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%	2.51%	3.00%	4.42%	3.45%	3.49%	375.42	402.24	362.69	416.36
Weekly	8.50%	7.59%	8.80%	10.58%	7.59%	7.68%	360.18	419.26	333.84	452.34
Monthly	15.11%	15.32%	15.75%	22.08%	15.81%	16.00%	331.77	455.16	283.26	533.12
Quarterly	29.56%	29.48%	29.25%	40.02%	27.38%	27.71%	295.52	511.00	224.73	671.96
Annual	—	—	—	—	54.77%	55.41%	224.73	671.96	129.96	1161.96
Option Time Horizon	—	—	—	—	21.06%	21.31%	314.79	479.72	255.00	592.20

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $388.60 | Strike (K): $390.00 (first OTM call ≥ spot) | Observed Mid-Price: $32.6500 (Bid $31.6000 / Ask $33.7000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 54.77% (CRR binomial tree, American, n=20 steps) | BS IV: 54.28% (European Black-Scholes) | Yahoo IV (Annual): 55.41% → 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 0.19. Further, an Excess Kurtosis of 2.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.40%	11	0.65%	0.65%
-10.40% to -7.75%	20	1.19%	1.84%
-7.75% to -5.11%	63	3.75%	5.59%
-5.11% to -2.47%	223	13.26%	18.85%
-2.47% to 0.17%	520	30.92%	49.76%
0.17% to 2.82%	544	32.34%	82.10%
2.82% to 5.46%	213	12.66%	94.77%
5.46% to 8.10%	54	3.21%	97.98%
8.10% to 10.75%	17	1.01%	98.99%
Greater than 10.75%	17	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.35%	3.70%	75.98%	68.27%
±2σ	-6.87%	7.22%	94.35%	95.45%
±3σ	-10.40%	10.75%	98.34%	99.73%

Descriptive Statistics

Mean	0.175%
Standard Error	0.086%
Median	0.183%
Mode	-0.889%
Standard Deviation	3.524%
Sample Variance	12.420%
Kurtosis	2.79
Skewness	0.19
Range	33.953%
Minimum	-16.536%
Maximum	17.417%
Count	1682

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.613%	879	52.26%	1.366%
Negative	-2.497%	802	47.68%	-1.191%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.19%
20	1 Month	5.08%
60	1 Quarter	3.83%
250	1 Year	4.01%
750	3 Years	3.86%
1,250	5 Years	4.42%
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 -2.88%	0	0.00%	0.00%
-2.88% to -1.00%	0	0.00%	0.00%
-1.00% to 0.88%	0	0.00%	0.00%
0.88% to 2.77%	341	20.26%	20.26%
2.77% to 4.65%	708	42.07%	62.33%
4.65% to 6.53%	338	20.08%	82.41%
6.53% to 8.41%	161	9.57%	91.98%
8.41% to 10.29%	71	4.22%	96.20%
10.29% to 12.17%	35	2.08%	98.28%
Greater than 12.17%	29	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.14%	7.16%	79.14%	68.27%
±2σ	-0.37%	9.66%	95.13%	95.45%
±3σ	-2.88%	12.17%	98.28%	99.73%

Descriptive Statistics

Mean	4.647%
Standard Error	0.061%
Median	3.992%
Mode	2.141%
Standard Deviation	2.509%
Sample Variance	6.295%
Kurtosis	5.13
Skewness	1.84
Range	19.180%
Minimum	0.905%
Maximum	20.085%
Count	1683

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.647%	1683	100.00%	4.647%
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 0.09. Further, an Excess Kurtosis of 1.90 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.97%	7	0.42%	0.42%
-8.97% to -6.72%	23	1.37%	1.78%
-6.72% to -4.47%	61	3.62%	5.41%
-4.47% to -2.23%	227	13.49%	18.89%
-2.23% to 0.02%	563	33.45%	52.35%
0.02% to 2.27%	484	28.76%	81.11%
2.27% to 4.51%	203	12.06%	93.17%
4.51% to 6.76%	78	4.63%	97.80%
6.76% to 9.01%	24	1.43%	99.23%
Greater than 9.01%	13	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.98%	3.02%	74.33%	68.27%
±2σ	-5.97%	6.01%	94.24%	95.45%
±3σ	-8.97%	9.01%	98.81%	99.73%

