DBX - 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	2.43%	1.93%	2.10%	2.69%	1.87%	2.29%	25.01	25.96	24.55	26.45
Weekly	5.40%	5.00%	5.46%	6.25%	4.11%	5.03%	24.45	26.55	23.47	27.66
Monthly	8.68%	8.79%	9.30%	13.29%	8.55%	10.47%	23.39	27.75	21.47	30.23
Quarterly	15.03%	13.67%	14.95%	24.19%	14.81%	18.14%	21.97	29.55	18.95	34.26
Annual	—	—	—	—	29.62%	36.28%	18.95	34.26	14.09	46.08
Option Time Horizon	—	—	—	—	11.39%	13.95%	22.74	28.55	20.29	32.00

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $25.48 | Strike (K): $26.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.0000 (Bid $0.8000 / Ask $1.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 29.62% (CRR binomial tree, American, n=20 steps) | BS IV: 29.95% (European Black-Scholes) | Yahoo IV (Annual): 36.28% → 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 -0.27. Further, an Excess Kurtosis of 10.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.27%	16	0.80%	0.80%
-7.27% to -5.45%	21	1.06%	1.86%
-5.45% to -3.62%	54	2.72%	4.58%
-3.62% to -1.80%	233	11.72%	16.30%
-1.80% to 0.02%	639	32.14%	48.44%
0.02% to 1.85%	697	35.06%	83.50%
1.85% to 3.67%	249	12.53%	96.03%
3.67% to 5.50%	48	2.41%	98.44%
5.50% to 7.32%	16	0.80%	99.25%
Greater than 7.32%	15	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.41%	2.46%	78.27%	68.27%
±2σ	-4.84%	4.89%	95.62%	95.45%
±3σ	-7.27%	7.32%	98.44%	99.73%

Descriptive Statistics

Mean	0.024%
Standard Error	0.055%
Median	0.111%
Mode	0.000%
Standard Deviation	2.432%
Sample Variance	5.913%
Kurtosis	10.93
Skewness	-0.27
Range	42.883%
Minimum	-22.926%
Maximum	19.957%
Count	1988

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.639%	1025	51.56%	0.845%
Negative	-1.732%	942	47.38%	-0.821%
Zero	0.000%	21	1.06%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.30%
20	1 Month	2.87%
60	1 Quarter	2.52%
250	1 Year	2.59%
750	3 Years	2.43%
1,250	5 Years	2.69%
2,500	10 Years	3.21%
5,000	20 Years	3.21%
12,500	50 Years	3.21%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.67. Further, an Excess Kurtosis of 10.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.70%	0	0.00%	0.00%
-2.70% to -1.25%	0	0.00%	0.00%
-1.25% to 0.20%	0	0.00%	0.00%
0.20% to 1.65%	293	14.73%	14.73%
1.65% to 3.10%	980	49.27%	64.00%
3.10% to 4.55%	427	21.47%	85.47%
4.55% to 6.00%	160	8.04%	93.51%
6.00% to 7.45%	54	2.71%	96.23%
7.45% to 8.90%	32	1.61%	97.84%
Greater than 8.90%	43	2.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.17%	5.04%	86.32%	68.27%
±2σ	-0.76%	6.97%	95.53%	95.45%
±3σ	-2.70%	8.90%	97.84%	99.73%

Descriptive Statistics

Mean	3.103%
Standard Error	0.043%
Median	2.584%
Mode	1.557%
Standard Deviation	1.933%
Sample Variance	3.737%
Kurtosis	10.55
Skewness	2.67
Range	17.524%
Minimum	0.750%
Maximum	18.274%
Count	1989

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.103%	1989	100.00%	3.103%
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 0.24. Further, an Excess Kurtosis of 4.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.29%	15	0.75%	0.75%
-6.29% to -4.72%	24	1.21%	1.96%
-4.72% to -3.15%	56	2.82%	4.78%
-3.15% to -1.57%	260	13.07%	17.85%
-1.57% to -0.00%	644	32.38%	50.23%
-0.00% to 1.57%	649	32.63%	82.86%
1.57% to 3.15%	225	11.31%	94.17%
3.15% to 4.72%	81	4.07%	98.24%
4.72% to 6.29%	21	1.06%	99.30%
Greater than 6.29%	14	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.10%	2.10%	76.57%	68.27%
±2σ	-4.20%	4.19%	94.97%	95.45%
±3σ	-6.29%	6.29%	98.54%	99.73%

