CRWD - 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	3.52%	2.50%	3.00%	4.39%	2.87%	2.99%	400.76	424.42	389.43	436.77
Weekly	8.54%	7.59%	8.87%	10.54%	6.31%	6.57%	387.19	439.30	363.50	467.92
Monthly	15.09%	15.21%	15.75%	22.10%	13.14%	13.69%	361.63	470.34	317.10	536.40
Quarterly	29.42%	28.94%	29.14%	40.44%	22.76%	23.70%	328.46	517.84	261.60	650.20
Annual	—	—	—	—	45.52%	47.41%	261.60	650.20	165.93	1025.08
Option Time Horizon	—	—	—	—	17.18%	17.89%	347.31	489.74	292.48	581.55

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $412.42 | Strike (K): $420.00 (first OTM call ≥ spot) | Observed Mid-Price: $25.9750 (Bid $25.3500 / Ask $26.6000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 45.52% (CRR binomial tree, American, n=20 steps) | BS IV: 45.77% (European Black-Scholes) | Yahoo IV (Annual): 47.41% → 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 0.17. Further, an Excess Kurtosis of 2.78 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.39%	11	0.65%	0.65%
-10.39% to -7.75%	22	1.29%	1.94%
-7.75% to -5.11%	62	3.64%	5.58%
-5.11% to -2.46%	226	13.27%	18.85%
-2.46% to 0.18%	525	30.83%	49.68%
0.18% to 2.82%	551	32.35%	82.03%
2.82% to 5.46%	218	12.80%	94.83%
5.46% to 8.10%	54	3.17%	98.00%
8.10% to 10.75%	17	1.00%	99.00%
Greater than 10.75%	17	1.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.35%	3.70%	75.87%	68.27%
±2σ	-6.87%	7.22%	94.36%	95.45%
±3σ	-10.39%	10.75%	98.36%	99.73%

Descriptive Statistics

Mean	0.177%
Standard Error	0.085%
Median	0.188%
Mode	-0.889%
Standard Deviation	3.523%
Sample Variance	12.409%
Kurtosis	2.78
Skewness	0.17
Range	33.953%
Minimum	-16.536%
Maximum	17.417%
Count	1703

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.606%	893	52.44%	1.367%
Negative	-2.503%	809	47.50%	-1.189%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.05%
20	1 Month	4.56%
60	1 Quarter	4.39%
250	1 Year	3.90%
750	3 Years	3.89%
1,250	5 Years	4.39%
2,500	10 Years	4.86%
5,000	20 Years	4.86%
12,500	50 Years	4.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.84. Further, an Excess Kurtosis of 5.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.87%	0	0.00%	0.00%
-2.87% to -0.99%	0	0.00%	0.00%
-0.99% to 0.89%	0	0.00%	0.00%
0.89% to 2.77%	347	20.36%	20.36%
2.77% to 4.65%	715	41.96%	62.32%
4.65% to 6.53%	343	20.13%	82.45%
6.53% to 8.41%	163	9.57%	92.02%
8.41% to 10.29%	71	4.17%	96.19%
10.29% to 12.16%	34	2.00%	98.18%
Greater than 12.16%	31	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.14%	7.15%	78.99%	68.27%
±2σ	-0.36%	9.66%	95.13%	95.45%
±3σ	-2.87%	12.16%	98.24%	99.73%

Descriptive Statistics

Mean	4.649%
Standard Error	0.061%
Median	4.006%
Mode	2.141%
Standard Deviation	2.505%
Sample Variance	6.274%
Kurtosis	5.13
Skewness	1.84
Range	19.180%
Minimum	0.905%
Maximum	20.085%
Count	1704

