XNCR - 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	3.46%	3.08%	3.24%	4.86%	9.17%	9.04%	11.15	13.39	10.17	14.68
Weekly	7.65%	6.89%	7.46%	10.79%	20.18%	19.91%	9.99	14.95	8.16	18.29
Monthly	15.35%	13.99%	14.68%	23.12%	42.00%	41.44%	8.03	18.60	5.28	28.31
Quarterly	25.09%	27.17%	26.02%	41.23%	72.75%	71.78%	5.90	25.29	2.85	52.36
Annual	—	—	—	—	145.50%	143.55%	2.85	52.36	0.67	224.33
Option Time Horizon	—	—	—	—	54.92%	54.18%	7.06	21.16	4.07	36.65

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $12.22 | Strike (K): $12.50 (first OTM call ≥ spot) | Observed Mid-Price: $2.5500 (Bid $0.1000 / Ask $5.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 145.50% (CRR binomial tree, American, n=20 steps) | BS IV: 144.85% (European Black-Scholes) | Yahoo IV (Annual): 143.55% → 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 0.91. Further, an Excess Kurtosis of 11.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.31%	15	0.49%	0.49%
-10.31% to -7.71%	29	0.94%	1.42%
-7.71% to -5.12%	100	3.23%	4.66%
-5.12% to -2.52%	407	13.16%	17.82%
-2.52% to 0.07%	1062	34.35%	52.17%
0.07% to 2.67%	959	31.02%	83.18%
2.67% to 5.26%	349	11.29%	94.47%
5.26% to 7.85%	121	3.91%	98.38%
7.85% to 10.45%	29	0.94%	99.32%
Greater than 10.45%	21	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.39%	3.53%	76.65%	68.27%
±2σ	-6.85%	6.99%	95.47%	95.45%
±3σ	-10.31%	10.45%	98.84%	99.73%

Descriptive Statistics

Mean	0.071%
Standard Error	0.062%
Median	-0.044%
Mode	0.000%
Standard Deviation	3.459%
Sample Variance	11.963%
Kurtosis	11.41
Skewness	0.91
Range	59.584%
Minimum	-21.836%
Maximum	37.748%
Count	3092

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.558%	1506	48.71%	1.246%
Negative	-2.326%	1561	50.48%	-1.174%
Zero	0.000%	25	0.81%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.96%
20	1 Month	7.33%
60	1 Quarter	6.28%
250	1 Year	6.79%
750	3 Years	5.11%
1,250	5 Years	4.86%
2,500	10 Years	4.88%
5,000	20 Years	5.12%
12,500	50 Years	5.12%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.94. Further, an Excess Kurtosis of 32.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.07%	0	0.00%	0.00%
-4.07% to -1.76%	0	0.00%	0.00%
-1.76% to 0.54%	0	0.00%	0.00%
0.54% to 2.85%	458	14.81%	14.81%
2.85% to 5.16%	1474	47.66%	62.46%
5.16% to 7.46%	726	23.47%	85.94%
7.46% to 9.77%	259	8.37%	94.31%
9.77% to 12.08%	91	2.94%	97.25%
12.08% to 14.38%	37	1.20%	98.45%
Greater than 14.38%	48	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.08%	8.23%	86.03%	68.27%
±2σ	-0.99%	11.31%	96.77%	95.45%
±3σ	-4.07%	14.38%	98.45%	99.73%

Descriptive Statistics

Mean	5.157%
Standard Error	0.055%
Median	4.470%
Mode	3.450%
Standard Deviation	3.075%
Sample Variance	9.453%
Kurtosis	32.82
Skewness	3.94
Range	46.933%
Minimum	0.716%
Maximum	47.649%
Count	3093