Descriptive Statistics

Mean	-0.001%
Standard Error	0.047%
Median	-0.036%
Mode	0.000%
Standard Deviation	2.098%
Sample Variance	4.404%
Kurtosis	4.22
Skewness	0.24
Range	23.239%
Minimum	-10.078%
Maximum	13.161%
Count	1989

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.540%	968	48.67%	0.749%
Negative	-1.493%	999	50.23%	-0.750%
Zero	0.000%	22	1.11%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.48. Further, an Excess Kurtosis of 8.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.10%	4	0.97%	0.97%
-16.10% to -12.05%	3	0.73%	1.69%
-12.05% to -8.00%	17	4.12%	5.81%
-8.00% to -3.95%	50	12.11%	17.92%
-3.95% to 0.10%	124	30.02%	47.94%
0.10% to 4.15%	147	35.59%	83.54%
4.15% to 8.20%	51	12.35%	95.88%
8.20% to 12.25%	11	2.66%	98.55%
12.25% to 16.30%	3	0.73%	99.27%
Greater than 16.30%	3	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.30%	5.50%	77.72%	68.27%
±2σ	-10.70%	10.90%	95.88%	95.45%
±3σ	-16.10%	16.30%	98.31%	99.73%

Descriptive Statistics

Mean	0.102%
Standard Error	0.266%
Median	0.269%
Mode	-2.782%
Standard Deviation	5.401%
Sample Variance	29.169%
Kurtosis	8.46
Skewness	0.48
Range	62.223%
Minimum	-22.688%
Maximum	39.535%
Count	413

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.629%	218	52.78%	1.916%
Negative	-3.881%	193	46.73%	-1.814%
Zero	0.000%	2	0.48%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.15%
12	1 Quarter	5.71%
52	1 Year	5.64%
156	3 Years	5.71%
260	5 Years	6.25%
520	10 Years	7.45%
1,040	20 Years	7.45%
2,600	50 Years	7.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.91. Further, an Excess Kurtosis of 13.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.20%	0	0.00%	0.00%
-7.20% to -3.44%	0	0.00%	0.00%
-3.44% to 0.31%	0	0.00%	0.00%
0.31% to 4.06%	66	15.94%	15.94%
4.06% to 7.81%	189	45.65%	61.59%
7.81% to 11.56%	103	24.88%	86.47%
11.56% to 15.31%	33	7.97%	94.44%
15.31% to 19.06%	7	1.69%	96.14%
19.06% to 22.81%	7	1.69%	97.83%
Greater than 22.81%	9	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.81%	12.81%	87.20%	68.27%
±2σ	-2.20%	17.81%	95.65%	95.45%
±3σ	-7.20%	22.81%	97.83%	99.73%

Descriptive Statistics

Mean	7.807%
Standard Error	0.246%
Median	6.630%
Mode	3.974%
Standard Deviation	5.001%
Sample Variance	25.006%
Kurtosis	13.13
Skewness	2.91
Range	43.118%
Minimum	2.270%
Maximum	45.388%
Count	414

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.807%	414	100.00%	7.807%
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 0.76. Further, an Excess Kurtosis of 5.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.17%	1	0.24%	0.24%
-16.17% to -12.07%	5	1.21%	1.45%
-12.07% to -7.98%	7	1.69%	3.14%
-7.98% to -3.88%	56	13.53%	16.67%
-3.88% to 0.21%	160	38.65%	55.31%
0.21% to 4.31%	116	28.02%	83.33%
4.31% to 8.40%	47	11.35%	94.69%
8.40% to 12.50%	13	3.14%	97.83%
12.50% to 16.59%	4	0.97%	98.79%
Greater than 16.59%	5	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.25%	5.67%	76.57%	68.27%
±2σ	-10.71%	11.13%	95.41%	95.45%
±3σ	-16.17%	16.59%	98.55%	99.73%

