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%	2.62%	2.98%	4.69%	3.74%	3.76%	123.14	132.70	118.62	137.75
Weekly	7.95%	6.29%	7.88%	11.09%	8.23%	8.29%	117.74	138.79	108.44	150.69
Monthly	14.88%	12.52%	13.50%	22.14%	17.12%	17.25%	107.71	151.71	90.76	180.04
Quarterly	33.55%	22.45%	24.78%	42.69%	29.66%	29.88%	95.02	171.97	70.63	231.34
Annual	—	—	—	—	59.32%	59.77%	70.63	231.34	39.03	418.67
Option Time Horizon	—	—	—	—	22.39%	22.56%	102.19	159.91	81.69	200.04

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $127.83 | Strike (K): $130.00 (first OTM call ≥ spot) | Observed Mid-Price: $10.7500 (Bid $10.2000 / Ask $11.3000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 59.32% (CRR binomial tree, American, n=20 steps) | BS IV: 59.40% (European Black-Scholes) | Yahoo IV (Annual): 59.77% → 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 0.70. Further, an Excess Kurtosis of 5.93 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%	7	0.43%	0.43%
-10.96% to -8.19%	12	0.73%	1.16%
-8.19% to -5.41%	67	4.10%	5.26%
-5.41% to -2.63%	205	12.55%	17.81%
-2.63% to 0.14%	539	32.99%	50.80%
0.14% to 2.92%	549	33.60%	84.39%
2.92% to 5.70%	166	10.16%	94.55%
5.70% to 8.47%	58	3.55%	98.10%
8.47% to 11.25%	15	0.92%	99.02%
Greater than 11.25%	16	0.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.56%	3.84%	76.44%	68.27%
±2σ	-7.26%	7.55%	94.68%	95.45%
±3σ	-10.96%	11.25%	98.59%	99.73%

Descriptive Statistics

Mean	0.143%
Standard Error	0.092%
Median	0.085%
Mode	-1.552%
Standard Deviation	3.702%
Sample Variance	13.708%
Kurtosis	5.93
Skewness	0.70
Range	46.340%
Minimum	-17.867%
Maximum	28.473%
Count	1634

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.697%	832	50.92%	1.373%
Negative	-2.517%	799	48.90%	-1.231%
Zero	0.000%	3	0.18%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.87%
20	1 Month	5.38%
60	1 Quarter	5.37%
250	1 Year	4.11%
750	3 Years	3.86%
1,250	5 Years	4.69%
2,500	10 Years	5.03%
5,000	20 Years	5.03%
12,500	50 Years	5.03%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.63. Further, an Excess Kurtosis of 3.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.10%	0	0.00%	0.00%
-3.10% to -1.14%	0	0.00%	0.00%
-1.14% to 0.83%	1	0.06%	0.06%
0.83% to 2.80%	361	22.08%	22.14%
2.80% to 4.76%	612	37.43%	59.57%
4.76% to 6.73%	375	22.94%	82.51%
6.73% to 8.70%	158	9.66%	92.17%
8.70% to 10.67%	72	4.40%	96.57%
10.67% to 12.63%	29	1.77%	98.35%
Greater than 12.63%	27	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.14%	7.39%	77.49%	68.27%
±2σ	-0.48%	10.01%	95.17%	95.45%
±3σ	-3.10%	12.63%	98.35%	99.73%

Descriptive Statistics

Mean	4.765%
Standard Error	0.065%
Median	4.104%
Mode	2.132%
Standard Deviation	2.623%
Sample Variance	6.878%
Kurtosis	3.97
Skewness	1.63
Range	20.502%
Minimum	0.725%
Maximum	21.227%
Count	1635

