DXPE - 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	5.47%	11.35%	4.13%	4.08%	3.38%	3.46%	144.17	154.26	139.38	159.56
Weekly	10.66%	24.79%	9.37%	9.30%	7.44%	7.62%	138.43	160.65	128.50	173.07
Monthly	20.92%	66.25%	20.44%	21.24%	15.49%	15.85%	127.72	174.12	109.39	203.30
Quarterly	32.01%	162.78%	30.99%	39.23%	26.84%	27.46%	114.03	195.04	87.19	255.07
Annual	—	—	—	—	53.67%	54.91%	87.19	255.07	50.98	436.28
Option Time Horizon	—	—	—	—	25.44%	26.03%	115.63	192.33	89.66	248.05

Calculation Notes: Computed at 2026-02-22T12:58 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $149.13 | Strike (K): $150.00 (first OTM call ≥ spot) | Observed Mid-Price: $15.1500 (Bid $13.0000 / Ask $17.3000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 53.67% (CRR binomial tree, American, n=20 steps) | BS IV: 53.26% (European Black-Scholes) | Yahoo IV (Annual): 54.91% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.08. Further, an Excess Kurtosis of 85.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.23%	44	0.74%	0.74%
-16.23% to -12.12%	31	0.52%	1.26%
-12.12% to -8.01%	82	1.38%	2.64%
-8.01% to -3.91%	379	6.38%	9.02%
-3.91% to 0.20%	2619	44.09%	53.11%
0.20% to 4.31%	2243	37.76%	90.88%
4.31% to 8.41%	384	6.46%	97.34%
8.41% to 12.52%	68	1.14%	98.48%
12.52% to 16.62%	37	0.62%	99.11%
Greater than 16.62%	53	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.27%	5.67%	88.67%	68.27%
±2σ	-10.75%	11.15%	96.87%	95.45%
±3σ	-16.22%	16.62%	98.37%	99.73%

Descriptive Statistics

Mean	0.200%
Standard Error	0.071%
Median	0.000%
Mode	0.000%
Standard Deviation	5.475%
Sample Variance	29.971%
Kurtosis	85.63
Skewness	4.08
Range	180.882%
Minimum	-50.000%
Maximum	130.882%
Count	5940

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.094%	2934	49.39%	1.528%
Negative	-2.729%	2892	48.69%	-1.329%
Zero	0.000%	114	1.92%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.58%
20	1 Month	4.48%
60	1 Quarter	4.29%
250	1 Year	4.73%
750	3 Years	3.99%
1,250	5 Years	4.08%
2,500	10 Years	4.48%
5,000	20 Years	4.55%
12,500	50 Years	5.51%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 42.72. Further, an Excess Kurtosis of 2447.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.66%	0	0.00%	0.00%
-28.66% to -20.15%	0	0.00%	0.00%
-20.15% to -11.63%	0	0.00%	0.00%
-11.63% to -3.12%	0	0.00%	0.00%
-3.12% to 5.39%	4187	70.48%	70.48%
5.39% to 13.90%	1520	25.58%	96.06%
13.90% to 22.41%	149	2.51%	98.57%
22.41% to 30.92%	40	0.67%	99.24%
30.92% to 39.43%	16	0.27%	99.51%
Greater than 39.43%	29	0.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.96%	16.73%	97.39%	68.27%
±2σ	-17.31%	28.08%	99.09%	95.45%
±3σ	-28.66%	39.43%	99.51%	99.73%

Descriptive Statistics

Mean	5.387%
Standard Error	0.147%
Median	3.893%
Mode	11.111%
Standard Deviation	11.348%
Sample Variance	128.770%
Kurtosis	2447.97
Skewness	42.72
Range	699.796%
Minimum	0.204%
Maximum	700.000%
Count	5941

