to 11.28%	50	12.66%	94.94%
11.28% to 17.52%	13	3.29%	98.23%
17.52% to 23.75%	6	1.52%	99.75%
Greater than 23.75%	1	0.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.50%	7.13%	76.46%	68.27%
±2σ	-17.82%	15.44%	95.95%	95.45%
±3σ	-26.13%	23.75%	99.49%	99.73%

Descriptive Statistics

Mean	-1.187%
Standard Error	0.418%
Median	-1.674%
Mode	0.000%
Standard Deviation	8.314%
Sample Variance	69.128%
Kurtosis	12.77
Skewness	1.40
Range	104.786%
Minimum	-36.215%
Maximum	68.571%
Count	395

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.980%	160	40.51%	2.422%
Negative	-6.172%	231	58.48%	-3.609%
Zero	0.000%	4	1.01%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.11. Further, an Excess Kurtosis of 0.60 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.43%	1	0.76%	0.76%
-34.43% to -24.37%	0	0.00%	0.76%
-24.37% to -14.30%	5	3.79%	4.55%
-14.30% to -4.24%	24	18.18%	22.73%
-4.24% to 5.82%	39	29.55%	52.27%
5.82% to 15.89%	34	25.76%	78.03%
15.89% to 25.95%	16	12.12%	90.15%
25.95% to 36.01%	12	9.09%	99.24%
36.01% to 46.08%	0	0.00%	99.24%
Greater than 46.08%	1	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.59%	19.24%	70.45%	68.27%
±2σ	-21.01%	32.66%	96.97%	95.45%
±3σ	-34.43%	46.08%	98.48%	99.73%

Descriptive Statistics

Mean	5.823%
Standard Error	1.168%
Median	4.774%
Mode	-39.828%
Standard Deviation	13.418%
Sample Variance	180.047%
Kurtosis	0.60
Skewness	0.11
Range	87.397%
Minimum	-39.828%
Maximum	47.569%
Count	132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.509%	90	68.18%	8.529%
Negative	-8.506%	42	31.82%	-2.706%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	12.97%
12	3 Years	13.61%
20	5 Years	15.71%
40	10 Years	18.24%
80	20 Years	19.64%
200	50 Years	22.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.22. Further, an Excess Kurtosis of 7.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.31%	0	0.00%	0.00%
-21.31% to -9.52%	0	0.00%	0.00%
-9.52% to 2.28%	0	0.00%	0.00%
2.28% to 14.07%	22	16.54%	16.54%
14.07% to 25.86%	65	48.87%	65.41%
25.86% to 37.66%	25	18.80%	84.21%
37.66% to 49.45%	11	8.27%	92.48%
49.45% to 61.24%	5	3.76%	96.24%
61.24% to 73.04%	3	2.26%	98.50%
Greater than 73.04%	2	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.14%	41.59%	84.96%	68.27%
±2σ	-5.58%	57.31%	95.49%	95.45%
±3σ	-21.31%	73.04%	98.50%	99.73%

Descriptive Statistics

Mean	25.864%
Standard Error	1.363%
Median	21.389%
Mode	6.850%
Standard Deviation	15.724%
Sample Variance	247.231%
Kurtosis	7.01
Skewness	2.22
Range	97.695%
Minimum	6.850%
Maximum	104.545%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.864%	133	100.00%	25.864%
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 1.24. Further, an Excess Kurtosis of 5.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.85%	0	0.00%	0.00%
-42.85% to -33.09%	0	0.00%	0.00%
-33.09% to -23.33%	3	2.26%	2.26%
-23.33% to -13.57%	27	20.30%	22.56%
-13.57% to -3.81%	41	30.83%	53.38%
-3.81% to 5.95%	37	27.82%	81.20%
5.95% to 15.71%	19	14.29%	95.49%
15.71% to 25.47%	4	3.01%	98.50%
25.47% to 35.23%	1	0.75%	99.25%
Greater than 35.23%	1	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.82%	9.21%	72.93%	68.27%
±2σ	-29.83%	22.22%	96.24%	95.45%
±3σ	-42.85%	35.23%	99.25%	99.73%

Descriptive Statistics

Mean	-3.808%
Standard Error	1.128%
Median	-4.733%
Mode	-31.948%
Standard Deviation	13.013%
Sample Variance	169.344%
Kurtosis	5.33
Skewness	1.24
Range	98.138%
Minimum	-31.948%
Maximum	66.190%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.932%	44	33.08%	3.286%
Negative	-10.601%	89	66.92%	-7.094%
Zero	0.000%	0	0.00%	0.000%

ORLY Deep Analytical Report