Descriptive Statistics

Mean	0.019%
Standard Error	0.073%
Median	-0.088%
Mode	-2.393%
Standard Deviation	2.996%
Sample Variance	8.975%
Kurtosis	1.90
Skewness	0.09
Range	29.485%
Minimum	-16.065%
Maximum	13.420%
Count	1683

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.332%	807	47.95%	1.118%
Negative	-2.116%	874	51.93%	-1.099%
Zero	0.000%	2	0.12%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.39. Further, an Excess Kurtosis of 5.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.66%	3	0.86%	0.86%
-24.66% to -18.28%	5	1.43%	2.29%
-18.28% to -11.90%	10	2.87%	5.16%
-11.90% to -5.53%	46	13.18%	18.34%
-5.53% to 0.85%	100	28.65%	46.99%
0.85% to 7.23%	121	34.67%	81.66%
7.23% to 13.61%	46	13.18%	94.84%
13.61% to 19.98%	13	3.72%	98.57%
19.98% to 26.36%	4	1.15%	99.71%
Greater than 26.36%	1	0.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.65%	9.36%	76.79%	68.27%
±2σ	-16.16%	17.86%	95.13%	95.45%
±3σ	-24.66%	26.36%	98.85%	99.73%

Descriptive Statistics

Mean	0.851%
Standard Error	0.455%
Median	1.134%
Mode	-8.551%
Standard Deviation	8.504%
Sample Variance	72.319%
Kurtosis	5.71
Skewness	0.39
Range	85.928%
Minimum	-30.066%
Maximum	55.862%
Count	349

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.261%	196	56.16%	3.516%
Negative	-6.080%	153	43.84%	-2.665%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.25%
12	1 Quarter	8.01%
52	1 Year	9.23%
156	3 Years	9.45%
260	5 Years	10.58%
520	10 Years	11.61%
1,040	20 Years	11.61%
2,600	50 Years	11.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.63. Further, an Excess Kurtosis of 10.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.29%	0	0.00%	0.00%
-10.29% to -4.60%	0	0.00%	0.00%
-4.60% to 1.09%	0	0.00%	0.00%
1.09% to 6.79%	54	15.43%	15.43%
6.79% to 12.48%	171	48.86%	64.29%
12.48% to 18.17%	77	22.00%	86.29%
18.17% to 23.86%	23	6.57%	92.86%
23.86% to 29.55%	12	3.43%	96.29%
29.55% to 35.24%	6	1.71%	98.00%
Greater than 35.24%	7	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.89%	20.07%	85.43%	68.27%
±2σ	-2.70%	27.65%	94.57%	95.45%
±3σ	-10.29%	35.24%	98.00%	99.73%

Descriptive Statistics

Mean	12.477%
Standard Error	0.406%
Median	10.582%
Mode	6.139%
Standard Deviation	7.588%
Sample Variance	57.584%
Kurtosis	10.68
Skewness	2.63
Range	63.140%
Minimum	2.744%
Maximum	65.884%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.477%	350	100.00%	12.477%
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 5.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.31%	1	0.29%	0.29%
-26.31% to -19.70%	0	0.00%	0.29%
-19.70% to -13.10%	9	2.57%	2.86%
-13.10% to -6.50%	55	15.71%	18.57%
-6.50% to 0.11%	129	36.86%	55.43%
0.11% to 6.71%	98	28.00%	83.43%
6.71% to 13.32%	38	10.86%	94.29%
13.32% to 19.92%	10	2.86%	97.14%
19.92% to 26.52%	5	1.43%	98.57%
Greater than 26.52%	5	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.70%	8.91%	78.86%	68.27%
±2σ	-17.50%	17.72%	96.00%	95.45%
±3σ	-26.31%	26.52%	98.29%	99.73%

