CTXR - 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	6.69%	9.65%	6.56%	8.56%	9.82%	9.74%	0.64	0.78	0.58	0.86
Weekly	14.54%	24.51%	14.68%	19.92%	21.61%	21.45%	0.57	0.88	0.46	1.09
Monthly	29.54%	63.43%	31.55%	44.31%	44.99%	44.65%	0.45	1.11	0.29	1.74
Quarterly	41.54%	101.90%	66.92%	72.03%	77.93%	77.34%	0.33	1.55	0.15	3.37
Annual	—	—	—	—	155.86%	154.69%	0.15	3.37	0.03	16.01
Option Time Horizon	—	—	—	—	73.87%	73.32%	0.34	1.48	0.16	3.11

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $0.71 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1250 (Bid $0.1000 / Ask $0.1500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 155.86% (CRR binomial tree, American, n=20 steps) | BS IV: 154.25% (European Black-Scholes) | Yahoo IV (Annual): 154.69% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.16. Further, an Excess Kurtosis of 12.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.11%	17	0.70%	0.70%
-20.11% to -15.09%	17	0.70%	1.39%
-15.09% to -10.08%	70	2.86%	4.25%
-10.08% to -5.06%	252	10.31%	14.56%
-5.06% to -0.05%	909	37.18%	51.74%
-0.05% to 4.97%	812	33.21%	84.95%
4.97% to 9.99%	235	9.61%	94.56%
9.99% to 15.00%	85	3.48%	98.04%
15.00% to 20.02%	25	1.02%	99.06%
Greater than 20.02%	23	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.73%	6.64%	80.45%	68.27%
±2σ	-13.42%	13.33%	95.34%	95.45%
±3σ	-20.11%	20.02%	98.36%	99.73%

Descriptive Statistics

Mean	-0.046%
Standard Error	0.135%
Median	-0.429%
Mode	0.000%
Standard Deviation	6.688%
Sample Variance	44.727%
Kurtosis	12.54
Skewness	1.16
Range	109.378%
Minimum	-39.024%
Maximum	70.354%
Count	2445

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.123%	1040	42.54%	2.179%
Negative	-4.295%	1267	51.82%	-2.226%
Zero	0.000%	138	5.64%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.00%
20	1 Month	8.82%
60	1 Quarter	9.35%
250	1 Year	11.35%
750	3 Years	9.62%
1,250	5 Years	8.56%
2,500	10 Years	9.81%
5,000	20 Years	9.81%
12,500	50 Years	9.81%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.20. Further, an Excess Kurtosis of 73.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.90%	0	0.00%	0.00%
-18.90% to -11.66%	0	0.00%	0.00%
-11.66% to -4.43%	0	0.00%	0.00%
-4.43% to 2.81%	124	5.07%	5.07%
2.81% to 10.04%	1512	61.82%	66.88%
10.04% to 17.28%	524	21.42%	88.31%
17.28% to 24.51%	163	6.66%	94.97%
24.51% to 31.75%	56	2.29%	97.26%
31.75% to 38.98%	25	1.02%	98.28%
Greater than 38.98%	42	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.39%	19.69%	91.21%	68.27%
±2σ	-9.25%	29.33%	96.69%	95.45%
±3σ	-18.90%	38.98%	98.28%	99.73%

Descriptive Statistics

Mean	10.041%
Standard Error	0.195%
Median	7.551%
Mode	5.000%
Standard Deviation	9.646%
Sample Variance	93.040%
Kurtosis	73.54
Skewness	6.20
Range	170.470%
Minimum	0.118%
Maximum	170.588%
Count	2446

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.041%	2446	100.00%	10.041%
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 0.99. Further, an Excess Kurtosis of 11.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.15%	17	0.70%	0.70%
-19.15% to -14.22%	21	0.86%	1.55%
-14.22% to -9.30%	77	3.15%	4.70%
-9.30% to -4.38%	268	10.96%	15.66%
-4.38% to 0.54%	870	35.57%	51.23%
0.54% to 5.46%	848	34.67%	85.90%
5.46% to 10.38%	217	8.87%	94.77%
10.38% to 15.30%	82	3.35%	98.12%
15.30% to 20.23%	26	1.06%	99.18%
Greater than 20.23%	20	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.02%	7.10%	80.17%	68.27%
±2σ	-12.58%	13.66%	95.22%	95.45%
±3σ	-19.15%	20.23%	98.49%	99.73%

