DKNG - 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	4.08%	3.24%	3.61%	5.29%	3.63%	3.70%	21.52	23.13	20.75	23.99
Weekly	9.98%	9.52%	9.94%	12.59%	7.99%	8.14%	20.60	24.16	19.02	26.17
Monthly	22.40%	20.91%	20.02%	26.82%	16.62%	16.94%	18.89	26.34	16.00	31.11
Quarterly	30.98%	37.39%	33.30%	42.47%	28.79%	29.35%	16.73	29.75	12.54	39.68
Annual	—	—	—	—	57.59%	58.69%	12.54	39.68	7.05	70.58
Option Time Horizon	—	—	—	—	18.82%	19.19%	18.48	26.93	15.31	32.51

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $22.31 | Strike (K): $23.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.4300 (Bid $1.2200 / Ask $1.6400) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 57.59% (CRR binomial tree, American, n=20 steps) | BS IV: 58.18% (European Black-Scholes) | Yahoo IV (Annual): 58.69% → 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 -0.05. Further, an Excess Kurtosis of 3.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.10%	10	0.63%	0.63%
-12.10% to -9.04%	11	0.69%	1.33%
-9.04% to -5.98%	54	3.41%	4.73%
-5.98% to -2.92%	223	14.08%	18.81%
-2.92% to 0.14%	528	33.33%	52.15%
0.14% to 3.19%	476	30.05%	82.20%
3.19% to 6.25%	183	11.55%	93.75%
6.25% to 9.31%	62	3.91%	97.66%
9.31% to 12.37%	23	1.45%	99.12%
Greater than 12.37%	14	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.94%	4.21%	75.19%	68.27%
±2σ	-8.02%	8.29%	95.08%	95.45%
±3σ	-12.10%	12.37%	98.48%	99.73%

Descriptive Statistics

Mean	0.136%
Standard Error	0.102%
Median	0.000%
Mode	0.000%
Standard Deviation	4.077%
Sample Variance	16.623%
Kurtosis	3.96
Skewness	-0.05
Range	45.094%
Minimum	-27.824%
Maximum	17.270%
Count	1584

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.083%	785	49.56%	1.528%
Negative	-2.831%	779	49.18%	-1.392%
Zero	0.000%	20	1.26%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.82%
20	1 Month	5.84%
60	1 Quarter	4.71%
250	1 Year	4.46%
750	3 Years	4.33%
1,250	5 Years	5.29%
2,500	10 Years	5.65%
5,000	20 Years	5.65%
12,500	50 Years	5.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.58. Further, an Excess Kurtosis of 3.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.21%	0	0.00%	0.00%
-4.21% to -1.77%	0	0.00%	0.00%
-1.77% to 0.66%	32	2.02%	2.02%
0.66% to 3.09%	305	19.24%	21.26%
3.09% to 5.53%	631	39.81%	61.07%
5.53% to 7.96%	333	21.01%	82.08%
7.96% to 10.39%	165	10.41%	92.49%
10.39% to 12.82%	56	3.53%	96.03%
12.82% to 15.26%	36	2.27%	98.30%
Greater than 15.26%	27	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.28%	8.77%	78.42%	68.27%
±2σ	-0.96%	12.01%	95.02%	95.45%
±3σ	-4.21%	15.26%	98.30%	99.73%

Descriptive Statistics

Mean	5.526%
Standard Error	0.081%
Median	4.752%
Mode	0.102%
Standard Deviation	3.244%
Sample Variance	10.522%
Kurtosis	3.96
Skewness	1.58
Range	26.049%
Minimum	0.030%
Maximum	26.079%
Count	1585

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.526%	1585	100.00%	5.526%
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 2.03 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.70%	10	0.63%	0.63%
-10.70% to -7.99%	19	1.20%	1.83%
-7.99% to -5.28%	61	3.85%	5.68%
-5.28% to -2.57%	205	12.93%	18.61%
-2.57% to 0.14%	507	31.99%	50.60%
0.14% to 2.85%	487	30.73%	81.32%
2.85% to 5.56%	211	13.31%	94.64%
5.56% to 8.27%	52	3.28%	97.92%
8.27% to 10.98%	21	1.32%	99.24%
Greater than 10.98%	12	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.47%	3.75%	74.20%	68.27%
±2σ	-7.08%	7.37%	94.45%	95.45%
±3σ	-10.70%	10.98%	98.61%	99.73%