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.157%	3093	100.00%	5.157%
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 -0.07. Further, an Excess Kurtosis of 7.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.61%	15	0.48%	0.48%
-9.61% to -7.17%	30	0.97%	1.45%
-7.17% to -4.74%	117	3.78%	5.24%
-4.74% to -2.31%	391	12.64%	17.88%
-2.31% to 0.13%	997	32.23%	50.11%
0.13% to 2.56%	992	32.07%	82.19%
2.56% to 4.99%	394	12.74%	94.92%
4.99% to 7.42%	108	3.49%	98.42%
7.42% to 9.86%	28	0.91%	99.32%
Greater than 9.86%	21	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.12%	3.37%	75.91%	68.27%
±2σ	-6.36%	6.61%	95.73%	95.45%
±3σ	-9.61%	9.86%	98.84%	99.73%

Descriptive Statistics

Mean	0.126%
Standard Error	0.058%
Median	0.117%
Mode	0.000%
Standard Deviation	3.244%
Sample Variance	10.525%
Kurtosis	7.63
Skewness	-0.07
Range	53.834%
Minimum	-28.657%
Maximum	25.177%
Count	3093

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.390%	1583	51.18%	1.223%
Negative	-2.286%	1484	47.98%	-1.097%
Zero	0.000%	26	0.84%	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 6.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.60%	2	0.31%	0.31%
-22.60% to -16.86%	5	0.78%	1.09%
-16.86% to -11.13%	22	3.43%	4.52%
-11.13% to -5.39%	80	12.48%	17.00%
-5.39% to 0.34%	238	37.13%	54.13%
0.34% to 6.08%	188	29.33%	83.46%
6.08% to 11.82%	66	10.30%	93.76%
11.82% to 17.55%	26	4.06%	97.82%
17.55% to 23.29%	8	1.25%	99.06%
Greater than 23.29%	6	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.30%	7.99%	78.00%	68.27%
±2σ	-14.95%	15.64%	95.63%	95.45%
±3σ	-22.60%	23.29%	98.75%	99.73%

Descriptive Statistics

Mean	0.345%
Standard Error	0.302%
Median	-0.236%
Mode	-0.203%
Standard Deviation	7.649%
Sample Variance	58.507%
Kurtosis	6.07
Skewness	1.04
Range	83.032%
Minimum	-32.075%
Maximum	50.957%
Count	641

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.994%	309	48.21%	2.889%
Negative	-4.928%	331	51.64%	-2.545%
Zero	0.000%	1	0.16%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.92%
12	1 Quarter	13.05%
52	1 Year	15.28%
156	3 Years	11.62%
260	5 Years	10.79%
520	10 Years	10.95%
1,040	20 Years	11.41%
2,600	50 Years	11.41%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.66. Further, an Excess Kurtosis of 12.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.47%	0	0.00%	0.00%
-8.47% to -3.30%	0	0.00%	0.00%
-3.30% to 1.87%	0	0.00%	0.00%
1.87% to 7.04%	111	17.29%	17.29%
7.04% to 12.21%	287	44.70%	61.99%
12.21% to 17.38%	140	21.81%	83.80%
17.38% to 22.55%	64	9.97%	93.77%
22.55% to 27.72%	21	3.27%	97.04%
27.72% to 32.89%	10	1.56%	98.60%
Greater than 32.89%	9	1.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.32%	19.11%	81.78%	68.27%
±2σ	-1.58%	26.00%	96.11%	95.45%
±3σ	-8.47%	32.89%	98.60%	99.73%

Descriptive Statistics

Mean	12.211%
Standard Error	0.272%
Median	10.348%
Mode	5.041%
Standard Deviation	6.894%
Sample Variance	47.530%
Kurtosis	12.52
Skewness	2.66
Range	60.145%
Minimum	3.421%
Maximum	63.566%
Count	642

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.211%	642	100.00%	12.211%
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 0.51. Further, an Excess Kurtosis of 4.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.09%	4	0.62%	0.62%
-22.09% to -16.50%	7	1.09%	1.71%
-16.50% to -10.91%	26	4.05%	5.76%
-10.91% to -5.32%	81	12.62%	18.38%
-5.32% to 0.28%	202	31.46%	49.84%
0.28% to 5.87%	212	33.02%	82.87%
5.87% to 11.46%	76	11.84%	94.70%
11.46% to 17.05%	24	3.74%	98.44%
17.05% to 22.65%	6	0.93%	99.38%
Greater than 22.65%	4	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.18%	7.73%	76.79%	68.27%
±2σ	-14.64%	15.19%	95.17%	95.45%
±3σ	-22.09%	22.65%	98.75%	99.73%

