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%	9.62%	6.56%	8.60%	10.79%	10.63%	0.69	0.85	0.62	0.95
Weekly	14.53%	24.44%	14.67%	20.04%	23.76%	23.40%	0.60	0.97	0.48	1.23
Monthly	29.42%	63.16%	31.46%	44.69%	49.46%	48.71%	0.47	1.26	0.28	2.06
Quarterly	41.56%	101.48%	67.00%	73.05%	85.66%	84.38%	0.33	1.80	0.14	4.25
Annual	—	—	—	—	171.32%	168.75%	0.14	4.25	0.02	23.57
Option Time Horizon	—	—	—	—	64.66%	63.69%	0.40	1.46	0.21	2.79

Calculation Notes: Computed at 2026-03-23T16:38 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $0.77 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1250 (Bid $0.1000 / Ask $0.1500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 171.32% (CRR binomial tree, American, n=20 steps) | BS IV: 170.29% (European Black-Scholes) | Yahoo IV (Annual): 168.75% → 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 1.15. Further, an Excess Kurtosis of 12.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.12%	17	0.69%	0.69%
-20.12% to -15.10%	16	0.65%	1.34%
-15.10% to -10.08%	72	2.92%	4.26%
-10.08% to -5.06%	255	10.34%	14.60%
-5.06% to -0.04%	918	37.23%	51.82%
-0.04% to 4.98%	815	33.05%	84.87%
4.98% to 10.00%	235	9.53%	94.40%
10.00% to 15.02%	89	3.61%	98.01%
15.02% to 20.04%	26	1.05%	99.07%
Greater than 20.04%	23	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.74%	6.65%	80.29%	68.27%
±2σ	-13.43%	13.35%	95.38%	95.45%
±3σ	-20.12%	20.04%	98.38%	99.73%

Descriptive Statistics

Mean	-0.041%
Standard Error	0.135%
Median	-0.438%
Mode	0.000%
Standard Deviation	6.694%
Sample Variance	44.816%
Kurtosis	12.37
Skewness	1.15
Range	109.378%
Minimum	-39.024%
Maximum	70.354%
Count	2466

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.142%	1049	42.54%	2.187%
Negative	-4.296%	1279	51.87%	-2.228%
Zero	0.000%	138	5.60%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	9.99%
20	1 Month	12.15%
60	1 Quarter	10.43%
250	1 Year	11.66%
750	3 Years	9.77%
1,250	5 Years	8.60%
2,500	10 Years	9.83%
5,000	20 Years	9.83%
12,500	50 Years	9.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.19. Further, an Excess Kurtosis of 73.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.80%	0	0.00%	0.00%
-18.80% to -11.59%	0	0.00%	0.00%
-11.59% to -4.37%	0	0.00%	0.00%
-4.37% to 2.85%	130	5.27%	5.27%
2.85% to 10.06%	1517	61.49%	66.76%
10.06% to 17.27%	530	21.48%	88.24%
17.27% to 24.49%	165	6.69%	94.93%
24.49% to 31.70%	58	2.35%	97.28%
31.70% to 38.92%	25	1.01%	98.30%
Greater than 38.92%	42	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.44%	19.68%	91.12%	68.27%
±2σ	-9.18%	29.30%	96.72%	95.45%
±3σ	-18.80%	38.92%	98.30%	99.73%

Descriptive Statistics

Mean	10.060%
Standard Error	0.194%
Median	7.568%
Mode	5.000%
Standard Deviation	9.620%
Sample Variance	92.553%
Kurtosis	73.64
Skewness	6.19
Range	170.470%
Minimum	0.118%
Maximum	170.588%
Count	2467

