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%	2.22%	2.54%	2.66%	148.94	156.70	145.20	160.73
Weekly	6.75%	8.53%	6.71%	5.01%	5.59%	5.86%	144.46	161.55	136.61	170.84
Monthly	13.18%	19.11%	13.22%	10.50%	11.63%	12.20%	135.99	171.62	121.05	192.79
Quarterly	23.52%	38.70%	19.89%	17.50%	20.15%	21.14%	124.89	186.87	102.09	228.60
Annual	—	—	—	—	40.30%	42.27%	102.09	228.60	68.23	342.06
Option Time Horizon	—	—	—	—	15.21%	15.96%	131.21	177.87	112.69	207.09

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $152.77 | Strike (K): $175.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.5750 (Bid $2.2000 / Ask $2.9500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 40.30% (CRR binomial tree, American, n=20 steps) | BS IV: 39.66% (European Black-Scholes) | Yahoo IV (Annual): 42.27% → 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 13.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.20%	67	0.90%	0.90%
-9.20% to -6.88%	73	0.98%	1.87%
-6.88% to -4.55%	182	2.43%	4.31%
-4.55% to -2.23%	617	8.25%	12.56%
-2.23% to 0.10%	2933	39.22%	51.77%
0.10% to 2.42%	2727	36.46%	88.23%
2.42% to 4.75%	529	7.07%	95.31%
4.75% to 7.07%	171	2.29%	97.59%
7.07% to 9.40%	95	1.27%	98.86%
Greater than 9.40%	85	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.00%	3.20%	82.99%	68.27%
±2σ	-6.10%	6.30%	94.58%	95.45%
±3σ	-9.20%	9.40%	97.97%	99.73%

Descriptive Statistics

Mean	0.096%
Standard Error	0.036%
Median	0.022%
Mode	0.000%
Standard Deviation	3.100%
Sample Variance	9.610%
Kurtosis	13.22
Skewness	0.67
Range	59.392%
Minimum	-27.057%
Maximum	32.335%
Count	7479

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.951%	3770	50.41%	0.983%
Negative	-1.831%	3623	48.44%	-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	2.28%
20	1 Month	2.96%
60	1 Quarter	3.14%
250	1 Year	2.77%
750	3 Years	2.25%
1,250	5 Years	2.22%
2,500	10 Years	2.15%
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 3.10. Further, an Excess Kurtosis of 15.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.95%	0	0.00%	0.00%
-5.95% to -3.59%	0	0.00%	0.00%
-3.59% to -1.23%	0	0.00%	0.00%
-1.23% to 1.13%	523	6.99%	6.99%
1.13% to 3.49%	4648	62.14%	69.13%
3.49% to 5.85%	1210	16.18%	85.31%
5.85% to 8.21%	528	7.06%	92.37%
8.21% to 10.57%	278	3.72%	96.08%
10.57% to 12.93%	151	2.02%	98.10%
Greater than 12.93%	142	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.34%	6.64%	88.25%	68.27%
±2σ	-2.80%	9.78%	95.16%	95.45%
±3σ	-5.95%	12.93%	98.10%	99.73%

Descriptive Statistics

Mean	3.489%
Standard Error	0.036%
Median	2.390%
Mode	1.924%
Standard Deviation	3.147%
Sample Variance	9.901%
Kurtosis	15.79
Skewness	3.10
Range	39.427%
Minimum	0.311%
Maximum	39.738%
Count	7480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.489%	7480	100.00%	3.489%
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 15.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.23%	69	0.92%	0.92%
-8.23% to -6.16%	82	1.10%	2.02%
-6.16% to -4.10%	168	2.25%	4.26%
-4.10% to -2.03%	613	8.20%	12.46%
-2.03% to 0.04%	2992	40.00%	52.46%
0.04% to 2.10%	2615	34.96%	87.42%
2.10% to 4.17%	563	7.53%	94.95%
4.17% to 6.24%	211	2.82%	97.77%
6.24% to 8.30%	82	1.10%	98.86%
Greater than 8.30%	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	-5.47%	5.55%	94.45%	95.45%
±3σ	-8.23%	8.30%	97.94%	99.73%

Descriptive Statistics

Mean	0.037%
Standard Error	0.032%
Median	-0.043%
Mode	0.000%
Standard Deviation	2.756%
Sample Variance	7.596%
Kurtosis	15.84
Skewness	0.95
Range	63.982%
Minimum	-25.587%
Maximum	38.395%
Count	7480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.802%	3600	48.13%	0.867%
Negative	-1.629%	3811	50.95%	-0.830%
Zero	0.000%	69	0.92%	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 -19.78%	10	0.64%	0.64%
-19.78% to -14.72%	22	1.42%	2.06%
-14.72% to -9.66%	49	3.16%	5.22%
-9.66% to -4.60%	129	8.32%	13.54%
-4.60% to 0.46%	586	37.78%	51.32%
0.46% to 5.52%	555	35.78%	87.11%
5.52% to 10.58%	111	7.16%	94.26%
10.58% to 15.64%	48	3.09%	97.36%
15.64% to 20.70%	24	1.55%	98.90%
Greater than 20.70%	17	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.29%	7.20%	82.14%	68.27%
±2σ	-13.03%	13.95%	93.94%	95.45%
±3σ	-19.78%	20.70%	98.26%	99.73%

