DDOG - 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	3.70%	2.63%	2.97%	4.69%	3.48%	3.58%	111.70	119.76	107.88	124.00
Weekly	7.88%	6.22%	7.77%	11.06%	7.67%	7.88%	107.12	124.88	99.22	134.83
Monthly	14.87%	12.56%	13.43%	22.02%	15.96%	16.41%	98.60	135.68	84.05	159.16
Quarterly	33.73%	22.88%	24.90%	42.38%	27.65%	28.42%	87.72	152.49	66.53	201.06
Annual	—	—	—	—	55.29%	56.84%	66.53	201.06	38.27	349.51
Option Time Horizon	—	—	—	—	21.27%	21.86%	93.50	143.07	75.59	176.98

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $115.66 | Strike (K): $120.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.3250 (Bid $7.6500 / Ask $9.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 55.29% (CRR binomial tree, American, n=20 steps) | BS IV: 55.90% (European Black-Scholes) | Yahoo IV (Annual): 56.84% → 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 0.73. 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 -10.96%	6	0.37%	0.37%
-10.96% to -8.19%	12	0.74%	1.12%
-8.19% to -5.41%	67	4.15%	5.27%
-5.41% to -2.64%	202	12.52%	17.79%
-2.64% to 0.14%	533	33.04%	50.84%
0.14% to 2.91%	539	33.42%	84.25%
2.91% to 5.68%	165	10.23%	94.48%
5.68% to 8.46%	58	3.60%	98.08%
8.46% to 11.23%	15	0.93%	99.01%
Greater than 11.23%	16	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.56%	3.84%	76.57%	68.27%
±2σ	-7.26%	7.54%	94.67%	95.45%
±3σ	-10.96%	11.23%	98.64%	99.73%

Descriptive Statistics

Mean	0.137%
Standard Error	0.092%
Median	0.070%
Mode	-1.552%
Standard Deviation	3.699%
Sample Variance	13.680%
Kurtosis	6.02
Skewness	0.73
Range	46.340%
Minimum	-17.867%
Maximum	28.473%
Count	1613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.692%	819	50.77%	1.367%
Negative	-2.508%	791	49.04%	-1.230%
Zero	0.000%	3	0.19%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.77%
20	1 Month	6.27%
60	1 Quarter	4.31%
250	1 Year	3.97%
750	3 Years	3.84%
1,250	5 Years	4.69%
2,500	10 Years	5.02%
5,000	20 Years	5.02%
12,500	50 Years	5.02%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.64. Further, an Excess Kurtosis of 3.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.12%	0	0.00%	0.00%
-3.12% to -1.16%	0	0.00%	0.00%
-1.16% to 0.82%	1	0.06%	0.06%
0.82% to 2.79%	359	22.24%	22.30%
2.79% to 4.76%	607	37.61%	59.91%
4.76% to 6.73%	365	22.61%	82.53%
6.73% to 8.70%	155	9.60%	92.13%
8.70% to 10.67%	72	4.46%	96.59%
10.67% to 12.64%	28	1.73%	98.33%
Greater than 12.64%	27	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.13%	7.38%	77.82%	68.27%
±2σ	-0.50%	10.01%	95.17%	95.45%
±3σ	-3.12%	12.64%	98.33%	99.73%

Descriptive Statistics

Mean	4.756%
Standard Error	0.065%
Median	4.094%
Mode	2.132%
Standard Deviation	2.627%
Sample Variance	6.899%
Kurtosis	3.99
Skewness	1.64
Range	20.502%
Minimum	0.725%
Maximum	21.227%
Count	1614

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.756%	1614	100.00%	4.756%
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 1.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.86%	8	0.50%	0.50%
-8.86% to -6.63%	15	0.93%	1.43%
-6.63% to -4.41%	69	4.28%	5.70%
-4.41% to -2.18%	217	13.44%	19.14%
-2.18% to 0.04%	507	31.41%	50.56%
0.04% to 2.27%	497	30.79%	81.35%
2.27% to 4.49%	190	11.77%	93.12%
4.49% to 6.72%	68	4.21%	97.34%
6.72% to 8.94%	31	1.92%	99.26%
Greater than 8.94%	12	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.93%	3.01%	73.79%	68.27%
±2σ	-5.89%	5.98%	94.18%	95.45%
±3σ	-8.86%	8.94%	98.76%	99.73%