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.060%	2467	100.00%	10.060%
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 0.98. Further, an Excess Kurtosis of 11.51 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	0.69%	0.69%
-19.15% to -14.23%	21	0.85%	1.54%
-14.23% to -9.31%	79	3.20%	4.74%
-9.31% to -4.38%	271	10.99%	15.73%
-4.38% to 0.54%	878	35.59%	51.32%
0.54% to 5.46%	851	34.50%	85.81%
5.46% to 10.38%	220	8.92%	94.73%
10.38% to 15.31%	84	3.40%	98.14%
15.31% to 20.23%	26	1.05%	99.19%
Greater than 20.23%	20	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.03%	7.10%	80.06%	68.27%
±2σ	-12.59%	13.67%	95.22%	95.45%
±3σ	-19.15%	20.23%	98.50%	99.73%

Descriptive Statistics

Mean	0.538%
Standard Error	0.132%
Median	0.317%
Mode	0.000%
Standard Deviation	6.564%
Sample Variance	43.088%
Kurtosis	11.51
Skewness	0.98
Range	93.500%
Minimum	-34.000%
Maximum	59.500%
Count	2467

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.746%	1265	51.28%	2.434%
Negative	-4.420%	1058	42.89%	-1.896%
Zero	0.000%	144	5.84%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 5.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.77%	1	0.19%	0.19%
-43.77% to -32.88%	6	1.13%	1.32%
-32.88% to -21.98%	12	2.26%	3.57%
-21.98% to -11.09%	53	9.96%	13.53%
-11.09% to -0.19%	229	43.05%	56.58%
-0.19% to 10.70%	149	28.01%	84.59%
10.70% to 21.60%	49	9.21%	93.80%
21.60% to 32.49%	18	3.38%	97.18%
32.49% to 43.39%	8	1.50%	98.68%
Greater than 43.39%	7	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.72%	14.33%	80.08%	68.27%
±2σ	-29.25%	28.86%	94.36%	95.45%
±3σ	-43.77%	43.39%	98.50%	99.73%

Descriptive Statistics

Mean	-0.192%
Standard Error	0.630%
Median	-1.901%
Mode	0.000%
Standard Deviation	14.527%
Sample Variance	211.025%
Kurtosis	5.52
Skewness	1.20
Range	128.033%
Minimum	-50.111%
Maximum	77.922%
Count	532

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.563%	221	41.54%	4.803%
Negative	-8.771%	303	56.95%	-4.996%
Zero	0.000%	8	1.50%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	28.97%
12	1 Quarter	21.09%
52	1 Year	30.68%
156	3 Years	23.35%
260	5 Years	20.04%
520	10 Years	22.31%
1,040	20 Years	22.49%
2,600	50 Years	22.49%

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 23.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -47.89%	0	0.00%	0.00%
-47.89% to -29.56%	0	0.00%	0.00%
-29.56% to -11.23%	0	0.00%	0.00%
-11.23% to 7.10%	35	6.57%	6.57%
7.10% to 25.43%	337	63.23%	69.79%
25.43% to 43.76%	96	18.01%	87.80%
43.76% to 62.09%	35	6.57%	94.37%
62.09% to 80.42%	13	2.44%	96.81%
80.42% to 98.75%	8	1.50%	98.31%
Greater than 98.75%	9	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.99%	49.87%	90.62%	68.27%
±2σ	-23.45%	74.31%	96.25%	95.45%
±3σ	-47.89%	98.75%	98.31%	99.73%

Descriptive Statistics

Mean	25.428%
Standard Error	1.059%
Median	18.889%
Mode	20.000%
Standard Deviation	24.440%
Sample Variance	597.316%
Kurtosis	23.99
Skewness	4.07
Range	223.628%
Minimum	0.962%
Maximum	224.590%
Count	533

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.428%	533	100.00%	25.428%
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 1.39. Further, an Excess Kurtosis of 8.63 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%	1.50%
-31.06% to -20.06%	18	3.38%	4.88%
-20.06% to -9.05%	64	12.01%	16.89%
-9.05% to 1.95%	183	34.33%	51.22%
1.95% to 12.96%	191	35.83%	87.05%
12.96% to 23.96%	38	7.13%	94.18%
23.96% to 34.97%	20	3.75%	97.94%
34.97% to 45.98%	5	0.94%	98.87%
Greater than 45.98%	6	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.72%	16.63%	78.80%	68.27%
±2σ	-27.39%	31.30%	95.31%	95.45%
±3σ	-42.07%	45.98%	98.50%	99.73%