Descriptive Statistics

Mean	0.277%
Standard Error	0.294%
Median	0.377%
Mode	-6.332%
Standard Deviation	7.457%
Sample Variance	55.605%
Kurtosis	4.96
Skewness	0.51
Range	82.574%
Minimum	-31.100%
Maximum	51.474%
Count	642

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.588%	328	51.09%	2.855%
Negative	-5.287%	313	48.75%	-2.578%
Zero	0.000%	1	0.16%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.69. Further, an Excess Kurtosis of 0.45 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.74%	0	0.00%	0.00%
-44.74% to -33.23%	0	0.00%	0.00%
-33.23% to -21.71%	5	3.40%	3.40%
-21.71% to -10.20%	30	20.41%	23.81%
-10.20% to 1.31%	45	30.61%	54.42%
1.31% to 12.82%	38	25.85%	80.27%
12.82% to 24.33%	16	10.88%	91.16%
24.33% to 35.84%	9	6.12%	97.28%
35.84% to 47.35%	3	2.04%	99.32%
Greater than 47.35%	1	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.04%	16.66%	72.79%	68.27%
±2σ	-29.39%	32.00%	93.88%	95.45%
±3σ	-44.74%	47.35%	99.32%	99.73%

Descriptive Statistics

Mean	1.308%
Standard Error	1.266%
Median	-1.127%
Mode	-30.729%
Standard Deviation	15.348%
Sample Variance	235.566%
Kurtosis	0.45
Skewness	0.69
Range	79.205%
Minimum	-30.729%
Maximum	48.476%
Count	147

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.832%	70	47.62%	6.587%
Negative	-10.077%	77	52.38%	-5.278%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.51%
12	1 Year	32.77%
36	3 Years	25.23%
60	5 Years	23.12%
120	10 Years	23.26%
240	20 Years	24.22%
600	50 Years	24.22%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.83. Further, an Excess Kurtosis of 4.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.97%	0	0.00%	0.00%
-13.97% to -3.47%	0	0.00%	0.00%
-3.47% to 7.02%	0	0.00%	0.00%
7.02% to 17.51%	28	18.92%	18.92%
17.51% to 28.01%	64	43.24%	62.16%
28.01% to 38.50%	35	23.65%	85.81%
38.50% to 48.99%	9	6.08%	91.89%
48.99% to 59.49%	5	3.38%	95.27%
59.49% to 69.98%	3	2.03%	97.30%
Greater than 69.98%	4	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.02%	42.00%	80.41%	68.27%
±2σ	0.03%	55.99%	94.59%	95.45%
±3σ	-13.97%	69.98%	97.30%	99.73%

Descriptive Statistics

Mean	28.007%
Standard Error	1.150%
Median	25.294%
Mode	8.725%
Standard Deviation	13.991%
Sample Variance	195.760%
Kurtosis	4.31
Skewness	1.83
Range	80.840%
Minimum	8.725%
Maximum	89.565%
Count	148

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.007%	148	100.00%	28.007%
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 0.02. Further, an Excess Kurtosis of -0.02 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 -32.33%	1	0.68%	0.68%
-32.33% to -21.32%	9	6.08%	6.76%
-21.32% to -10.31%	21	14.19%	20.95%
-10.31% to 0.70%	43	29.05%	50.00%
0.70% to 11.71%	39	26.35%	76.35%
11.71% to 22.72%	26	17.57%	93.92%
22.72% to 33.73%	6	4.05%	97.97%
33.73% to 44.74%	3	2.03%	100.00%
Greater than 44.74%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.98%	15.38%	69.59%	68.27%
±2σ	-28.66%	30.06%	94.59%	95.45%
±3σ	-43.34%	44.74%	100.00%	99.73%