Descriptive Statistics

Mean	0.458%
Standard Error	0.171%
Median	0.314%
Mode	0.000%
Standard Deviation	6.746%
Sample Variance	45.515%
Kurtosis	7.55
Skewness	0.69
Range	87.413%
Minimum	-34.187%
Maximum	53.226%
Count	1551

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.440%	825	53.19%	2.362%
Negative	-4.124%	716	46.16%	-1.904%
Zero	0.000%	10	0.65%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.20%
12	1 Quarter	7.28%
52	1 Year	6.11%
156	3 Years	5.09%
260	5 Years	5.01%
520	10 Years	4.86%
1,040	20 Years	5.24%
2,600	50 Years	8.38%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.62%	0	0.00%	0.00%
-16.62% to -10.23%	0	0.00%	0.00%
-10.23% to -3.83%	0	0.00%	0.00%
-3.83% to 2.56%	83	5.35%	5.35%
2.56% to 8.96%	1004	64.69%	70.04%
8.96% to 15.36%	228	14.69%	84.73%
15.36% to 21.75%	118	7.60%	92.33%
21.75% to 28.15%	52	3.35%	95.68%
28.15% to 34.55%	30	1.93%	97.62%
Greater than 34.55%	37	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.43%	17.49%	87.24%	68.27%
±2σ	-8.10%	26.02%	94.78%	95.45%
±3σ	-16.62%	34.55%	97.62%	99.73%

Descriptive Statistics

Mean	8.962%
Standard Error	0.216%
Median	5.801%
Mode	2.494%
Standard Deviation	8.529%
Sample Variance	72.744%
Kurtosis	9.64
Skewness	2.68
Range	71.060%
Minimum	1.447%
Maximum	72.507%
Count	1552

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.962%	1552	100.00%	8.962%
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 9.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.06%	10	0.64%	0.64%
-20.06% to -15.03%	17	1.10%	1.74%
-15.03% to -10.00%	52	3.35%	5.09%
-10.00% to -4.96%	108	6.96%	12.05%
-4.96% to 0.07%	656	42.27%	54.32%
0.07% to 5.10%	514	33.12%	87.44%
5.10% to 10.13%	113	7.28%	94.72%
10.13% to 15.16%	41	2.64%	97.36%
15.16% to 20.19%	19	1.22%	98.58%
Greater than 20.19%	22	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.64%	6.77%	82.67%	68.27%
±2σ	-13.35%	13.48%	94.14%	95.45%
±3σ	-20.06%	20.19%	97.94%	99.73%

Descriptive Statistics

Mean	0.066%
Standard Error	0.170%
Median	-0.327%
Mode	-2.833%
Standard Deviation	6.708%
Sample Variance	44.993%
Kurtosis	9.63
Skewness	1.21
Range	89.216%
Minimum	-34.211%
Maximum	55.005%
Count	1552

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.573%	717	46.20%	2.113%
Negative	-3.819%	832	53.61%	-2.047%
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 -27.79%	7	1.96%	2.24%
-27.79% to -17.90%	11	3.08%	5.32%
-17.90% to -8.02%	32	8.96%	14.29%
-8.02% to 1.86%	143	40.06%	54.34%
1.86% to 11.74%	111	31.09%	85.43%
11.74% to 21.62%	31	8.68%	94.12%
21.62% to 31.51%	10	2.80%	96.92%
31.51% to 41.39%	8	2.24%	99.16%
Greater than 41.39%	3	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.32%	15.04%	79.83%	68.27%
±2σ	-24.49%	28.21%	93.00%	95.45%
±3σ	-37.67%	41.39%	98.88%	99.73%

Descriptive Statistics

Mean	1.860%
Standard Error	0.697%
Median	1.253%
Mode	0.556%
Standard Deviation	13.176%
Sample Variance	173.605%
Kurtosis	6.02
Skewness	0.87
Range	125.404%
Minimum	-40.296%
Maximum	85.108%
Count	357

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.057%	209	58.54%	5.302%
Negative	-8.303%	148	41.46%	-3.442%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.95%
12	1 Year	12.39%
36	3 Years	10.80%
60	5 Years	10.50%
120	10 Years	10.28%
240	20 Years	10.78%
600	50 Years	17.77%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.82%	0	0.00%	0.00%
-36.82% to -22.48%	0	0.00%	0.00%
-22.48% to -8.15%	0	0.00%	0.00%
-8.15% to 6.18%	21	5.87%	5.87%
6.18% to 20.52%	230	64.25%	70.11%
20.52% to 34.85%	49	13.69%	83.80%
34.85% to 49.19%	23	6.42%	90.22%
49.19% to 63.52%	16	4.47%	94.69%
63.52% to 77.86%	10	2.79%	97.49%
Greater than 77.86%	9	2.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.41%	39.63%	86.31%	68.27%
±2σ	-17.71%	58.75%	94.13%	95.45%
±3σ	-36.82%	77.86%	97.49%	99.73%