Descriptive Statistics

Mean	0.540%
Standard Error	0.133%
Median	0.326%
Mode	0.000%
Standard Deviation	6.562%
Sample Variance	43.066%
Kurtosis	11.63
Skewness	0.99
Range	93.500%
Minimum	-34.000%
Maximum	59.500%
Count	2446

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.733%	1256	51.35%	2.430%
Negative	-4.420%	1046	42.76%	-1.890%
Zero	0.000%	144	5.89%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.21. Further, an Excess Kurtosis of 5.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.84%	1	0.19%	0.19%
-43.84% to -32.93%	6	1.14%	1.33%
-32.93% to -22.02%	12	2.27%	3.60%
-22.02% to -11.12%	51	9.66%	13.26%
-11.12% to -0.21%	230	43.56%	56.82%
-0.21% to 10.69%	147	27.84%	84.66%
10.69% to 21.59%	48	9.09%	93.75%
21.59% to 32.50%	18	3.41%	97.16%
32.50% to 43.41%	8	1.52%	98.67%
Greater than 43.41%	7	1.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.75%	14.32%	80.11%	68.27%
±2σ	-29.29%	28.86%	94.32%	95.45%
±3σ	-43.84%	43.40%	98.48%	99.73%

Descriptive Statistics

Mean	-0.215%
Standard Error	0.633%
Median	-1.945%
Mode	0.000%
Standard Deviation	14.540%
Sample Variance	211.405%
Kurtosis	5.55
Skewness	1.21
Range	128.033%
Minimum	-50.111%
Maximum	77.922%
Count	528

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.586%	218	41.29%	4.784%
Negative	-8.739%	302	57.20%	-4.998%
Zero	0.000%	8	1.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	17.52%
12	1 Quarter	19.72%
52	1 Year	29.61%
156	3 Years	22.94%
260	5 Years	19.92%
520	10 Years	22.42%
1,040	20 Years	22.43%
2,600	50 Years	22.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.07. Further, an Excess Kurtosis of 23.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.15%	0	0.00%	0.00%
-48.15% to -29.77%	0	0.00%	0.00%
-29.77% to -11.39%	0	0.00%	0.00%
-11.39% to 6.99%	35	6.62%	6.62%
6.99% to 25.37%	336	63.52%	70.13%
25.37% to 43.76%	94	17.77%	87.90%
43.76% to 62.14%	34	6.43%	94.33%
62.14% to 80.52%	13	2.46%	96.79%
80.52% to 98.90%	8	1.51%	98.30%
Greater than 98.90%	9	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.87%	49.88%	90.74%	68.27%
±2σ	-23.64%	74.39%	96.22%	95.45%
±3σ	-48.15%	98.90%	98.30%	99.73%

Descriptive Statistics

Mean	25.374%
Standard Error	1.066%
Median	18.796%
Mode	20.000%
Standard Deviation	24.508%
Sample Variance	600.655%
Kurtosis	23.93
Skewness	4.07
Range	223.628%
Minimum	0.962%
Maximum	224.590%
Count	529

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.374%	529	100.00%	25.374%
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 1.40. Further, an Excess Kurtosis of 8.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.07%	2	0.38%	0.38%
-42.07% to -31.06%	6	1.13%	1.51%
-31.06% to -20.05%	18	3.40%	4.91%
-20.05% to -9.04%	63	11.91%	16.82%
-9.04% to 1.97%	182	34.40%	51.23%
1.97% to 12.97%	191	36.11%	87.33%
12.97% to 23.98%	36	6.81%	94.14%
23.98% to 34.99%	20	3.78%	97.92%
34.99% to 46.00%	5	0.95%	98.87%
Greater than 46.00%	6	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.71%	16.64%	79.02%	68.27%
±2σ	-27.39%	31.32%	95.27%	95.45%
±3σ	-42.07%	46.00%	98.49%	99.73%