Descriptive Statistics

Mean	0.141%
Standard Error	0.091%
Median	0.099%
Mode	0.000%
Standard Deviation	3.612%
Sample Variance	13.047%
Kurtosis	2.03
Skewness	0.09
Range	33.140%
Minimum	-15.987%
Maximum	17.153%
Count	1585

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.730%	811	51.17%	1.397%
Negative	-2.605%	764	48.20%	-1.256%
Zero	0.000%	10	0.63%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.58. Further, an Excess Kurtosis of 2.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.22%	1	0.30%	0.30%
-29.22% to -21.73%	5	1.49%	1.79%
-21.73% to -14.25%	12	3.58%	5.37%
-14.25% to -6.76%	41	12.24%	17.61%
-6.76% to 0.73%	121	36.12%	53.73%
0.73% to 8.22%	99	29.55%	83.28%
8.22% to 15.71%	36	10.75%	94.03%
15.71% to 23.20%	11	3.28%	97.31%
23.20% to 30.69%	6	1.79%	99.10%
Greater than 30.69%	3	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.25%	10.72%	77.31%	68.27%
±2σ	-19.24%	20.70%	93.73%	95.45%
±3σ	-29.22%	30.69%	98.81%	99.73%

Descriptive Statistics

Mean	0.732%
Standard Error	0.546%
Median	0.120%
Mode	-7.251%
Standard Deviation	9.985%
Sample Variance	99.694%
Kurtosis	2.68
Skewness	0.58
Range	80.749%
Minimum	-30.629%
Maximum	50.120%
Count	335

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.773%	171	51.05%	3.968%
Negative	-6.691%	162	48.36%	-3.236%
Zero	0.000%	2	0.60%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.17%
12	1 Quarter	10.04%
52	1 Year	10.03%
156	3 Years	10.06%
260	5 Years	12.59%
520	10 Years	13.21%
1,040	20 Years	13.21%
2,600	50 Years	13.21%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.81. Further, an Excess Kurtosis of 5.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.33%	0	0.00%	0.00%
-14.33% to -7.19%	0	0.00%	0.00%
-7.19% to -0.05%	0	0.00%	0.00%
-0.05% to 7.09%	59	17.56%	17.56%
7.09% to 14.23%	150	44.64%	62.20%
14.23% to 21.37%	72	21.43%	83.63%
21.37% to 28.51%	26	7.74%	91.37%
28.51% to 35.65%	18	5.36%	96.73%
35.65% to 42.79%	6	1.79%	98.51%
Greater than 42.79%	5	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.71%	23.75%	79.17%	68.27%
±2σ	-4.81%	33.27%	94.35%	95.45%
±3σ	-14.33%	42.79%	98.51%	99.73%

Descriptive Statistics

Mean	14.229%
Standard Error	0.519%
Median	11.556%
Mode	0.102%
Standard Deviation	9.521%
Sample Variance	90.655%
Kurtosis	5.18
Skewness	1.81
Range	69.618%
Minimum	0.099%
Maximum	69.717%
Count	336

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.229%	336	100.00%	14.229%
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 3.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.42%	2	0.60%	0.60%
-29.42% to -21.97%	4	1.19%	1.79%
-21.97% to -14.51%	10	2.98%	4.76%
-14.51% to -7.06%	42	12.50%	17.26%
-7.06% to 0.40%	125	37.20%	54.46%
0.40% to 7.86%	100	29.76%	84.23%
7.86% to 15.31%	31	9.23%	93.45%
15.31% to 22.77%	12	3.57%	97.02%
22.77% to 30.22%	5	1.49%	98.51%
Greater than 30.22%	5	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.54%	10.34%	79.76%	68.27%
±2σ	-19.48%	20.28%	94.35%	95.45%
±3σ	-29.42%	30.22%	97.92%	99.73%