Descriptive Statistics

Mean	20.520%
Standard Error	1.010%
Median	12.875%
Mode	7.769%
Standard Deviation	19.113%
Sample Variance	365.312%
Kurtosis	4.96
Skewness	2.15
Range	118.182%
Minimum	3.657%
Maximum	121.839%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.520%	358	100.00%	20.520%
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 1.34. Further, an Excess Kurtosis of 5.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.87%	1	0.28%	0.28%
-39.87% to -29.96%	2	0.56%	0.84%
-29.96% to -20.04%	14	3.91%	4.75%
-20.04% to -10.12%	33	9.22%	13.97%
-10.12% to -0.20%	155	43.30%	57.26%
-0.20% to 9.72%	110	30.73%	87.99%
9.72% to 19.63%	22	6.15%	94.13%
19.63% to 29.55%	7	1.96%	96.09%
29.55% to 39.47%	5	1.40%	97.49%
Greater than 39.47%	9	2.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.43%	13.02%	81.01%	68.27%
±2σ	-26.65%	26.25%	93.30%	95.45%
±3σ	-39.87%	39.47%	97.21%	99.73%

Descriptive Statistics

Mean	-0.202%
Standard Error	0.699%
Median	-1.457%
Mode	1.915%
Standard Deviation	13.224%
Sample Variance	174.867%
Kurtosis	5.25
Skewness	1.34
Range	107.858%
Minimum	-43.671%
Maximum	64.187%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.097%	148	41.34%	4.174%
Negative	-7.496%	209	58.38%	-4.376%
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 6.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.86%	0	0.00%	0.00%
-64.86% to -47.23%	1	0.84%	0.84%
-47.23% to -29.59%	2	1.68%	2.52%
-29.59% to -11.95%	13	10.92%	13.45%
-11.95% to 5.69%	59	49.58%	63.03%
5.69% to 23.33%	31	26.05%	89.08%
23.33% to 40.97%	6	5.04%	94.12%
40.97% to 58.61%	2	1.68%	95.80%
58.61% to 76.24%	2	1.68%	97.48%
Greater than 76.24%	3	2.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.83%	29.21%	86.55%	68.27%
±2σ	-41.35%	52.73%	93.28%	95.45%
±3σ	-64.86%	76.24%	97.48%	99.73%

Descriptive Statistics

Mean	5.690%
Standard Error	2.156%
Median	2.995%
Mode	-50.274%
Standard Deviation	23.518%
Sample Variance	553.085%
Kurtosis	6.29
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	-10.794%	50	42.02%	-4.535%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	19.23%
12	3 Years	19.52%
20	5 Years	17.50%
40	10 Years	17.08%
80	20 Years	18.42%
200	50 Years	31.22%

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 -76.71%	0	0.00%	0.00%
-76.71% to -47.69%	0	0.00%	0.00%
-47.69% to -18.66%	0	0.00%	0.00%
-18.66% to 10.36%	6	5.00%	5.00%
10.36% to 39.38%	82	68.33%	73.33%
39.38% to 68.41%	11	9.17%	82.50%
68.41% to 97.43%	6	5.00%	87.50%
97.43% to 126.45%	7	5.83%	93.33%
126.45% to 155.48%	5	4.17%	97.50%
Greater than 155.48%	3	2.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.69%	78.08%	85.00%	68.27%
±2σ	-38.01%	116.78%	93.33%	95.45%
±3σ	-76.71%	155.48%	97.50%	99.73%

Descriptive Statistics

Mean	39.384%
Standard Error	3.533%
Median	23.237%
Mode	7.764%
Standard Deviation	38.698%
Sample Variance	1497.520%
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	39.384%	120	100.00%	39.384%
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 1.17. Further, an Excess Kurtosis of 5.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.92%	0	0.00%	0.00%
-60.92% to -46.00%	3	2.50%	2.50%
-46.00% to -31.08%	4	3.33%	5.83%
-31.08% to -16.16%	10	8.33%	14.17%
-16.16% to -1.25%	49	40.83%	55.00%
-1.25% to 13.67%	38	31.67%	86.67%
13.67% to 28.59%	10	8.33%	95.00%
28.59% to 43.51%	2	1.67%	96.67%
43.51% to 58.42%	2	1.67%	98.33%
Greater than 58.42%	2	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.14%	18.64%	83.33%	68.27%
±2σ	-41.03%	38.53%	91.67%	95.45%
±3σ	-60.92%	58.42%	98.33%	99.73%

Descriptive Statistics

Mean	-1.247%
Standard Error	1.816%
Median	-2.364%
Mode	-52.577%
Standard Deviation	19.890%
Sample Variance	395.601%
Kurtosis	5.79
Skewness	1.17
Range	149.822%
Minimum	-52.577%
Maximum	97.245%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.009%	51	42.50%	5.954%
Negative	-12.523%	69	57.50%	-7.201%
Zero	0.000%	0	0.00%	0.000%

CHKP Deep Analytical Report