Descriptive Statistics

Mean	0.042%
Standard Error	0.074%
Median	-0.018%
Mode	-0.747%
Standard Deviation	2.967%
Sample Variance	8.803%
Kurtosis	1.66
Skewness	0.15
Range	26.273%
Minimum	-13.453%
Maximum	12.820%
Count	1614

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.254%	804	49.81%	1.123%
Negative	-2.156%	809	50.12%	-1.081%
Zero	0.000%	1	0.06%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.18. Further, an Excess Kurtosis of 1.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.00%	1	0.30%	0.30%
-23.00% to -17.09%	4	1.19%	1.49%
-17.09% to -11.17%	16	4.78%	6.27%
-11.17% to -5.26%	51	15.22%	21.49%
-5.26% to 0.66%	101	30.15%	51.64%
0.66% to 6.57%	99	29.55%	81.19%
6.57% to 12.48%	42	12.54%	93.73%
12.48% to 18.40%	13	3.88%	97.61%
18.40% to 24.31%	6	1.79%	99.40%
Greater than 24.31%	2	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.23%	8.54%	72.54%	68.27%
±2σ	-15.11%	16.43%	94.93%	95.45%
±3σ	-23.00%	24.31%	99.10%	99.73%

Descriptive Statistics

Mean	0.656%
Standard Error	0.431%
Median	0.243%
Mode	-0.472%
Standard Deviation	7.885%
Sample Variance	62.169%
Kurtosis	1.07
Skewness	0.18
Range	56.449%
Minimum	-25.399%
Maximum	31.050%
Count	335

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.427%	174	51.94%	3.338%
Negative	-5.580%	161	48.06%	-2.682%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.58%
12	1 Quarter	11.05%
52	1 Year	10.10%
156	3 Years	9.35%
260	5 Years	11.06%
520	10 Years	11.73%
1,040	20 Years	11.73%
2,600	50 Years	11.73%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.04. Further, an Excess Kurtosis of 1.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.33%	0	0.00%	0.00%
-6.33% to -1.66%	0	0.00%	0.00%
-1.66% to 3.01%	2	0.60%	0.60%
3.01% to 7.68%	86	25.60%	26.19%
7.68% to 12.35%	105	31.25%	57.44%
12.35% to 17.01%	75	22.32%	79.76%
17.01% to 21.68%	37	11.01%	90.77%
21.68% to 26.35%	19	5.65%	96.43%
26.35% to 31.02%	10	2.98%	99.40%
Greater than 31.02%	2	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.12%	18.57%	70.54%	68.27%
±2σ	-0.10%	24.80%	94.35%	95.45%
±3σ	-6.33%	31.02%	99.40%	99.73%

Descriptive Statistics

Mean	12.345%
Standard Error	0.340%
Median	11.504%
Mode	7.160%
Standard Deviation	6.225%
Sample Variance	38.752%
Kurtosis	1.02
Skewness	1.04
Range	35.179%
Minimum	2.806%
Maximum	37.985%
Count	336

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.345%	336	100.00%	12.345%
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 0.71. Further, an Excess Kurtosis of 1.84 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.23%	0	0.00%	0.00%
-23.23% to -17.40%	2	0.60%	0.60%
-17.40% to -11.57%	13	3.87%	4.46%
-11.57% to -5.75%	54	16.07%	20.54%
-5.75% to 0.08%	116	34.52%	55.06%
0.08% to 5.91%	84	25.00%	80.06%
5.91% to 11.74%	40	11.90%	91.96%
11.74% to 17.56%	20	5.95%	97.92%
17.56% to 23.39%	4	1.19%	99.11%
Greater than 23.39%	3	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.69%	7.85%	72.02%	68.27%
±2σ	-15.46%	15.62%	95.54%	95.45%
±3σ	-23.23%	23.39%	99.11%	99.73%