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.765%	1635	100.00%	4.765%
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 0.18. Further, an Excess Kurtosis of 1.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.91%	8	0.49%	0.49%
-8.91% to -6.68%	14	0.86%	1.35%
-6.68% to -4.44%	72	4.40%	5.75%
-4.44% to -2.21%	222	13.58%	19.33%
-2.21% to 0.03%	513	31.38%	50.70%
0.03% to 2.26%	502	30.70%	81.41%
2.26% to 4.50%	191	11.68%	93.09%
4.50% to 6.74%	69	4.22%	97.31%
6.74% to 8.97%	31	1.90%	99.20%
Greater than 8.97%	13	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.95%	3.01%	73.64%	68.27%
±2σ	-5.93%	5.99%	94.25%	95.45%
±3σ	-8.91%	8.97%	98.72%	99.73%

Descriptive Statistics

Mean	0.028%
Standard Error	0.074%
Median	-0.061%
Mode	-0.747%
Standard Deviation	2.981%
Sample Variance	8.888%
Kurtosis	1.65
Skewness	0.18
Range	26.273%
Minimum	-13.453%
Maximum	12.820%
Count	1635

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.264%	810	49.54%	1.122%
Negative	-2.171%	824	50.40%	-1.094%
Zero	0.000%	1	0.06%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 1.03 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.15%	1	0.29%	0.29%
-23.15% to -17.19%	5	1.47%	1.77%
-17.19% to -11.23%	15	4.42%	6.19%
-11.23% to -5.27%	51	15.04%	21.24%
-5.27% to 0.69%	102	30.09%	51.33%
0.69% to 6.65%	102	30.09%	81.42%
6.65% to 12.61%	41	12.09%	93.51%
12.61% to 18.57%	14	4.13%	97.64%
18.57% to 24.52%	7	2.06%	99.71%
Greater than 24.52%	1	0.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.26%	8.63%	73.16%	68.27%
±2σ	-15.20%	16.58%	94.99%	95.45%
±3σ	-23.15%	24.52%	99.41%	99.73%

Descriptive Statistics

Mean	0.689%
Standard Error	0.432%
Median	0.290%
Mode	-0.472%
Standard Deviation	7.945%
Sample Variance	63.122%
Kurtosis	1.03
Skewness	0.15
Range	56.449%
Minimum	-25.399%
Maximum	31.050%
Count	339

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.462%	177	52.21%	3.374%
Negative	-5.619%	162	47.79%	-2.685%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.12%
12	1 Quarter	14.42%
52	1 Year	10.70%
156	3 Years	9.50%
260	5 Years	11.09%
520	10 Years	11.79%
1,040	20 Years	11.79%
2,600	50 Years	11.79%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.02. Further, an Excess Kurtosis of 0.89 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.47%	0	0.00%	0.00%
-6.47% to -1.75%	0	0.00%	0.00%
-1.75% to 2.97%	2	0.59%	0.59%
2.97% to 7.69%	87	25.59%	26.18%
7.69% to 12.41%	106	31.18%	57.35%
12.41% to 17.13%	75	22.06%	79.41%
17.13% to 21.86%	41	12.06%	91.47%
21.86% to 26.57%	17	5.00%	96.47%
26.57% to 31.30%	10	2.94%	99.41%
Greater than 31.30%	2	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.12%	18.71%	70.29%	68.27%
±2σ	-0.17%	25.00%	94.71%	95.45%
±3σ	-6.47%	31.30%	99.41%	99.73%

Descriptive Statistics

Mean	12.414%
Standard Error	0.341%
Median	11.504%
Mode	7.160%
Standard Deviation	6.294%
Sample Variance	39.617%
Kurtosis	0.89
Skewness	1.02
Range	35.179%
Minimum	2.806%
Maximum	37.985%
Count	340

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.414%	340	100.00%	12.414%
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 0.72. Further, an Excess Kurtosis of 1.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.59%	0	0.00%	0.00%
-23.59% to -17.68%	2	0.59%	0.59%
-17.68% to -11.77%	12	3.53%	4.12%
-11.77% to -5.86%	56	16.47%	20.59%
-5.86% to 0.05%	118	34.71%	55.29%
0.05% to 5.96%	85	25.00%	80.29%
5.96% to 11.87%	41	12.06%	92.35%
11.87% to 17.77%	18	5.29%	97.65%
17.77% to 23.68%	5	1.47%	99.12%
Greater than 23.68%	3	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.83%	7.93%	72.65%	68.27%
±2σ	-15.71%	15.80%	95.29%	95.45%
±3σ	-23.59%	23.68%	99.12%	99.73%