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.649%	1704	100.00%	4.649%
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 0.10. Further, an Excess Kurtosis of 1.88 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.00%	7	0.41%	0.41%
-9.00% to -6.75%	23	1.35%	1.76%
-6.75% to -4.49%	63	3.70%	5.46%
-4.49% to -2.24%	231	13.56%	19.01%
-2.24% to 0.01%	567	33.27%	52.29%
0.01% to 2.27%	491	28.81%	81.10%
2.27% to 4.52%	206	12.09%	93.19%
4.52% to 6.77%	78	4.58%	97.77%
6.77% to 9.03%	24	1.41%	99.18%
Greater than 9.03%	14	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.99%	3.02%	74.30%	68.27%
±2σ	-6.00%	6.02%	94.31%	95.45%
±3σ	-9.00%	9.03%	98.77%	99.73%

Descriptive Statistics

Mean	0.013%
Standard Error	0.073%
Median	-0.096%
Mode	-2.393%
Standard Deviation	3.004%
Sample Variance	9.021%
Kurtosis	1.88
Skewness	0.10
Range	29.485%
Minimum	-16.065%
Maximum	13.420%
Count	1704

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.340%	814	47.77%	1.118%
Negative	-2.120%	888	52.11%	-1.105%
Zero	0.000%	2	0.12%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of 5.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.76%	3	0.85%	0.85%
-24.76% to -18.35%	6	1.70%	2.55%
-18.35% to -11.95%	10	2.83%	5.38%
-11.95% to -5.54%	45	12.75%	18.13%
-5.54% to 0.87%	102	28.90%	47.03%
0.87% to 7.27%	123	34.84%	81.87%
7.27% to 13.68%	46	13.03%	94.90%
13.68% to 20.08%	13	3.68%	98.58%
20.08% to 26.49%	4	1.13%	99.72%
Greater than 26.49%	1	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.67%	9.41%	76.77%	68.27%
±2σ	-16.21%	17.95%	94.90%	95.45%
±3σ	-24.76%	26.49%	98.87%	99.73%

Descriptive Statistics

Mean	0.867%
Standard Error	0.455%
Median	1.134%
Mode	-8.551%
Standard Deviation	8.541%
Sample Variance	72.944%
Kurtosis	5.54
Skewness	0.36
Range	85.928%
Minimum	-30.066%
Maximum	55.862%
Count	353

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.312%	198	56.09%	3.540%
Negative	-6.089%	155	43.91%	-2.674%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.65%
12	1 Quarter	10.82%
52	1 Year	9.13%
156	3 Years	9.56%
260	5 Years	10.54%
520	10 Years	11.64%
1,040	20 Years	11.64%
2,600	50 Years	11.64%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.27%	0	0.00%	0.00%
-10.27% to -4.58%	0	0.00%	0.00%
-4.58% to 1.12%	0	0.00%	0.00%
1.12% to 6.82%	55	15.54%	15.54%
6.82% to 12.51%	172	48.59%	64.12%
12.51% to 18.21%	77	21.75%	85.88%
18.21% to 23.90%	24	6.78%	92.66%
23.90% to 29.60%	13	3.67%	96.33%
29.60% to 35.30%	6	1.69%	98.02%
Greater than 35.30%	7	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.92%	20.11%	85.31%	68.27%
±2σ	-2.68%	27.70%	94.63%	95.45%
±3σ	-10.27%	35.30%	98.02%	99.73%

Descriptive Statistics

Mean	12.511%
Standard Error	0.404%
Median	10.582%
Mode	6.139%
Standard Deviation	7.595%
Sample Variance	57.691%
Kurtosis	10.45
Skewness	2.59
Range	63.140%
Minimum	2.744%
Maximum	65.884%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.511%	354	100.00%	12.511%
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 5.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.51%	1	0.28%	0.28%
-26.51% to -19.86%	0	0.00%	0.28%
-19.86% to -13.21%	10	2.82%	3.11%
-13.21% to -6.56%	55	15.54%	18.64%
-6.56% to 0.09%	130	36.72%	55.37%
0.09% to 6.74%	100	28.25%	83.62%
6.74% to 13.39%	37	10.45%	94.07%
13.39% to 20.05%	10	2.82%	96.89%
20.05% to 26.70%	6	1.69%	98.59%
Greater than 26.70%	5	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.77%	8.96%	78.53%	68.27%
±2σ	-17.64%	17.83%	95.76%	95.45%
±3σ	-26.51%	26.70%	98.31%	99.73%