Descriptive Statistics

Mean	0.400%
Standard Error	0.542%
Median	-0.104%
Mode	0.000%
Standard Deviation	9.941%
Sample Variance	98.828%
Kurtosis	3.24
Skewness	0.72
Range	79.867%
Minimum	-30.206%
Maximum	49.661%
Count	336

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.766%	160	47.62%	3.698%
Negative	-6.442%	172	51.19%	-3.298%
Zero	0.000%	4	1.19%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.59. Further, an Excess Kurtosis of 5.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.04%	0	0.00%	0.00%
-64.04% to -47.24%	0	0.00%	0.00%
-47.24% to -30.43%	1	1.28%	1.28%
-30.43% to -13.63%	17	21.79%	23.08%
-13.63% to 3.17%	23	29.49%	52.56%
3.17% to 19.97%	27	34.62%	87.18%
19.97% to 36.78%	5	6.41%	93.59%
36.78% to 53.58%	2	2.56%	96.15%
53.58% to 70.38%	2	2.56%	98.72%
Greater than 70.38%	1	1.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.23%	25.57%	76.92%	68.27%
±2σ	-41.63%	47.98%	96.15%	95.45%
±3σ	-64.04%	70.38%	98.72%	99.73%

Descriptive Statistics

Mean	3.171%
Standard Error	2.537%
Median	1.340%
Mode	-39.837%
Standard Deviation	22.403%
Sample Variance	501.891%
Kurtosis	5.03
Skewness	1.59
Range	143.845%
Minimum	-39.837%
Maximum	104.008%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.873%	41	52.56%	9.395%
Negative	-13.484%	36	46.15%	-6.223%
Zero	0.000%	1	1.28%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	21.85%
12	1 Year	21.88%
36	3 Years	22.46%
60	5 Years	26.82%
120	10 Years	29.51%
240	20 Years	29.51%
600	50 Years	29.51%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.23. Further, an Excess Kurtosis of 2.20 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.18%	0	0.00%	0.00%
-28.18% to -12.49%	0	0.00%	0.00%
-12.49% to 3.19%	4	5.06%	5.06%
3.19% to 18.88%	12	15.19%	20.25%
18.88% to 34.57%	30	37.97%	58.23%
34.57% to 50.25%	21	26.58%	84.81%
50.25% to 65.94%	6	7.59%	92.41%
65.94% to 81.63%	2	2.53%	94.94%
81.63% to 97.31%	2	2.53%	97.47%
Greater than 97.31%	2	2.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.65%	55.48%	74.68%	68.27%
±2σ	-7.26%	76.40%	94.94%	95.45%
±3σ	-28.18%	97.31%	97.47%	99.73%

Descriptive Statistics

Mean	34.568%
Standard Error	2.353%
Median	31.349%
Mode	0.813%
Standard Deviation	20.915%
Sample Variance	437.447%
Kurtosis	2.20
Skewness	1.23
Range	108.919%
Minimum	0.813%
Maximum	109.732%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.568%	79	100.00%	34.568%
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 0.50. Further, an Excess Kurtosis of 1.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.86%	0	0.00%	0.00%
-58.86% to -43.85%	1	1.27%	1.27%
-43.85% to -28.83%	3	3.80%	5.06%
-28.83% to -13.82%	10	12.66%	17.72%
-13.82% to 1.19%	30	37.97%	55.70%
1.19% to 16.20%	17	21.52%	77.22%
16.20% to 31.21%	13	16.46%	93.67%
31.21% to 46.23%	4	5.06%	98.73%
46.23% to 61.24%	0	0.00%	98.73%
Greater than 61.24%	1	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.83%	21.21%	72.15%	68.27%
±2σ	-38.84%	41.22%	94.94%	95.45%
±3σ	-58.86%	61.24%	98.73%	99.73%