Descriptive Statistics

Mean	0.213%
Standard Error	0.268%
Median	-0.222%
Mode	0.000%
Standard Deviation	5.460%
Sample Variance	29.811%
Kurtosis	5.46
Skewness	0.76
Range	55.201%
Minimum	-28.048%
Maximum	27.153%
Count	414

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.252%	195	47.10%	2.003%
Negative	-3.447%	215	51.93%	-1.790%
Zero	0.000%	4	0.97%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.33. Further, an Excess Kurtosis of 0.59 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.86%	0	0.00%	0.00%
-25.86% to -19.36%	2	2.11%	2.11%
-19.36% to -12.85%	3	3.16%	5.26%
-12.85% to -6.34%	14	14.74%	20.00%
-6.34% to 0.17%	28	29.47%	49.47%
0.17% to 6.68%	25	26.32%	75.79%
6.68% to 13.19%	18	18.95%	94.74%
13.19% to 19.69%	4	4.21%	98.95%
19.69% to 26.20%	1	1.05%	100.00%
Greater than 26.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.51%	8.85%	76.84%	68.27%
±2σ	-17.19%	17.53%	92.63%	95.45%
±3σ	-25.87%	26.20%	100.00%	99.73%

Descriptive Statistics

Mean	0.169%
Standard Error	0.890%
Median	0.299%
Mode	-24.400%
Standard Deviation	8.678%
Sample Variance	75.302%
Kurtosis	0.59
Skewness	-0.33
Range	45.350%
Minimum	-24.400%
Maximum	20.950%
Count	95

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.787%	48	50.53%	3.429%
Negative	-6.734%	46	48.42%	-3.261%
Zero	0.000%	1	1.05%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	9.59%
12	1 Year	10.75%
36	3 Years	12.45%
60	5 Years	13.29%
120	10 Years	15.77%
240	20 Years	15.77%
600	50 Years	15.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.48. Further, an Excess Kurtosis of 2.04 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.94%	0	0.00%	0.00%
-8.94% to -2.35%	0	0.00%	0.00%
-2.35% to 4.25%	0	0.00%	0.00%
4.25% to 10.84%	21	21.88%	21.88%
10.84% to 17.44%	40	41.67%	63.54%
17.44% to 24.03%	18	18.75%	82.29%
24.03% to 30.63%	9	9.38%	91.67%
30.63% to 37.23%	2	2.08%	93.75%
37.23% to 43.82%	4	4.17%	97.92%
Greater than 43.82%	2	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.64%	26.23%	75.00%	68.27%
±2σ	-0.15%	35.03%	93.75%	95.45%
±3σ	-8.94%	43.82%	97.92%	99.73%

Descriptive Statistics

Mean	17.439%
Standard Error	0.898%
Median	14.976%
Mode	5.501%
Standard Deviation	8.794%
Sample Variance	77.338%
Kurtosis	2.04
Skewness	1.48
Range	42.358%
Minimum	5.501%
Maximum	47.859%
Count	96

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.439%	96	100.00%	17.439%
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 0.93. Further, an Excess Kurtosis of 1.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.28%	0	0.00%	0.00%
-27.28% to -20.30%	0	0.00%	0.00%
-20.30% to -13.33%	4	4.17%	4.17%
-13.33% to -6.36%	18	18.75%	22.92%
-6.36% to 0.62%	31	32.29%	55.21%
0.62% to 7.59%	27	28.12%	83.33%
7.59% to 14.57%	10	10.42%	93.75%
14.57% to 21.54%	3	3.12%	96.88%
21.54% to 28.52%	1	1.04%	97.92%
Greater than 28.52%	2	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.68%	9.92%	78.12%	68.27%
±2σ	-17.98%	19.22%	93.75%	95.45%
±3σ	-27.28%	28.51%	97.92%	99.73%