Descriptive Statistics

Mean	0.094%
Standard Error	0.471%
Median	-0.978%
Mode	-3.166%
Standard Deviation	8.867%
Sample Variance	78.623%
Kurtosis	5.48
Skewness	1.32
Range	80.886%
Minimum	-34.052%
Maximum	46.834%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.091%	159	44.91%	3.185%
Negative	-5.641%	194	54.80%	-3.091%
Zero	0.000%	1	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.13. Further, an Excess Kurtosis of 0.04 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.89%	0	0.00%	0.00%
-41.89% to -30.57%	1	1.23%	1.23%
-30.57% to -19.25%	4	4.94%	6.17%
-19.25% to -7.93%	16	19.75%	25.93%
-7.93% to 3.38%	19	23.46%	49.38%
3.38% to 14.70%	25	30.86%	80.25%
14.70% to 26.02%	11	13.58%	93.83%
26.02% to 37.34%	4	4.94%	98.77%
37.34% to 48.66%	1	1.23%	100.00%
Greater than 48.66%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.71%	18.47%	70.37%	68.27%
±2σ	-26.80%	33.56%	93.83%	95.45%
±3σ	-41.89%	48.66%	100.00%	99.73%

Descriptive Statistics

Mean	3.383%
Standard Error	1.677%
Median	5.357%
Mode	-39.466%
Standard Deviation	15.091%
Sample Variance	227.746%
Kurtosis	0.04
Skewness	-0.13
Range	77.658%
Minimum	-39.466%
Maximum	38.192%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.434%	48	59.26%	7.961%
Negative	-11.237%	33	40.74%	-4.578%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.29%
12	1 Year	18.19%
36	3 Years	21.39%
60	5 Years	22.10%
120	10 Years	24.71%
240	20 Years	24.71%
600	50 Years	24.71%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.77. Further, an Excess Kurtosis of 3.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.51%	0	0.00%	0.00%
-16.51% to -5.10%	0	0.00%	0.00%
-5.10% to 6.30%	0	0.00%	0.00%
6.30% to 17.70%	19	23.17%	23.17%
17.70% to 29.11%	35	42.68%	65.85%
29.11% to 40.51%	16	19.51%	85.37%
40.51% to 51.92%	4	4.88%	90.24%
51.92% to 63.32%	4	4.88%	95.12%
63.32% to 74.72%	2	2.44%	97.56%
Greater than 74.72%	2	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.90%	44.31%	81.71%	68.27%
±2σ	-1.30%	59.52%	93.90%	95.45%
±3σ	-16.51%	74.72%	97.56%	99.73%

Descriptive Statistics

Mean	29.109%
Standard Error	1.679%
Median	25.955%
Mode	9.550%
Standard Deviation	15.205%
Sample Variance	231.200%
Kurtosis	3.71
Skewness	1.77
Range	81.279%
Minimum	9.550%
Maximum	90.829%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.109%	82	100.00%	29.109%
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 1.31. Further, an Excess Kurtosis of 3.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.23%	0	0.00%	0.00%
-48.23% to -36.42%	0	0.00%	0.00%
-36.42% to -24.61%	3	3.66%	3.66%
-24.61% to -12.80%	13	15.85%	19.51%
-12.80% to -0.98%	32	39.02%	58.54%
-0.98% to 10.83%	17	20.73%	79.27%
10.83% to 22.64%	12	14.63%	93.90%
22.64% to 34.45%	2	2.44%	96.34%
34.45% to 46.26%	2	2.44%	98.78%
Greater than 46.26%	1	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.73%	14.76%	79.27%	68.27%
±2σ	-32.48%	30.51%	96.34%	95.45%
±3σ	-48.23%	46.26%	98.78%	99.73%