Descriptive Statistics

Mean	1.190%
Standard Error	2.252%
Median	-0.812%
Mode	-51.159%
Standard Deviation	20.016%
Sample Variance	400.639%
Kurtosis	1.68
Skewness	0.50
Range	125.679%
Minimum	-51.159%
Maximum	74.520%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.245%	37	46.84%	8.077%
Negative	-13.269%	41	51.90%	-6.886%
Zero	0.000%	1	1.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.20. Further, an Excess Kurtosis of -0.58 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.36%	0	0.00%	0.00%
-85.36% to -62.12%	0	0.00%	0.00%
-62.12% to -38.89%	1	3.85%	3.85%
-38.89% to -15.65%	4	15.38%	19.23%
-15.65% to 7.59%	11	42.31%	61.54%
7.59% to 30.83%	2	7.69%	69.23%
30.83% to 54.07%	7	26.92%	96.15%
54.07% to 77.30%	1	3.85%	100.00%
77.30% to 100.54%	0	0.00%	100.00%
Greater than 100.54%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.39%	38.57%	65.38%	68.27%
±2σ	-54.38%	69.56%	96.15%	95.45%
±3σ	-85.36%	100.54%	100.00%	99.73%

Descriptive Statistics

Mean	7.590%
Standard Error	6.076%
Median	2.539%
Mode	-52.586%
Standard Deviation	30.984%
Sample Variance	959.998%
Kurtosis	-0.58
Skewness	0.20
Range	124.092%
Minimum	-52.586%
Maximum	71.506%
Count	26

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.125%	14	53.85%	16.221%
Negative	-18.701%	12	46.15%	-8.631%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	36.18%
12	3 Years	38.05%
20	5 Years	42.47%
40	10 Years	50.99%
80	20 Years	50.99%
200	50 Years	50.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.61. Further, an Excess Kurtosis of 3.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.03%	0	0.00%	0.00%
-50.03% to -21.99%	0	0.00%	0.00%
-21.99% to 6.05%	1	3.70%	3.70%
6.05% to 34.09%	3	11.11%	14.81%
34.09% to 62.13%	13	48.15%	62.96%
62.13% to 90.17%	5	18.52%	81.48%
90.17% to 118.21%	3	11.11%	92.59%
118.21% to 146.25%	1	3.70%	96.30%
146.25% to 174.29%	0	0.00%	96.30%
Greater than 174.29%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.75%	99.52%	81.48%	68.27%
±2σ	-12.64%	136.91%	96.30%	95.45%
±3σ	-50.03%	174.29%	96.30%	99.73%

Descriptive Statistics

Mean	62.133%
Standard Error	7.195%
Median	51.892%
Mode	3.889%
Standard Deviation	37.387%
Sample Variance	1397.753%
Kurtosis	3.21
Skewness	1.61
Range	178.248%
Minimum	3.889%
Maximum	182.137%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	62.133%	27	100.00%	62.133%
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 1.56. Further, an Excess Kurtosis of 3.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -98.18%	0	0.00%	0.00%
-98.18% to -73.20%	0	0.00%	0.00%
-73.20% to -48.22%	0	0.00%	0.00%
-48.22% to -23.24%	8	29.63%	29.63%
-23.24% to 1.73%	7	25.93%	55.56%
1.73% to 26.71%	9	33.33%	88.89%
26.71% to 51.69%	1	3.70%	92.59%
51.69% to 76.67%	1	3.70%	96.30%
76.67% to 101.65%	0	0.00%	96.30%
Greater than 101.65%	1	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.57%	35.04%	81.48%	68.27%
±2σ	-64.87%	68.34%	96.30%	95.45%
±3σ	-98.18%	101.65%	96.30%	99.73%

Descriptive Statistics

Mean	1.734%
Standard Error	6.409%
Median	-3.075%
Mode	-41.903%
Standard Deviation	33.304%
Sample Variance	1109.138%
Kurtosis	3.66
Skewness	1.56
Range	154.443%
Minimum	-41.903%
Maximum	112.540%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.466%	12	44.44%	12.651%
Negative	-19.652%	15	55.56%	-10.918%
Zero	0.000%	0	0.00%	0.000%

DKNG Deep Analytical Report