Descriptive Statistics

Mean	1.965%
Standard Error	0.638%
Median	1.770%
Mode	0.000%
Standard Deviation	14.678%
Sample Variance	215.454%
Kurtosis	8.69
Skewness	1.40
Range	155.076%
Minimum	-45.255%
Maximum	109.821%
Count	529

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.347%	301	56.90%	5.887%
Negative	-9.788%	212	40.08%	-3.923%
Zero	0.000%	16	3.02%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.51. Further, an Excess Kurtosis of 4.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -89.60%	0	0.00%	0.00%
-89.60% to -67.45%	0	0.00%	0.00%
-67.45% to -45.29%	5	3.97%	3.97%
-45.29% to -23.14%	19	15.08%	19.05%
-23.14% to -0.98%	52	41.27%	60.32%
-0.98% to 21.17%	30	23.81%	84.13%
21.17% to 43.33%	12	9.52%	93.65%
43.33% to 65.48%	4	3.17%	96.83%
65.48% to 87.64%	2	1.59%	98.41%
Greater than 87.64%	2	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.52%	28.56%	78.57%	68.27%
±2σ	-60.06%	58.10%	96.03%	95.45%
±3σ	-89.60%	87.64%	98.41%	99.73%

Descriptive Statistics

Mean	-0.984%
Standard Error	2.632%
Median	-5.614%
Mode	-11.111%
Standard Deviation	29.540%
Sample Variance	872.619%
Kurtosis	4.83
Skewness	1.51
Range	198.221%
Minimum	-64.397%
Maximum	133.824%
Count	126

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.007%	49	38.89%	10.114%
Negative	-18.160%	77	61.11%	-11.098%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	42.33%
12	1 Year	64.12%
36	3 Years	49.51%
60	5 Years	44.31%
120	10 Years	50.32%
240	20 Years	50.22%
600	50 Years	50.22%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.83. Further, an Excess Kurtosis of 20.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -123.36%	0	0.00%	0.00%
-123.36% to -75.79%	0	0.00%	0.00%
-75.79% to -28.22%	0	0.00%	0.00%
-28.22% to 19.35%	7	5.51%	5.51%
19.35% to 66.92%	76	59.84%	65.35%
66.92% to 114.48%	29	22.83%	88.19%
114.48% to 162.05%	9	7.09%	95.28%
162.05% to 209.62%	2	1.57%	96.85%
209.62% to 257.19%	2	1.57%	98.43%
Greater than 257.19%	2	1.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.49%	130.34%	92.13%	68.27%
±2σ	-59.94%	193.77%	96.85%	95.45%
±3σ	-123.36%	257.19%	98.43%	99.73%

Descriptive Statistics

Mean	66.915%
Standard Error	5.628%
Median	48.571%
Mode	27.083%
Standard Deviation	63.426%
Sample Variance	4022.894%
Kurtosis	20.01
Skewness	3.83
Range	475.354%
Minimum	6.999%
Maximum	482.353%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	66.915%	127	100.00%	66.915%
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 1.61. Further, an Excess Kurtosis of 6.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.45%	0	0.00%	0.00%
-86.45% to -62.79%	0	0.00%	0.00%
-62.79% to -39.13%	4	3.15%	3.15%
-39.13% to -15.47%	23	18.11%	21.26%
-15.47% to 8.19%	46	36.22%	57.48%
8.19% to 31.85%	34	26.77%	84.25%
31.85% to 55.51%	10	7.87%	92.13%
55.51% to 79.17%	6	4.72%	96.85%
79.17% to 102.84%	3	2.36%	99.21%
Greater than 102.84%	1	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.36%	39.74%	78.74%	68.27%
±2σ	-54.90%	71.29%	96.06%	95.45%
±3σ	-86.45%	102.84%	99.21%	99.73%