Descriptive Statistics

Mean	0.082%
Standard Error	0.424%
Median	-0.782%
Mode	-5.089%
Standard Deviation	7.769%
Sample Variance	60.363%
Kurtosis	1.84
Skewness	0.71
Range	57.992%
Minimum	-20.734%
Maximum	37.258%
Count	336

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.590%	152	45.24%	2.981%
Negative	-5.295%	184	54.76%	-2.900%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close 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 2.03 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.02%	0	0.00%	0.00%
-42.02% to -30.86%	0	0.00%	0.00%
-30.86% to -19.71%	3	3.90%	3.90%
-19.71% to -8.56%	14	18.18%	22.08%
-8.56% to 2.60%	26	33.77%	55.84%
2.60% to 13.75%	17	22.08%	77.92%
13.75% to 24.91%	13	16.88%	94.81%
24.91% to 36.06%	1	1.30%	96.10%
36.06% to 47.22%	2	2.60%	98.70%
Greater than 47.22%	1	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.27%	17.47%	70.13%	68.27%
±2σ	-27.15%	32.34%	96.10%	95.45%
±3σ	-42.02%	47.22%	98.70%	99.73%

Descriptive Statistics

Mean	2.599%
Standard Error	1.695%
Median	1.537%
Mode	-21.022%
Standard Deviation	14.873%
Sample Variance	221.195%
Kurtosis	2.03
Skewness	1.08
Range	78.979%
Minimum	-21.022%
Maximum	57.957%
Count	77

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.392%	39	50.65%	6.783%
Negative	-8.478%	38	49.35%	-4.184%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.38%
12	1 Year	19.47%
36	3 Years	20.07%
60	5 Years	22.02%
120	10 Years	24.09%
240	20 Years	24.09%
600	50 Years	24.09%

High-to-Low 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 2.27 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.95%	0	0.00%	0.00%
-9.95% to -0.53%	0	0.00%	0.00%
-0.53% to 8.89%	0	0.00%	0.00%
8.89% to 18.31%	16	20.51%	20.51%
18.31% to 27.73%	31	39.74%	60.26%
27.73% to 37.15%	18	23.08%	83.33%
37.15% to 46.57%	6	7.69%	91.03%
46.57% to 55.99%	5	6.41%	97.44%
55.99% to 65.41%	0	0.00%	97.44%
Greater than 65.41%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.17%	40.29%	74.36%	68.27%
±2σ	2.61%	52.85%	94.87%	95.45%
±3σ	-9.95%	65.41%	97.44%	99.73%

Descriptive Statistics

Mean	27.729%
Standard Error	1.422%
Median	24.638%
Mode	11.082%
Standard Deviation	12.561%
Sample Variance	157.775%
Kurtosis	2.27
Skewness	1.35
Range	62.799%
Minimum	11.082%
Maximum	73.881%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.729%	78	100.00%	27.729%
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 -0.26. Further, an Excess Kurtosis of 0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.49%	0	0.00%	0.00%
-40.49% to -30.42%	1	1.28%	1.28%
-30.42% to -20.34%	3	3.85%	5.13%
-20.34% to -10.27%	12	15.38%	20.51%
-10.27% to -0.20%	22	28.21%	48.72%
-0.20% to 9.87%	22	28.21%	76.92%
9.87% to 19.95%	13	16.67%	93.59%
19.95% to 30.02%	5	6.41%	100.00%
30.02% to 40.09%	0	0.00%	100.00%
Greater than 40.09%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.63%	13.23%	65.38%	68.27%
±2σ	-27.06%	26.66%	96.15%	95.45%
±3σ	-40.49%	40.09%	100.00%	99.73%