Descriptive Statistics

Mean	0.109%
Standard Error	0.471%
Median	-0.978%
Mode	-3.166%
Standard Deviation	8.805%
Sample Variance	77.529%
Kurtosis	5.70
Skewness	1.34
Range	80.886%
Minimum	-34.052%
Maximum	46.834%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.058%	157	44.86%	3.166%
Negative	-5.574%	192	54.86%	-3.058%
Zero	0.000%	1	0.29%	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 0.04 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.99%	0	0.00%	0.00%
-41.99% to -30.66%	1	1.25%	1.25%
-30.66% to -19.33%	4	5.00%	6.25%
-19.33% to -8.00%	16	20.00%	26.25%
-8.00% to 3.33%	19	23.75%	50.00%
3.33% to 14.66%	24	30.00%	80.00%
14.66% to 25.99%	11	13.75%	93.75%
25.99% to 37.32%	4	5.00%	98.75%
37.32% to 48.65%	1	1.25%	100.00%
Greater than 48.65%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.77%	18.44%	70.00%	68.27%
±2σ	-26.88%	33.54%	93.75%	95.45%
±3σ	-41.99%	48.65%	100.00%	99.73%

Descriptive Statistics

Mean	3.332%
Standard Error	1.689%
Median	4.012%
Mode	-39.466%
Standard Deviation	15.106%
Sample Variance	228.203%
Kurtosis	0.04
Skewness	-0.11
Range	77.658%
Minimum	-39.466%
Maximum	38.192%
Count	80

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.481%	47	58.75%	7.920%
Negative	-11.123%	33	41.25%	-4.588%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.51%
12	1 Year	17.83%
36	3 Years	21.03%
60	5 Years	22.08%
120	10 Years	24.65%
240	20 Years	24.65%
600	50 Years	24.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.76. Further, an Excess Kurtosis of 3.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.91%	0	0.00%	0.00%
-16.91% to -5.42%	0	0.00%	0.00%
-5.42% to 6.07%	0	0.00%	0.00%
6.07% to 17.56%	19	23.46%	23.46%
17.56% to 29.05%	35	43.21%	66.67%
29.05% to 40.54%	15	18.52%	85.19%
40.54% to 52.03%	4	4.94%	90.12%
52.03% to 63.52%	4	4.94%	95.06%
63.52% to 75.01%	2	2.47%	97.53%
Greater than 75.01%	2	2.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.73%	44.37%	82.72%	68.27%
±2σ	-1.59%	59.69%	93.83%	95.45%
±3σ	-16.91%	75.01%	97.53%	99.73%

Descriptive Statistics

Mean	29.049%
Standard Error	1.702%
Median	25.949%
Mode	9.550%
Standard Deviation	15.321%
Sample Variance	234.743%
Kurtosis	3.62
Skewness	1.76
Range	81.279%
Minimum	9.550%
Maximum	90.829%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.049%	81	100.00%	29.049%
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 1.30. Further, an Excess Kurtosis of 3.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.21%	0	0.00%	0.00%
-48.21% to -36.39%	0	0.00%	0.00%
-36.39% to -24.58%	3	3.70%	3.70%
-24.58% to -12.76%	13	16.05%	19.75%
-12.76% to -0.95%	31	38.27%	58.02%
-0.95% to 10.87%	17	20.99%	79.01%
10.87% to 22.68%	12	14.81%	93.83%
22.68% to 34.50%	2	2.47%	96.30%
34.50% to 46.31%	2	2.47%	98.77%
Greater than 46.31%	1	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.70%	14.81%	80.25%	68.27%
±2σ	-32.45%	30.56%	96.30%	95.45%
±3σ	-48.21%	46.31%	98.77%	99.73%