Descriptive Statistics

Mean	8.192%
Standard Error	2.799%
Median	3.868%
Mode	0.000%
Standard Deviation	31.548%
Sample Variance	995.255%
Kurtosis	6.33
Skewness	1.61
Range	234.837%
Minimum	-54.717%
Maximum	180.120%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.258%	72	56.69%	15.453%
Negative	-17.400%	53	41.73%	-7.261%
Zero	0.000%	2	1.57%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.75. Further, an Excess Kurtosis of 0.69 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -129.22%	0	0.00%	0.00%
-129.22% to -98.06%	0	0.00%	0.00%
-98.06% to -66.91%	2	4.55%	4.55%
-66.91% to -35.75%	7	15.91%	20.45%
-35.75% to -4.59%	15	34.09%	54.55%
-4.59% to 26.57%	12	27.27%	81.82%
26.57% to 57.73%	5	11.36%	93.18%
57.73% to 88.88%	2	4.55%	97.73%
88.88% to 120.04%	1	2.27%	100.00%
Greater than 120.04%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-46.13%	36.95%	72.73%	68.27%
±2σ	-87.68%	78.50%	93.18%	95.45%
±3σ	-129.22%	120.04%	100.00%	99.73%

Descriptive Statistics

Mean	-4.591%
Standard Error	6.263%
Median	-11.348%
Mode	-71.561%
Standard Deviation	41.544%
Sample Variance	1725.944%
Kurtosis	0.69
Skewness	0.75
Range	190.080%
Minimum	-71.561%
Maximum	118.519%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.424%	17	38.64%	14.459%
Negative	-31.045%	27	61.36%	-19.050%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	103.40%
12	3 Years	80.93%
20	5 Years	72.03%
40	10 Years	77.86%
80	20 Years	76.02%
200	50 Years	76.02%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.74. Further, an Excess Kurtosis of 3.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -175.46%	0	0.00%	0.00%
-175.46% to -99.03%	0	0.00%	0.00%
-99.03% to -22.61%	0	0.00%	0.00%
-22.61% to 53.82%	9	20.00%	20.00%
53.82% to 130.25%	20	44.44%	64.44%
130.25% to 206.67%	8	17.78%	82.22%
206.67% to 283.10%	5	11.11%	93.33%
283.10% to 359.53%	1	2.22%	95.56%
359.53% to 435.95%	1	2.22%	97.78%
Greater than 435.95%	1	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	28.35%	232.15%	84.44%	68.27%
±2σ	-73.56%	334.05%	93.33%	95.45%
±3σ	-175.46%	435.95%	97.78%	99.73%

Descriptive Statistics

Mean	130.248%
Standard Error	15.191%
Median	92.208%
Mode	25.000%
Standard Deviation	101.902%
Sample Variance	10383.949%
Kurtosis	3.27
Skewness	1.74
Range	457.353%
Minimum	25.000%
Maximum	482.353%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	130.248%	45	100.00%	130.248%
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 1.79. Further, an Excess Kurtosis of 3.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -173.85%	0	0.00%	0.00%
-173.85% to -123.66%	0	0.00%	0.00%
-123.66% to -73.47%	0	0.00%	0.00%
-73.47% to -23.27%	8	17.78%	17.78%
-23.27% to 26.92%	20	44.44%	62.22%
26.92% to 77.11%	10	22.22%	84.44%
77.11% to 127.31%	3	6.67%	91.11%
127.31% to 177.50%	2	4.44%	95.56%
177.50% to 227.69%	0	0.00%	95.56%
Greater than 227.69%	2	4.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-40.00%	93.84%	77.78%	68.27%
±2σ	-106.93%	160.77%	95.56%	95.45%
±3σ	-173.85%	227.69%	95.56%	99.73%

Descriptive Statistics

Mean	26.920%
Standard Error	9.977%
Median	11.982%
Mode	-52.542%
Standard Deviation	66.925%
Sample Variance	4479.011%
Kurtosis	3.58
Skewness	1.79
Range	298.947%
Minimum	-52.542%
Maximum	246.405%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	63.274%	26	57.78%	36.558%
Negative	-22.828%	19	42.22%	-9.638%
Zero	0.000%	0	0.00%	0.000%

CTXR Deep Analytical Report