Descriptive Statistics

Mean	1.953%
Standard Error	0.636%
Median	1.770%
Mode	0.000%
Standard Deviation	14.674%
Sample Variance	215.338%
Kurtosis	8.63
Skewness	1.39
Range	155.076%
Minimum	-45.255%
Maximum	109.821%
Count	533

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.364%	303	56.85%	5.892%
Negative	-9.810%	214	40.15%	-3.939%
Zero	0.000%	16	3.00%	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 4.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -89.19%	0	0.00%	0.00%
-89.19% to -67.12%	0	0.00%	0.00%
-67.12% to -45.05%	5	3.94%	3.94%
-45.05% to -22.98%	19	14.96%	18.90%
-22.98% to -0.92%	52	40.94%	59.84%
-0.92% to 21.15%	31	24.41%	84.25%
21.15% to 43.22%	12	9.45%	93.70%
43.22% to 65.29%	4	3.15%	96.85%
65.29% to 87.36%	2	1.57%	98.43%
Greater than 87.36%	2	1.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.34%	28.51%	78.74%	68.27%
±2σ	-59.76%	57.93%	96.06%	95.45%
±3σ	-89.19%	87.36%	98.43%	99.73%

Descriptive Statistics

Mean	-0.916%
Standard Error	2.611%
Median	-5.556%
Mode	-11.111%
Standard Deviation	29.424%
Sample Variance	865.777%
Kurtosis	4.87
Skewness	1.51
Range	198.221%
Minimum	-64.397%
Maximum	133.824%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.557%	50	39.37%	10.062%
Negative	-18.344%	76	59.84%	-10.978%
Zero	0.000%	1	0.79%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	43.45%
12	1 Year	63.92%
36	3 Years	50.56%
60	5 Years	44.69%
120	10 Years	50.61%
240	20 Years	50.30%
600	50 Years	50.30%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.85. Further, an Excess Kurtosis of 20.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -122.60%	0	0.00%	0.00%
-122.60% to -75.22%	0	0.00%	0.00%
-75.22% to -27.85%	0	0.00%	0.00%
-27.85% to 19.52%	7	5.47%	5.47%
19.52% to 66.90%	77	60.16%	65.62%
66.90% to 114.27%	29	22.66%	88.28%
114.27% to 161.65%	9	7.03%	95.31%
161.65% to 209.02%	2	1.56%	96.88%
209.02% to 256.39%	2	1.56%	98.44%
Greater than 256.39%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.73%	130.06%	92.19%	68.27%
±2σ	-59.43%	193.23%	96.88%	95.45%
±3σ	-122.60%	256.39%	98.44%	99.73%

Descriptive Statistics

Mean	66.898%
Standard Error	5.583%
Median	49.005%
Mode	27.083%
Standard Deviation	63.165%
Sample Variance	3989.866%
Kurtosis	20.21
Skewness	3.85
Range	475.354%
Minimum	6.999%
Maximum	482.353%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	66.898%	128	100.00%	66.898%
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 1.63. Further, an Excess Kurtosis of 6.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.36%	0	0.00%	0.00%
-86.36% to -62.77%	0	0.00%	0.00%
-62.77% to -39.17%	4	3.12%	3.12%
-39.17% to -15.57%	23	17.97%	21.09%
-15.57% to 8.03%	47	36.72%	57.81%
8.03% to 31.63%	34	26.56%	84.38%
31.63% to 55.22%	10	7.81%	92.19%
55.22% to 78.82%	5	3.91%	96.09%
78.82% to 102.42%	4	3.12%	99.22%
Greater than 102.42%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.44%	39.49%	78.91%	68.27%
±2σ	-54.90%	70.96%	96.09%	95.45%
±3σ	-86.36%	102.42%	99.22%	99.73%