Descriptive Statistics

Mean	-0.947%
Standard Error	1.750%
Median	-2.706%
Mode	-27.533%
Standard Deviation	15.754%
Sample Variance	248.187%
Kurtosis	3.42
Skewness	1.30
Range	93.631%
Minimum	-27.533%
Maximum	66.098%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.434%	31	38.27%	5.524%
Negative	-10.483%	50	61.73%	-6.471%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.44. 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 -79.19%	0	0.00%	0.00%
-79.19% to -57.02%	0	0.00%	0.00%
-57.02% to -34.85%	2	7.41%	7.41%
-34.85% to -12.68%	3	11.11%	18.52%
-12.68% to 9.49%	9	33.33%	51.85%
9.49% to 31.66%	8	29.63%	81.48%
31.66% to 53.83%	2	7.41%	88.89%
53.83% to 76.01%	3	11.11%	100.00%
76.01% to 98.18%	0	0.00%	100.00%
Greater than 98.18%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.07%	39.05%	74.07%	68.27%
±2σ	-49.63%	68.62%	96.30%	95.45%
±3σ	-79.20%	98.18%	100.00%	99.73%

Descriptive Statistics

Mean	9.491%
Standard Error	5.689%
Median	9.399%
Mode	-43.965%
Standard Deviation	29.562%
Sample Variance	873.920%
Kurtosis	0.28
Skewness	0.44
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	-20.973%	9	33.33%	-6.991%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	25.27%
12	3 Years	39.26%
20	5 Years	40.02%
40	10 Years	45.94%
80	20 Years	45.94%
200	50 Years	45.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.08. Further, an Excess Kurtosis of 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.84%	0	0.00%	0.00%
-28.84% to -6.72%	0	0.00%	0.00%
-6.72% to 15.39%	0	0.00%	0.00%
15.39% to 37.50%	8	28.57%	28.57%
37.50% to 59.61%	8	28.57%	57.14%
59.61% to 81.72%	7	25.00%	82.14%
81.72% to 103.84%	3	10.71%	92.86%
103.84% to 125.95%	0	0.00%	92.86%
125.95% to 148.06%	2	7.14%	100.00%
Greater than 148.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	30.13%	89.09%	78.57%	68.27%
±2σ	0.65%	118.58%	92.86%	95.45%
±3σ	-28.84%	148.06%	100.00%	99.73%

Descriptive Statistics

Mean	59.612%
Standard Error	5.572%
Median	53.331%
Mode	19.417%
Standard Deviation	29.483%
Sample Variance	869.252%
Kurtosis	0.77
Skewness	1.08
Range	115.325%
Minimum	19.417%
Maximum	134.742%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	59.612%	28	100.00%	59.612%
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 1.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.33%	0	0.00%	0.00%
-90.33% to -68.40%	0	0.00%	0.00%
-68.40% to -46.46%	0	0.00%	0.00%
-46.46% to -24.53%	6	21.43%	21.43%
-24.53% to -2.59%	12	42.86%	64.29%
-2.59% to 19.34%	5	17.86%	82.14%
19.34% to 41.28%	2	7.14%	89.29%
41.28% to 63.21%	2	7.14%	96.43%
63.21% to 85.15%	1	3.57%	100.00%
Greater than 85.15%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.84%	26.65%	78.57%	68.27%
±2σ	-61.08%	55.90%	96.43%	95.45%
±3σ	-90.33%	85.15%	100.00%	99.73%

Descriptive Statistics

Mean	-2.592%
Standard Error	5.527%
Median	-9.286%
Mode	-42.285%
Standard Deviation	29.246%
Sample Variance	855.300%
Kurtosis	1.55
Skewness	1.21
Range	122.750%
Minimum	-42.285%
Maximum	80.465%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.705%	10	35.71%	9.895%
Negative	-19.424%	18	64.29%	-12.487%
Zero	0.000%	0	0.00%	0.000%

CRWD Deep Analytical Report