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.387%	5941	100.00%	5.387%
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 0.28. Further, an Excess Kurtosis of 20.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.29%	41	0.69%	0.69%
-12.29% to -9.19%	45	0.76%	1.45%
-9.19% to -6.09%	121	2.04%	3.48%
-6.09% to -3.00%	545	9.17%	12.66%
-3.00% to 0.10%	2339	39.37%	52.03%
0.10% to 3.20%	2109	35.50%	87.53%
3.20% to 6.30%	505	8.50%	96.03%
6.30% to 9.40%	128	2.15%	98.18%
9.40% to 12.50%	46	0.77%	98.96%
Greater than 12.50%	62	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.03%	4.23%	84.26%	68.27%
±2σ	-8.16%	8.37%	95.78%	95.45%
±3σ	-12.29%	12.50%	98.27%	99.73%

Descriptive Statistics

Mean	0.103%
Standard Error	0.054%
Median	0.000%
Mode	0.000%
Standard Deviation	4.131%
Sample Variance	17.061%
Kurtosis	20.73
Skewness	0.28
Range	100.000%
Minimum	-50.000%
Maximum	50.000%
Count	5941

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.634%	2944	49.55%	1.305%
Negative	-2.459%	2905	48.90%	-1.202%
Zero	0.000%	92	1.55%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.26. Further, an Excess Kurtosis of 10.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.18%	9	0.68%	0.68%
-31.18% to -23.18%	15	1.13%	1.80%
-23.18% to -15.18%	29	2.18%	3.98%
-15.18% to -7.18%	108	8.11%	12.09%
-7.18% to 0.82%	555	41.67%	53.75%
0.82% to 8.81%	453	34.01%	87.76%
8.81% to 16.81%	109	8.18%	95.95%
16.81% to 24.81%	19	1.43%	97.37%
24.81% to 32.81%	15	1.13%	98.50%
Greater than 32.81%	20	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.85%	11.48%	83.93%	68.27%
±2σ	-20.51%	22.15%	94.52%	95.45%
±3σ	-31.18%	32.81%	97.82%	99.73%

Descriptive Statistics

Mean	0.816%
Standard Error	0.292%
Median	0.252%
Mode	0.000%
Standard Deviation	10.665%
Sample Variance	113.733%
Kurtosis	10.81
Skewness	1.26
Range	136.486%
Minimum	-50.000%
Maximum	86.486%
Count	1332

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.217%	682	51.20%	3.695%
Negative	-6.107%	628	47.15%	-2.879%
Zero	0.000%	22	1.65%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.34%
12	1 Quarter	10.59%
52	1 Year	10.94%
156	3 Years	9.45%
260	5 Years	9.30%
520	10 Years	10.47%
1,040	20 Years	10.60%
2,600	50 Years	12.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 18.42. Further, an Excess Kurtosis of 463.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.39%	0	0.00%	0.00%
-60.39% to -41.79%	0	0.00%	0.00%
-41.79% to -23.20%	0	0.00%	0.00%
-23.20% to -4.61%	0	0.00%	0.00%
-4.61% to 13.99%	962	72.17%	72.17%
13.99% to 32.58%	291	21.83%	94.00%
32.58% to 51.18%	50	3.75%	97.75%
51.18% to 69.77%	15	1.13%	98.87%
69.77% to 88.36%	7	0.53%	99.40%
Greater than 88.36%	8	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.80%	38.78%	95.95%	68.27%
±2σ	-35.60%	63.57%	98.80%	95.45%
±3σ	-60.39%	88.36%	99.40%	99.73%

Descriptive Statistics

Mean	13.988%
Standard Error	0.679%
Median	9.626%
Mode	10.000%
Standard Deviation	24.792%
Sample Variance	614.626%
Kurtosis	463.52
Skewness	18.42
Range	699.346%
Minimum	0.654%
Maximum	700.000%
Count	1333

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.988%	1333	100.00%	13.988%
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 1.06. Further, an Excess Kurtosis of 8.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.02%	8	0.60%	0.60%
-28.02% to -20.99%	18	1.35%	1.95%
-20.99% to -13.96%	27	2.03%	3.98%
-13.96% to -6.93%	134	10.05%	14.03%
-6.93% to 0.09%	520	39.01%	53.04%
0.09% to 7.12%	448	33.61%	86.65%
7.12% to 14.15%	115	8.63%	95.27%
14.15% to 21.17%	33	2.48%	97.75%
21.17% to 28.20%	10	0.75%	98.50%
Greater than 28.20%	20	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.28%	9.46%	81.47%	68.27%
±2σ	-18.65%	18.83%	94.60%	95.45%
±3σ	-28.02%	28.20%	97.90%	99.73%