Descriptive Statistics

Mean	8.028%
Standard Error	2.781%
Median	3.462%
Mode	0.000%
Standard Deviation	31.464%
Sample Variance	989.958%
Kurtosis	6.39
Skewness	1.63
Range	234.837%
Minimum	-54.717%
Maximum	180.120%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.197%	72	56.25%	15.298%
Negative	-17.233%	54	42.19%	-7.270%
Zero	0.000%	2	1.56%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.73. Further, an Excess Kurtosis of 0.67 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -129.10%	0	0.00%	0.00%
-129.10% to -97.93%	0	0.00%	0.00%
-97.93% to -66.76%	2	4.55%	4.55%
-66.76% to -35.59%	7	15.91%	20.45%
-35.59% to -4.42%	15	34.09%	54.55%
-4.42% to 26.76%	12	27.27%	81.82%
26.76% to 57.93%	5	11.36%	93.18%
57.93% to 89.10%	2	4.55%	97.73%
89.10% to 120.27%	1	2.27%	100.00%
Greater than 120.27%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-45.98%	37.15%	72.73%	68.27%
±2σ	-87.54%	78.71%	93.18%	95.45%
±3σ	-129.10%	120.27%	100.00%	99.73%

Descriptive Statistics

Mean	-4.415%
Standard Error	6.266%
Median	-11.348%
Mode	-71.561%
Standard Deviation	41.563%
Sample Variance	1727.447%
Kurtosis	0.67
Skewness	0.73
Range	190.080%
Minimum	-71.561%
Maximum	118.519%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.542%	18	40.91%	14.540%
Negative	-32.078%	26	59.09%	-18.955%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	108.50%
12	3 Years	82.62%
20	5 Years	73.05%
40	10 Years	78.37%
80	20 Years	76.48%
200	50 Years	76.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.75. Further, an Excess Kurtosis of 3.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -173.64%	0	0.00%	0.00%
-173.64% to -97.53%	0	0.00%	0.00%
-97.53% to -21.42%	0	0.00%	0.00%
-21.42% to 54.69%	10	22.22%	22.22%
54.69% to 130.79%	19	42.22%	64.44%
130.79% to 206.90%	8	17.78%	82.22%
206.90% to 283.01%	5	11.11%	93.33%
283.01% to 359.12%	1	2.22%	95.56%
359.12% to 435.22%	1	2.22%	97.78%
Greater than 435.22%	1	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	29.32%	232.27%	84.44%	68.27%
±2σ	-72.16%	333.75%	93.33%	95.45%
±3σ	-173.64%	435.22%	97.78%	99.73%

Descriptive Statistics

Mean	130.793%
Standard Error	15.127%
Median	92.208%
Mode	25.000%
Standard Deviation	101.477%
Sample Variance	10297.566%
Kurtosis	3.33
Skewness	1.75
Range	457.353%
Minimum	25.000%
Maximum	482.353%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	130.793%	45	100.00%	130.793%
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 1.80. 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 -174.24%	0	0.00%	0.00%
-174.24% to -123.99%	0	0.00%	0.00%
-123.99% to -73.75%	0	0.00%	0.00%
-73.75% to -23.50%	8	17.78%	17.78%
-23.50% to 26.75%	20	44.44%	62.22%
26.75% to 76.99%	10	22.22%	84.44%
76.99% to 127.24%	3	6.67%	91.11%
127.24% to 177.49%	2	4.44%	95.56%
177.49% to 227.73%	0	0.00%	95.56%
Greater than 227.73%	2	4.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-40.25%	93.74%	77.78%	68.27%
±2σ	-107.24%	160.74%	95.56%	95.45%
±3σ	-174.24%	227.73%	95.56%	99.73%

Descriptive Statistics

Mean	26.746%
Standard Error	9.987%
Median	11.982%
Mode	-52.542%
Standard Deviation	66.995%
Sample Variance	4488.310%
Kurtosis	3.57
Skewness	1.80
Range	298.947%
Minimum	-52.542%
Maximum	246.405%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	65.624%	25	55.56%	36.458%
Negative	-21.851%	20	44.44%	-9.711%
Zero	0.000%	0	0.00%	0.000%

CTXR Deep Analytical Report