Descriptive Statistics

Mean	-0.199%
Standard Error	1.521%
Median	-0.001%
Mode	-29.639%
Standard Deviation	13.430%
Sample Variance	180.359%
Kurtosis	0.03
Skewness	-0.26
Range	63.999%
Minimum	-38.263%
Maximum	25.736%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.311%	39	50.00%	5.156%
Negative	-10.708%	39	50.00%	-5.354%
Zero	0.000%	0	0.00%	0.000%

Close-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 1.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -92.03%	0	0.00%	0.00%
-92.03% to -66.74%	0	0.00%	0.00%
-66.74% to -41.44%	0	0.00%	0.00%
-41.44% to -16.15%	6	23.08%	23.08%
-16.15% to 9.14%	10	38.46%	61.54%
9.14% to 34.44%	4	15.38%	76.92%
34.44% to 59.73%	4	15.38%	92.31%
59.73% to 85.03%	1	3.85%	96.15%
85.03% to 110.32%	1	3.85%	100.00%
Greater than 110.32%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.58%	42.87%	76.92%	68.27%
±2σ	-58.31%	76.60%	96.15%	95.45%
±3σ	-92.03%	110.32%	100.00%	99.73%

Descriptive Statistics

Mean	9.145%
Standard Error	6.614%
Median	-2.836%
Mode	-30.200%
Standard Deviation	33.726%
Sample Variance	1137.413%
Kurtosis	1.66
Skewness	1.34
Range	138.223%
Minimum	-30.200%
Maximum	108.023%
Count	26

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.703%	12	46.15%	16.940%
Negative	-14.476%	14	53.85%	-7.795%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	39.63%
12	3 Years	41.53%
20	5 Years	42.38%
40	10 Years	46.04%
80	20 Years	46.04%
200	50 Years	46.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.07. Further, an Excess Kurtosis of 2.85 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.36%	0	0.00%	0.00%
-12.36% to 4.80%	0	0.00%	0.00%
4.80% to 21.96%	1	3.70%	3.70%
21.96% to 39.12%	4	14.81%	18.52%
39.12% to 56.27%	10	37.04%	55.56%
56.27% to 73.43%	6	22.22%	77.78%
73.43% to 90.59%	5	18.52%	96.30%
90.59% to 107.74%	0	0.00%	96.30%
107.74% to 124.90%	0	0.00%	96.30%
Greater than 124.90%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	33.40%	79.15%	77.78%	68.27%
±2σ	10.52%	102.03%	96.30%	95.45%
±3σ	-12.35%	124.90%	96.30%	99.73%

Descriptive Statistics

Mean	56.273%
Standard Error	4.402%
Median	55.724%
Mode	17.069%
Standard Deviation	22.876%
Sample Variance	523.308%
Kurtosis	2.85
Skewness	1.07
Range	112.430%
Minimum	17.069%
Maximum	129.499%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	56.273%	27	100.00%	56.273%
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 -0.40. Further, an Excess Kurtosis of -0.66 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.89%	0	0.00%	0.00%
-74.89% to -56.21%	0	0.00%	0.00%
-56.21% to -37.53%	2	7.41%	7.41%
-37.53% to -18.86%	5	18.52%	25.93%
-18.86% to -0.18%	4	14.81%	40.74%
-0.18% to 18.49%	9	33.33%	74.07%
18.49% to 37.17%	5	18.52%	92.59%
37.17% to 55.84%	2	7.41%	100.00%
55.84% to 74.52%	0	0.00%	100.00%
Greater than 74.52%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.08%	24.72%	70.37%	68.27%
±2σ	-49.98%	49.62%	96.30%	95.45%
±3σ	-74.89%	74.52%	100.00%	99.73%

Descriptive Statistics

Mean	-0.183%
Standard Error	4.792%
Median	5.587%
Mode	-53.122%
Standard Deviation	24.901%
Sample Variance	620.073%
Kurtosis	-0.66
Skewness	-0.40
Range	94.278%
Minimum	-53.122%
Maximum	41.156%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.434%	16	59.26%	10.331%
Negative	-25.808%	11	40.74%	-10.514%
Zero	0.000%	0	0.00%	0.000%

DDOG Deep Analytical Report