CHKP - 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	3.10%	3.15%	2.76%	2.21%	2.12%	2.37%	155.70	162.45	152.43	165.94
Weekly	6.75%	8.54%	6.71%	4.98%	4.67%	5.21%	151.78	166.65	144.85	174.62
Monthly	13.18%	19.13%	13.23%	10.41%	9.72%	10.84%	144.30	175.28	130.93	193.19
Quarterly	23.50%	38.72%	19.86%	17.30%	16.84%	18.78%	134.39	188.22	113.55	222.75
Annual	—	—	—	—	33.69%	37.56%	113.55	222.75	81.08	311.97
Option Time Horizon	—	—	—	—	12.96%	14.45%	139.71	181.04	122.73	206.09

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $159.04 | Strike (K): $160.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.1500 (Bid $7.5000 / Ask $8.8000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 33.69% (CRR binomial tree, American, n=20 steps) | BS IV: 33.58% (European Black-Scholes) | Yahoo IV (Annual): 37.56% → 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 0.67. Further, an Excess Kurtosis of 13.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.21%	67	0.90%	0.90%
-9.21% to -6.88%	72	0.97%	1.86%
-6.88% to -4.56%	183	2.45%	4.32%
-4.56% to -2.23%	615	8.25%	12.56%
-2.23% to 0.10%	2925	39.22%	51.78%
0.10% to 2.42%	2719	36.46%	88.24%
2.42% to 4.75%	528	7.08%	95.32%
4.75% to 7.08%	170	2.28%	97.60%
7.08% to 9.41%	94	1.26%	98.86%
Greater than 9.41%	85	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.01%	3.20%	82.97%	68.27%
±2σ	-6.11%	6.30%	94.58%	95.45%
±3σ	-9.21%	9.41%	97.96%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.036%
Median	0.023%
Mode	0.000%
Standard Deviation	3.103%
Sample Variance	9.628%
Kurtosis	13.20
Skewness	0.67
Range	59.392%
Minimum	-27.057%
Maximum	32.335%
Count	7458

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.953%	3760	50.42%	0.985%
Negative	-1.832%	3612	48.43%	-0.887%
Zero	0.000%	86	1.15%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.46%
20	1 Month	3.71%
60	1 Quarter	3.03%
250	1 Year	2.75%
750	3 Years	2.22%
1,250	5 Years	2.21%
2,500	10 Years	2.14%
5,000	20 Years	2.32%
12,500	50 Years	3.58%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 15.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.96%	0	0.00%	0.00%
-5.96% to -3.60%	0	0.00%	0.00%
-3.60% to -1.23%	0	0.00%	0.00%
-1.23% to 1.13%	523	7.01%	7.01%
1.13% to 3.49%	4633	62.11%	69.12%
3.49% to 5.85%	1207	16.18%	85.31%
5.85% to 8.22%	525	7.04%	92.34%
8.22% to 10.58%	279	3.74%	96.09%
10.58% to 12.94%	150	2.01%	98.10%
Greater than 12.94%	142	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.34%	6.64%	88.22%	68.27%
±2σ	-2.81%	9.79%	95.15%	95.45%
±3σ	-5.96%	12.94%	98.10%	99.73%

Descriptive Statistics

Mean	3.491%
Standard Error	0.036%
Median	2.388%
Mode	1.924%
Standard Deviation	3.150%
Sample Variance	9.926%
Kurtosis	15.74
Skewness	3.09
Range	39.427%
Minimum	0.311%
Maximum	39.738%
Count	7459

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.491%	7459	100.00%	3.491%
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 0.95. Further, an Excess Kurtosis of 15.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.24%	68	0.91%	0.91%
-8.24% to -6.17%	83	1.11%	2.02%
-6.17% to -4.10%	167	2.24%	4.26%
-4.10% to -2.03%	610	8.18%	12.44%
-2.03% to 0.04%	2986	40.03%	52.47%
0.04% to 2.11%	2606	34.94%	87.41%
2.11% to 4.17%	561	7.52%	94.93%
4.17% to 6.24%	212	2.84%	97.77%
6.24% to 8.31%	81	1.09%	98.86%
Greater than 8.31%	85	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.72%	2.79%	82.63%	68.27%
±2σ	-5.48%	5.55%	94.44%	95.45%
±3σ	-8.24%	8.31%	97.95%	99.73%