Descriptive Statistics

Mean	0.092%
Standard Error	0.257%
Median	-0.241%
Mode	0.000%
Standard Deviation	9.369%
Sample Variance	87.773%
Kurtosis	8.94
Skewness	1.06
Range	117.882%
Minimum	-50.000%
Maximum	67.882%
Count	1333

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.473%	631	47.34%	3.064%
Negative	-5.792%	684	51.31%	-2.972%
Zero	0.000%	18	1.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.96. Further, an Excess Kurtosis of 3.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.66%	0	0.00%	0.00%
-59.66% to -43.97%	4	1.22%	1.22%
-43.97% to -28.29%	13	3.95%	5.17%
-28.29% to -12.60%	42	12.77%	17.93%
-12.60% to 3.09%	115	34.95%	52.89%
3.09% to 18.78%	105	31.91%	84.80%
18.78% to 34.46%	34	10.33%	95.14%
34.46% to 50.15%	6	1.82%	96.96%
50.15% to 65.84%	4	1.22%	98.18%
Greater than 65.84%	6	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.83%	24.01%	77.20%	68.27%
±2σ	-38.75%	44.92%	94.22%	95.45%
±3σ	-59.66%	65.84%	98.18%	99.73%

Descriptive Statistics

Mean	3.089%
Standard Error	1.153%
Median	1.663%
Mode	-37.500%
Standard Deviation	20.917%
Sample Variance	437.501%
Kurtosis	3.55
Skewness	0.96
Range	165.614%
Minimum	-56.816%
Maximum	108.798%
Count	329

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.935%	177	53.80%	9.111%
Negative	-13.121%	151	45.90%	-6.022%
Zero	0.000%	1	0.30%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.42%
12	1 Year	23.73%
36	3 Years	22.25%
60	5 Years	21.24%
120	10 Years	24.44%
240	20 Years	23.97%
600	50 Years	28.98%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 12.29. Further, an Excess Kurtosis of 185.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -161.78%	0	0.00%	0.00%
-161.78% to -112.09%	0	0.00%	0.00%
-112.09% to -62.40%	0	0.00%	0.00%
-62.40% to -12.71%	0	0.00%	0.00%
-12.71% to 36.98%	238	72.12%	72.12%
36.98% to 86.67%	76	23.03%	95.15%
86.67% to 136.36%	9	2.73%	97.88%
136.36% to 186.05%	3	0.91%	98.79%
186.05% to 235.74%	1	0.30%	99.09%
Greater than 235.74%	3	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.27%	103.23%	96.36%	68.27%
±2σ	-95.53%	169.49%	98.48%	95.45%
±3σ	-161.78%	235.74%	99.09%	99.73%

Descriptive Statistics

Mean	36.980%
Standard Error	3.647%
Median	23.770%
Mode	66.667%
Standard Deviation	66.253%
Sample Variance	4389.400%
Kurtosis	185.40
Skewness	12.29
Range	1072.917%
Minimum	2.083%
Maximum	1075.000%
Count	330

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.980%	330	100.00%	36.980%
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 1.53. Further, an Excess Kurtosis of 7.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.24%	0	0.00%	0.00%
-61.24% to -45.91%	3	0.91%	0.91%
-45.91% to -30.59%	9	2.73%	3.64%
-30.59% to -15.26%	41	12.42%	16.06%
-15.26% to 0.07%	132	40.00%	56.06%
0.07% to 15.40%	91	27.58%	83.64%
15.40% to 30.73%	37	11.21%	94.85%
30.73% to 46.05%	9	2.73%	97.58%
46.05% to 61.38%	3	0.91%	98.48%
Greater than 61.38%	5	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.37%	20.51%	77.27%	68.27%
±2σ	-40.80%	40.94%	95.45%	95.45%
±3σ	-61.24%	61.38%	98.48%	99.73%

Descriptive Statistics

Mean	0.069%
Standard Error	1.125%
Median	-2.092%
Mode	0.000%
Standard Deviation	20.437%
Sample Variance	417.688%
Kurtosis	7.46
Skewness	1.53
Range	193.748%
Minimum	-60.714%
Maximum	133.034%
Count	330