Descriptive Statistics

Mean	-0.985%
Standard Error	1.739%
Median	-3.000%
Mode	-27.533%
Standard Deviation	15.749%
Sample Variance	248.040%
Kurtosis	3.38
Skewness	1.31
Range	93.631%
Minimum	-27.533%
Maximum	66.098%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.597%	31	37.80%	5.518%
Negative	-10.457%	51	62.20%	-6.504%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.43. 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 -78.57%	0	0.00%	0.00%
-78.57% to -56.50%	0	0.00%	0.00%
-56.50% to -34.43%	2	7.41%	7.41%
-34.43% to -12.37%	3	11.11%	18.52%
-12.37% to 9.70%	9	33.33%	51.85%
9.70% to 31.77%	8	29.63%	81.48%
31.77% to 53.84%	2	7.41%	88.89%
53.84% to 75.90%	3	11.11%	100.00%
75.90% to 97.97%	0	0.00%	100.00%
Greater than 97.97%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.72%	39.12%	74.07%	68.27%
±2σ	-49.14%	68.55%	96.30%	95.45%
±3σ	-78.57%	97.97%	100.00%	99.73%

Descriptive Statistics

Mean	9.702%
Standard Error	5.662%
Median	9.399%
Mode	-43.965%
Standard Deviation	29.423%
Sample Variance	865.710%
Kurtosis	0.32
Skewness	0.43
Range	118.222%
Minimum	-43.965%
Maximum	74.257%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.722%	18	66.67%	16.481%
Negative	-20.339%	9	33.33%	-6.780%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	27.35%
12	3 Years	39.95%
20	5 Years	40.44%
40	10 Years	46.25%
80	20 Years	46.25%
200	50 Years	46.25%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.16. Further, an Excess Kurtosis of 0.87 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.77%	0	0.00%	0.00%
-26.77% to -5.07%	0	0.00%	0.00%
-5.07% to 16.64%	0	0.00%	0.00%
16.64% to 38.35%	8	28.57%	28.57%
38.35% to 60.06%	9	32.14%	60.71%
60.06% to 81.76%	6	21.43%	82.14%
81.76% to 103.47%	3	10.71%	92.86%
103.47% to 125.18%	0	0.00%	92.86%
125.18% to 146.89%	2	7.14%	100.00%
Greater than 146.89%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	31.11%	89.00%	78.57%	68.27%
±2σ	2.17%	117.94%	92.86%	95.45%
±3σ	-26.77%	146.89%	100.00%	99.73%

Descriptive Statistics

Mean	60.057%
Standard Error	5.470%
Median	53.331%
Mode	28.013%
Standard Deviation	28.943%
Sample Variance	837.680%
Kurtosis	0.87
Skewness	1.16
Range	106.729%
Minimum	28.013%
Maximum	134.742%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	60.057%	28	100.00%	60.057%
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 1.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.25%	0	0.00%	0.00%
-90.25% to -68.39%	0	0.00%	0.00%
-68.39% to -46.54%	0	0.00%	0.00%
-46.54% to -24.69%	6	21.43%	21.43%
-24.69% to -2.84%	12	42.86%	64.29%
-2.84% to 19.01%	5	17.86%	82.14%
19.01% to 40.87%	2	7.14%	89.29%
40.87% to 62.72%	2	7.14%	96.43%
62.72% to 84.57%	1	3.57%	100.00%
Greater than 84.57%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.97%	26.30%	78.57%	68.27%
±2σ	-61.11%	55.43%	92.86%	95.45%
±3σ	-90.25%	84.57%	100.00%	99.73%

Descriptive Statistics

Mean	-2.838%
Standard Error	5.506%
Median	-9.286%
Mode	-42.285%
Standard Deviation	29.136%
Sample Variance	848.922%
Kurtosis	1.66
Skewness	1.24
Range	122.750%
Minimum	-42.285%
Maximum	80.465%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.016%	10	35.71%	9.648%
Negative	-19.424%	18	64.29%	-12.487%
Zero	0.000%	0	0.00%	0.000%

CRWD Deep Analytical Report