Descriptive Statistics

Mean	0.037%
Standard Error	0.032%
Median	-0.043%
Mode	0.000%
Standard Deviation	2.758%
Sample Variance	7.609%
Kurtosis	15.82
Skewness	0.95
Range	63.982%
Minimum	-25.587%
Maximum	38.395%
Count	7459

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.804%	3589	48.12%	0.868%
Negative	-1.630%	3801	50.96%	-0.831%
Zero	0.000%	69	0.93%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.69. Further, an Excess Kurtosis of 7.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.79%	10	0.65%	0.65%
-19.79% to -14.73%	22	1.42%	2.07%
-14.73% to -9.67%	48	3.10%	5.17%
-9.67% to -4.60%	129	8.34%	13.51%
-4.60% to 0.46%	585	37.82%	51.33%
0.46% to 5.52%	555	35.88%	87.20%
5.52% to 10.59%	109	7.05%	94.25%
10.59% to 15.65%	48	3.10%	97.35%
15.65% to 20.71%	24	1.55%	98.90%
Greater than 20.71%	17	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.29%	7.21%	82.09%	68.27%
±2σ	-13.04%	13.96%	93.92%	95.45%
±3σ	-19.79%	20.71%	98.25%	99.73%

Descriptive Statistics

Mean	0.461%
Standard Error	0.172%
Median	0.320%
Mode	0.000%
Standard Deviation	6.751%
Sample Variance	45.577%
Kurtosis	7.55
Skewness	0.69
Range	87.413%
Minimum	-34.187%
Maximum	53.226%
Count	1547

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.452%	822	53.13%	2.366%
Negative	-4.120%	715	46.22%	-1.904%
Zero	0.000%	10	0.65%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.75%
12	1 Quarter	6.91%
52	1 Year	6.05%
156	3 Years	5.02%
260	5 Years	4.98%
520	10 Years	4.83%
1,040	20 Years	5.24%
2,600	50 Years	8.39%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.68. Further, an Excess Kurtosis of 9.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.65%	0	0.00%	0.00%
-16.65% to -10.24%	0	0.00%	0.00%
-10.24% to -3.84%	0	0.00%	0.00%
-3.84% to 2.56%	82	5.30%	5.30%
2.56% to 8.97%	1003	64.79%	70.09%
8.97% to 15.37%	226	14.60%	84.69%
15.37% to 21.77%	118	7.62%	92.31%
21.77% to 28.18%	52	3.36%	95.67%
28.18% to 34.58%	30	1.94%	97.61%
Greater than 34.58%	37	2.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.43%	17.51%	87.27%	68.27%
±2σ	-8.11%	26.04%	94.83%	95.45%
±3σ	-16.65%	34.58%	97.61%	99.73%

Descriptive Statistics

Mean	8.967%
Standard Error	0.217%
Median	5.801%
Mode	2.494%
Standard Deviation	8.538%
Sample Variance	72.901%
Kurtosis	9.61
Skewness	2.68
Range	71.060%
Minimum	1.447%
Maximum	72.507%
Count	1548

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.967%	1548	100.00%	8.967%
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 1.21. Further, an Excess Kurtosis of 9.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.07%	10	0.65%	0.65%
-20.07% to -15.04%	17	1.10%	1.74%
-15.04% to -10.00%	52	3.36%	5.10%
-10.00% to -4.97%	107	6.91%	12.02%
-4.97% to 0.06%	654	42.25%	54.26%
0.06% to 5.10%	514	33.20%	87.47%
5.10% to 10.13%	113	7.30%	94.77%
10.13% to 15.16%	40	2.58%	97.35%
15.16% to 20.20%	19	1.23%	98.58%
Greater than 20.20%	22	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.65%	6.78%	82.62%	68.27%
±2σ	-13.36%	13.49%	94.12%	95.45%
±3σ	-20.07%	20.20%	97.93%	99.73%