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.311%	145	43.94%	7.167%
Negative	-13.012%	180	54.55%	-7.097%
Zero	0.000%	5	1.51%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.32. Further, an Excess Kurtosis of 4.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -88.59%	0	0.00%	0.00%
-88.59% to -64.58%	0	0.00%	0.00%
-64.58% to -40.58%	5	4.50%	4.50%
-40.58% to -16.57%	19	17.12%	21.62%
-16.57% to 7.43%	36	32.43%	54.05%
7.43% to 31.43%	35	31.53%	85.59%
31.43% to 55.44%	9	8.11%	93.69%
55.44% to 79.44%	4	3.60%	97.30%
79.44% to 103.45%	1	0.90%	98.20%
Greater than 103.45%	2	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.58%	39.44%	78.38%	68.27%
±2σ	-56.58%	71.44%	94.59%	95.45%
±3σ	-88.59%	103.45%	98.20%	99.73%

Descriptive Statistics

Mean	7.429%
Standard Error	3.038%
Median	5.642%
Mode	-56.966%
Standard Deviation	32.006%
Sample Variance	1024.378%
Kurtosis	4.19
Skewness	1.32
Range	213.543%
Minimum	-56.966%
Maximum	156.577%
Count	111

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.375%	67	60.36%	15.316%
Negative	-20.361%	43	38.74%	-7.888%
Zero	0.000%	1	0.90%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.11%
12	3 Years	44.15%
20	5 Years	39.23%
40	10 Years	44.88%
80	20 Years	43.51%
200	50 Years	54.52%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.70. Further, an Excess Kurtosis of 68.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -400.93%	0	0.00%	0.00%
-400.93% to -278.84%	0	0.00%	0.00%
-278.84% to -156.75%	0	0.00%	0.00%
-156.75% to -34.67%	0	0.00%	0.00%
-34.67% to 87.42%	87	77.68%	77.68%
87.42% to 209.50%	20	17.86%	95.54%
209.50% to 331.59%	2	1.79%	97.32%
331.59% to 453.68%	0	0.00%	97.32%
453.68% to 575.76%	2	1.79%	99.11%
Greater than 575.76%	1	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-75.36%	250.20%	97.32%	68.27%
±2σ	-238.14%	412.98%	97.32%	95.45%
±3σ	-400.93%	575.76%	99.11%	99.73%

Descriptive Statistics

Mean	87.418%
Standard Error	15.381%
Median	54.752%
Mode	15.753%
Standard Deviation	162.781%
Sample Variance	26497.738%
Kurtosis	68.77
Skewness	7.70
Range	1584.247%
Minimum	15.753%
Maximum	1600.000%
Count	112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	87.418%	112	100.00%	87.418%
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 1.36. Further, an Excess Kurtosis of 2.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -92.72%	0	0.00%	0.00%
-92.72% to -69.48%	0	0.00%	0.00%
-69.48% to -46.24%	2	1.79%	1.79%
-46.24% to -23.00%	18	16.07%	17.86%
-23.00% to 0.24%	49	43.75%	61.61%
0.24% to 23.48%	25	22.32%	83.93%
23.48% to 46.72%	7	6.25%	90.18%
46.72% to 69.96%	6	5.36%	95.54%
69.96% to 93.20%	4	3.57%	99.11%
Greater than 93.20%	1	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.74%	31.23%	75.89%	68.27%
±2σ	-61.73%	62.21%	94.64%	95.45%
±3σ	-92.72%	93.20%	99.11%	99.73%

Descriptive Statistics

Mean	0.242%
Standard Error	2.928%
Median	-7.028%
Mode	-62.079%
Standard Deviation	30.986%
Sample Variance	960.115%
Kurtosis	2.94
Skewness	1.36
Range	193.178%
Minimum	-62.079%
Maximum	131.099%
Count	112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.608%	43	38.39%	11.367%
Negative	-18.059%	69	61.61%	-11.126%
Zero	0.000%	0	0.00%	0.000%

DXPE Deep Analytical Report