Descriptive Statistics

Mean	0.702%
Standard Error	1.207%
Median	0.587%
Mode	-2.944%
Standard Deviation	14.680%
Sample Variance	215.501%
Kurtosis	-0.02
Skewness	0.02
Range	77.195%
Minimum	-34.902%
Maximum	42.293%
Count	148

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.235%	75	50.68%	6.200%
Negative	-11.146%	73	49.32%	-5.498%
Zero	0.000%	0	0.00%	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 0.84 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.64%	0	0.00%	0.00%
-71.64% to -52.82%	0	0.00%	0.00%
-52.82% to -34.00%	2	4.08%	4.08%
-34.00% to -15.18%	8	16.33%	20.41%
-15.18% to 3.64%	17	34.69%	55.10%
3.64% to 22.45%	13	26.53%	81.63%
22.45% to 41.27%	5	10.20%	91.84%
41.27% to 60.09%	3	6.12%	97.96%
60.09% to 78.91%	1	2.04%	100.00%
Greater than 78.91%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.46%	28.73%	75.51%	68.27%
±2σ	-46.55%	53.82%	91.84%	95.45%
±3σ	-71.64%	78.91%	100.00%	99.73%

Descriptive Statistics

Mean	3.636%
Standard Error	3.584%
Median	1.447%
Mode	-51.630%
Standard Deviation	25.091%
Sample Variance	629.538%
Kurtosis	0.84
Skewness	0.58
Range	128.433%
Minimum	-51.630%
Maximum	76.803%
Count	49

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.325%	25	51.02%	11.390%
Negative	-15.832%	24	48.98%	-7.755%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	56.88%
12	3 Years	45.66%
20	5 Years	41.23%
40	10 Years	41.26%
80	20 Years	43.55%
200	50 Years	43.55%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.73. Further, an Excess Kurtosis of 3.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.01%	0	0.00%	0.00%
-27.01% to -6.63%	0	0.00%	0.00%
-6.63% to 13.75%	0	0.00%	0.00%
13.75% to 34.13%	10	20.00%	20.00%
34.13% to 54.51%	21	42.00%	62.00%
54.51% to 74.88%	11	22.00%	84.00%
74.88% to 95.26%	5	10.00%	94.00%
95.26% to 115.64%	0	0.00%	94.00%
115.64% to 136.02%	2	4.00%	98.00%
Greater than 136.02%	1	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.33%	81.68%	80.00%	68.27%
±2σ	0.16%	108.85%	94.00%	95.45%
±3σ	-27.01%	136.02%	98.00%	99.73%

Descriptive Statistics

Mean	54.505%
Standard Error	3.843%
Median	47.331%
Mode	21.068%
Standard Deviation	27.171%
Sample Variance	738.264%
Kurtosis	3.57
Skewness	1.73
Range	134.379%
Minimum	21.068%
Maximum	155.447%
Count	50

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.505%	50	100.00%	54.505%
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 1.18. Further, an Excess Kurtosis of 2.80 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -76.48%	0	0.00%	0.00%
-76.48% to -56.97%	0	0.00%	0.00%
-56.97% to -37.45%	1	2.00%	2.00%
-37.45% to -17.93%	9	18.00%	20.00%
-17.93% to 1.59%	18	36.00%	56.00%
1.59% to 21.10%	14	28.00%	84.00%
21.10% to 40.62%	6	12.00%	96.00%
40.62% to 60.14%	0	0.00%	96.00%
60.14% to 79.66%	1	2.00%	98.00%
Greater than 79.66%	1	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.44%	27.61%	74.00%	68.27%
±2σ	-50.46%	53.63%	96.00%	95.45%
±3σ	-76.48%	79.66%	98.00%	99.73%

Descriptive Statistics

Mean	1.587%
Standard Error	3.680%
Median	-2.889%
Mode	-44.256%
Standard Deviation	26.023%
Sample Variance	677.222%
Kurtosis	2.80
Skewness	1.18
Range	141.948%
Minimum	-44.256%
Maximum	97.692%
Count	50

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.691%	24	48.00%	10.412%
Negative	-16.971%	26	52.00%	-8.825%
Zero	0.000%	0	0.00%	0.000%

XNCR Deep Analytical Report