Descriptive Statistics

Mean	0.618%
Standard Error	0.949%
Median	-0.083%
Mode	-19.223%
Standard Deviation	9.299%
Sample Variance	86.468%
Kurtosis	1.91
Skewness	0.93
Range	52.250%
Minimum	-19.223%
Maximum	33.027%
Count	96

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.847%	46	47.92%	3.760%
Negative	-6.156%	49	51.04%	-3.142%
Zero	0.000%	1	1.04%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.38. Further, an Excess Kurtosis of -0.61 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.53%	0	0.00%	0.00%
-44.53% to -33.26%	0	0.00%	0.00%
-33.26% to -21.99%	1	3.12%	3.12%
-21.99% to -10.72%	10	31.25%	34.38%
-10.72% to 0.55%	7	21.88%	56.25%
0.55% to 11.82%	7	21.88%	78.12%
11.82% to 23.09%	3	9.38%	87.50%
23.09% to 34.36%	4	12.50%	100.00%
34.36% to 45.63%	0	0.00%	100.00%
Greater than 45.63%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.48%	15.57%	68.75%	68.27%
±2σ	-29.50%	30.60%	96.88%	95.45%
±3σ	-44.53%	45.63%	100.00%	99.73%

Descriptive Statistics

Mean	0.549%
Standard Error	2.656%
Median	-1.874%
Mode	-26.894%
Standard Deviation	15.026%
Sample Variance	225.774%
Kurtosis	-0.61
Skewness	0.38
Range	59.392%
Minimum	-26.894%
Maximum	32.498%
Count	32

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.558%	14	43.75%	6.369%
Negative	-10.956%	17	53.12%	-5.820%
Zero	0.000%	1	3.12%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	17.52%
12	3 Years	24.45%
20	5 Years	24.19%
40	10 Years	28.14%
80	20 Years	28.14%
200	50 Years	28.14%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.77. Further, an Excess Kurtosis of 0.51 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.30%	0	0.00%	0.00%
-8.30% to 1.95%	0	0.00%	0.00%
1.95% to 12.20%	2	6.06%	6.06%
12.20% to 22.45%	4	12.12%	18.18%
22.45% to 32.70%	14	42.42%	60.61%
32.70% to 42.95%	7	21.21%	81.82%
42.95% to 53.20%	3	9.09%	90.91%
53.20% to 63.44%	1	3.03%	93.94%
63.44% to 73.69%	2	6.06%	100.00%
Greater than 73.69%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.03%	46.36%	69.70%	68.27%
±2σ	5.36%	60.03%	90.91%	95.45%
±3σ	-8.30%	73.69%	100.00%	99.73%

Descriptive Statistics

Mean	32.696%
Standard Error	2.379%
Median	30.976%
Mode	9.672%
Standard Deviation	13.666%
Sample Variance	186.765%
Kurtosis	0.51
Skewness	0.77
Range	53.952%
Minimum	9.672%
Maximum	63.624%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.696%	33	100.00%	32.696%
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 -0.37 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.34%	0	0.00%	0.00%
-43.34% to -32.13%	0	0.00%	0.00%
-32.13% to -20.92%	1	3.03%	3.03%
-20.92% to -9.71%	7	21.21%	24.24%
-9.71% to 1.50%	9	27.27%	51.52%
1.50% to 12.71%	6	18.18%	69.70%
12.71% to 23.92%	8	24.24%	93.94%
23.92% to 35.13%	1	3.03%	96.97%
35.13% to 46.35%	1	3.03%	100.00%
Greater than 46.35%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.45%	16.45%	63.64%	68.27%
±2σ	-28.39%	31.40%	96.97%	95.45%
±3σ	-43.34%	46.35%	100.00%	99.73%

Descriptive Statistics

Mean	1.502%
Standard Error	2.602%
Median	0.697%
Mode	-24.972%
Standard Deviation	14.948%
Sample Variance	223.445%
Kurtosis	-0.37
Skewness	0.26
Range	62.537%
Minimum	-24.972%
Maximum	37.565%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.211%	17	51.52%	6.806%
Negative	-10.939%	16	48.48%	-5.304%
Zero	0.000%	0	0.00%	0.000%

DBX Deep Analytical Report