Descriptive Statistics

Mean	0.064%
Standard Error	0.171%
Median	-0.326%
Mode	-2.833%
Standard Deviation	6.711%
Sample Variance	45.037%
Kurtosis	9.64
Skewness	1.21
Range	89.216%
Minimum	-34.211%
Maximum	55.005%
Count	1548

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.568%	716	46.25%	2.113%
Negative	-3.825%	829	53.55%	-2.048%
Zero	0.000%	3	0.19%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.87. Further, an Excess Kurtosis of 6.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.67%	1	0.28%	0.28%
-37.67% to -27.78%	7	1.97%	2.25%
-27.78% to -17.90%	11	3.09%	5.34%
-17.90% to -8.01%	32	8.99%	14.33%
-8.01% to 1.88%	142	39.89%	54.21%
1.88% to 11.76%	111	31.18%	85.39%
11.76% to 21.65%	31	8.71%	94.10%
21.65% to 31.53%	10	2.81%	96.91%
31.53% to 41.42%	8	2.25%	99.16%
Greater than 41.42%	3	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.31%	15.06%	79.78%	68.27%
±2σ	-24.49%	28.24%	92.98%	95.45%
±3σ	-37.67%	41.42%	98.88%	99.73%

Descriptive Statistics

Mean	1.875%
Standard Error	0.699%
Median	1.264%
Mode	-40.296%
Standard Deviation	13.182%
Sample Variance	173.756%
Kurtosis	6.02
Skewness	0.87
Range	125.404%
Minimum	-40.296%
Maximum	85.108%
Count	356

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.098%	208	58.43%	5.316%
Negative	-8.277%	148	41.57%	-3.441%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	12.59%
12	1 Year	12.03%
36	3 Years	10.57%
60	5 Years	10.41%
120	10 Years	10.22%
240	20 Years	10.77%
600	50 Years	17.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.15. Further, an Excess Kurtosis of 4.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.87%	0	0.00%	0.00%
-36.87% to -22.52%	0	0.00%	0.00%
-22.52% to -8.17%	0	0.00%	0.00%
-8.17% to 6.18%	21	5.88%	5.88%
6.18% to 20.53%	230	64.43%	70.31%
20.53% to 34.88%	48	13.45%	83.75%
34.88% to 49.23%	23	6.44%	90.20%
49.23% to 63.58%	16	4.48%	94.68%
63.58% to 77.93%	10	2.80%	97.48%
Greater than 77.93%	9	2.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.40%	39.66%	86.27%	68.27%
±2σ	-17.73%	58.80%	94.12%	95.45%
±3σ	-36.87%	77.93%	97.48%	99.73%

Descriptive Statistics

Mean	20.532%
Standard Error	1.013%
Median	12.875%
Mode	7.769%
Standard Deviation	19.133%
Sample Variance	366.055%
Kurtosis	4.94
Skewness	2.15
Range	118.182%
Minimum	3.657%
Maximum	121.839%
Count	357

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.532%	357	100.00%	20.532%
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 1.35. Further, an Excess Kurtosis of 5.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.90%	1	0.28%	0.28%
-39.90% to -29.98%	2	0.56%	0.84%
-29.98% to -20.06%	14	3.92%	4.76%
-20.06% to -10.14%	33	9.24%	14.01%
-10.14% to -0.22%	154	43.14%	57.14%
-0.22% to 9.70%	110	30.81%	87.96%
9.70% to 19.62%	22	6.16%	94.12%
19.62% to 29.54%	7	1.96%	96.08%
29.54% to 39.46%	5	1.40%	97.48%
Greater than 39.46%	9	2.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.45%	13.01%	81.23%	68.27%
±2σ	-26.67%	26.23%	93.28%	95.45%
±3σ	-39.90%	39.46%	97.20%	99.73%