Descriptive Statistics

Mean	0.047%
Standard Error	0.427%
Median	-0.794%
Mode	-5.089%
Standard Deviation	7.879%
Sample Variance	62.086%
Kurtosis	1.82
Skewness	0.72
Range	57.992%
Minimum	-20.734%
Maximum	37.258%
Count	340

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.650%	153	45.00%	2.992%
Negative	-5.356%	187	55.00%	-2.946%
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 1.04. Further, an Excess Kurtosis of 1.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.91%	0	0.00%	0.00%
-41.91% to -30.75%	0	0.00%	0.00%
-30.75% to -19.60%	3	3.85%	3.85%
-19.60% to -8.44%	14	17.95%	21.79%
-8.44% to 2.72%	26	33.33%	55.13%
2.72% to 13.88%	17	21.79%	76.92%
13.88% to 25.03%	14	17.95%	94.87%
25.03% to 36.19%	1	1.28%	96.15%
36.19% to 47.35%	2	2.56%	98.72%
Greater than 47.35%	1	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.16%	17.60%	67.95%	68.27%
±2σ	-27.04%	32.47%	96.15%	95.45%
±3σ	-41.91%	47.35%	98.72%	99.73%

Descriptive Statistics

Mean	2.719%
Standard Error	1.684%
Median	1.659%
Mode	-21.022%
Standard Deviation	14.877%
Sample Variance	221.323%
Kurtosis	1.94
Skewness	1.04
Range	78.979%
Minimum	-21.022%
Maximum	57.957%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.427%	40	51.28%	6.886%
Negative	-8.553%	38	48.72%	-4.167%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.09%
12	1 Year	20.66%
36	3 Years	20.41%
60	5 Years	22.14%
120	10 Years	24.19%
240	20 Years	24.19%
600	50 Years	24.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.33. Further, an Excess Kurtosis of 2.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.70%	0	0.00%	0.00%
-9.70% to -0.31%	0	0.00%	0.00%
-0.31% to 9.07%	0	0.00%	0.00%
9.07% to 18.46%	16	20.25%	20.25%
18.46% to 27.84%	31	39.24%	59.49%
27.84% to 37.23%	19	24.05%	83.54%
37.23% to 46.62%	6	7.59%	91.14%
46.62% to 56.00%	5	6.33%	97.47%
56.00% to 65.39%	0	0.00%	97.47%
Greater than 65.39%	2	2.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.33%	40.36%	74.68%	68.27%
±2σ	2.81%	52.88%	94.94%	95.45%
±3σ	-9.70%	65.39%	97.47%	99.73%

Descriptive Statistics

Mean	27.845%
Standard Error	1.408%
Median	24.985%
Mode	11.082%
Standard Deviation	12.515%
Sample Variance	156.627%
Kurtosis	2.22
Skewness	1.33
Range	62.799%
Minimum	11.082%
Maximum	73.881%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.845%	79	100.00%	27.845%
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 -0.23. Further, an Excess Kurtosis of -0.05 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.83%	0	0.00%	0.00%
-40.83% to -30.71%	1	1.27%	1.27%
-30.71% to -20.59%	3	3.80%	5.06%
-20.59% to -10.46%	13	16.46%	21.52%
-10.46% to -0.34%	22	27.85%	49.37%
-0.34% to 9.78%	21	26.58%	75.95%
9.78% to 19.91%	14	17.72%	93.67%
19.91% to 30.03%	5	6.33%	100.00%
30.03% to 40.15%	0	0.00%	100.00%
Greater than 40.15%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.84%	13.16%	63.29%	68.27%
±2σ	-27.34%	26.66%	96.20%	95.45%
±3σ	-40.83%	40.15%	100.00%	99.73%