Descriptive Statistics

Mean	-0.219%
Standard Error	0.700%
Median	-1.528%
Mode	1.915%
Standard Deviation	13.226%
Sample Variance	174.927%
Kurtosis	5.27
Skewness	1.35
Range	107.858%
Minimum	-43.671%
Maximum	64.187%
Count	357

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.126%	147	41.18%	4.169%
Negative	-7.496%	209	58.54%	-4.388%
Zero	0.000%	1	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.91. Further, an Excess Kurtosis of 6.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.77%	0	0.00%	0.00%
-64.77% to -47.15%	1	0.84%	0.84%
-47.15% to -29.52%	2	1.68%	2.52%
-29.52% to -11.90%	12	10.08%	12.61%
-11.90% to 5.72%	60	50.42%	63.03%
5.72% to 23.34%	32	26.89%	89.92%
23.34% to 40.96%	5	4.20%	94.12%
40.96% to 58.58%	2	1.68%	95.80%
58.58% to 76.20%	2	1.68%	97.48%
Greater than 76.20%	3	2.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.78%	29.21%	85.71%	68.27%
±2σ	-41.27%	52.71%	93.28%	95.45%
±3σ	-64.77%	76.20%	97.48%	99.73%

Descriptive Statistics

Mean	5.719%
Standard Error	2.154%
Median	2.995%
Mode	-50.274%
Standard Deviation	23.495%
Sample Variance	551.997%
Kurtosis	6.31
Skewness	1.91
Range	163.461%
Minimum	-50.274%
Maximum	113.187%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.636%	69	57.98%	10.226%
Negative	-10.726%	50	42.02%	-4.507%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.23%
12	3 Years	19.19%
20	5 Years	17.30%
40	10 Years	16.98%
80	20 Years	18.37%
200	50 Years	31.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.86. Further, an Excess Kurtosis of 2.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -76.82%	0	0.00%	0.00%
-76.82% to -47.78%	0	0.00%	0.00%
-47.78% to -18.74%	0	0.00%	0.00%
-18.74% to 10.30%	5	4.17%	4.17%
10.30% to 39.34%	83	69.17%	73.33%
39.34% to 68.38%	11	9.17%	82.50%
68.38% to 97.42%	6	5.00%	87.50%
97.42% to 126.46%	7	5.83%	93.33%
126.46% to 155.50%	5	4.17%	97.50%
Greater than 155.50%	3	2.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.62%	78.06%	85.00%	68.27%
±2σ	-38.10%	116.78%	93.33%	95.45%
±3σ	-76.82%	155.50%	97.50%	99.73%

Descriptive Statistics

Mean	39.337%
Standard Error	3.535%
Median	22.916%
Mode	7.764%
Standard Deviation	38.720%
Sample Variance	1499.274%
Kurtosis	2.57
Skewness	1.86
Range	159.219%
Minimum	7.764%
Maximum	166.983%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.337%	120	100.00%	39.337%
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 1.18. Further, an Excess Kurtosis of 5.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.86%	0	0.00%	0.00%
-60.86% to -45.97%	3	2.50%	2.50%
-45.97% to -31.07%	4	3.33%	5.83%
-31.07% to -16.18%	10	8.33%	14.17%
-16.18% to -1.28%	49	40.83%	55.00%
-1.28% to 13.61%	39	32.50%	87.50%
13.61% to 28.51%	9	7.50%	95.00%
28.51% to 43.40%	2	1.67%	96.67%
43.40% to 58.30%	2	1.67%	98.33%
Greater than 58.30%	2	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.14%	18.58%	83.33%	68.27%
±2σ	-41.00%	38.44%	91.67%	95.45%
±3σ	-60.86%	58.30%	98.33%	99.73%

Descriptive Statistics

Mean	-1.284%
Standard Error	1.813%
Median	-2.364%
Mode	-52.577%
Standard Deviation	19.860%
Sample Variance	394.427%
Kurtosis	5.85
Skewness	1.18
Range	149.822%
Minimum	-52.577%
Maximum	97.245%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.921%	51	42.50%	5.916%
Negative	-12.523%	69	57.50%	-7.201%
Zero	0.000%	0	0.00%	0.000%

CHKP Deep Analytical Report