Descriptive Statistics

Mean	-0.340%
Standard Error	1.519%
Median	-0.165%
Mode	-29.639%
Standard Deviation	13.498%
Sample Variance	182.205%
Kurtosis	-0.05
Skewness	-0.23
Range	63.999%
Minimum	-38.263%
Maximum	25.736%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.406%	39	49.37%	5.137%
Negative	-10.817%	40	50.63%	-5.477%
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 1.33. Further, an Excess Kurtosis of 1.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -91.12%	0	0.00%	0.00%
-91.12% to -65.96%	0	0.00%	0.00%
-65.96% to -40.80%	0	0.00%	0.00%
-40.80% to -15.63%	6	23.08%	23.08%
-15.63% to 9.53%	10	38.46%	61.54%
9.53% to 34.69%	4	15.38%	76.92%
34.69% to 59.85%	4	15.38%	92.31%
59.85% to 85.01%	1	3.85%	96.15%
85.01% to 110.17%	1	3.85%	100.00%
Greater than 110.17%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.02%	43.08%	76.92%	68.27%
±2σ	-57.57%	76.62%	96.15%	95.45%
±3σ	-91.12%	110.17%	100.00%	99.73%

Descriptive Statistics

Mean	9.527%
Standard Error	6.580%
Median	-1.489%
Mode	-30.200%
Standard Deviation	33.549%
Sample Variance	1125.538%
Kurtosis	1.69
Skewness	1.33
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	-13.766%	14	53.85%	-7.412%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	41.14%
12	3 Years	42.03%
20	5 Years	42.69%
40	10 Years	46.27%
80	20 Years	46.27%
200	50 Years	46.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.15. Further, an Excess Kurtosis of 3.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.70%	0	0.00%	0.00%
-10.70% to 6.14%	0	0.00%	0.00%
6.14% to 22.97%	1	3.70%	3.70%
22.97% to 39.81%	4	14.81%	18.52%
39.81% to 56.64%	10	37.04%	55.56%
56.64% to 73.48%	6	22.22%	77.78%
73.48% to 90.32%	5	18.52%	96.30%
90.32% to 107.15%	0	0.00%	96.30%
107.15% to 123.99%	0	0.00%	96.30%
Greater than 123.99%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	34.20%	79.09%	77.78%	68.27%
±2σ	11.75%	101.54%	96.30%	95.45%
±3σ	-10.70%	123.99%	96.30%	99.73%

Descriptive Statistics

Mean	56.644%
Standard Error	4.320%
Median	55.724%
Mode	17.069%
Standard Deviation	22.448%
Sample Variance	503.917%
Kurtosis	3.12
Skewness	1.15
Range	112.430%
Minimum	17.069%
Maximum	129.499%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	56.644%	27	100.00%	56.644%
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 -0.36. Further, an Excess Kurtosis of -0.64 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.94%	0	0.00%	0.00%
-74.94% to -56.36%	0	0.00%	0.00%
-56.36% to -37.77%	2	7.41%	7.41%
-37.77% to -19.18%	5	18.52%	25.93%
-19.18% to -0.60%	4	14.81%	40.74%
-0.60% to 17.99%	9	33.33%	74.07%
17.99% to 36.57%	5	18.52%	92.59%
36.57% to 55.16%	2	7.41%	100.00%
55.16% to 73.74%	0	0.00%	100.00%
Greater than 73.74%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.38%	24.18%	70.37%	68.27%
±2σ	-50.16%	48.96%	96.30%	95.45%
±3σ	-74.94%	73.74%	100.00%	99.73%

Descriptive Statistics

Mean	-0.599%
Standard Error	4.769%
Median	3.324%
Mode	-53.122%
Standard Deviation	24.781%
Sample Variance	614.108%
Kurtosis	-0.64
Skewness	-0.36
Range	94.278%
Minimum	-53.122%
Maximum	41.156%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.733%	16	59.26%	9.916%
Negative	-25.808%	11	40.74%	-10.514%
Zero	0.000%	0	0.00%	0.000%

DDOG Deep Analytical Report