CSIQ - 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	4.68%	3.91%	4.10%	5.97%	5.44%	5.52%	18.99	21.17	17.98	22.35
Weekly	11.00%	10.89%	10.77%	14.37%	11.97%	12.16%	17.79	22.60	15.78	25.48
Monthly	22.16%	28.83%	22.05%	28.76%	24.92%	25.32%	15.63	25.73	12.18	33.01
Quarterly	38.41%	58.55%	40.80%	47.44%	43.17%	43.85%	13.02	30.87	8.46	47.54
Annual	—	—	—	—	86.34%	87.70%	8.46	47.54	3.57	112.74
Option Time Horizon	—	—	—	—	33.21%	33.73%	14.38	27.95	10.32	38.96

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $20.05 | Strike (K): $21.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3250 (Bid $2.2000 / Ask $2.4500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 86.34% (CRR binomial tree, American, n=20 steps) | BS IV: 87.09% (European Black-Scholes) | Yahoo IV (Annual): 87.70% → 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 0.47. Further, an Excess Kurtosis of 4.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.93%	35	0.72%	0.72%
-13.93% to -10.42%	49	1.01%	1.73%
-10.42% to -6.91%	155	3.20%	4.93%
-6.91% to -3.40%	551	11.37%	16.30%
-3.40% to 0.11%	1707	35.21%	51.51%
0.11% to 3.62%	1547	31.91%	83.42%
3.62% to 7.13%	522	10.77%	94.18%
7.13% to 10.65%	162	3.34%	97.52%
10.65% to 14.16%	63	1.30%	98.82%
Greater than 14.16%	57	1.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.57%	4.79%	77.95%	68.27%
±2σ	-9.25%	9.48%	94.43%	95.45%
±3σ	-13.93%	14.16%	98.10%	99.73%

Descriptive Statistics

Mean	0.114%
Standard Error	0.067%
Median	0.000%
Mode	0.000%
Standard Deviation	4.681%
Sample Variance	21.910%
Kurtosis	4.46
Skewness	0.47
Range	56.276%
Minimum	-22.792%
Maximum	33.484%
Count	4848

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.421%	2395	49.40%	1.690%
Negative	-3.177%	2405	49.61%	-1.576%
Zero	0.000%	48	0.99%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.14%
20	1 Month	7.14%
60	1 Quarter	8.10%
250	1 Year	8.10%
750	3 Years	6.21%
1,250	5 Years	5.97%
2,500	10 Years	5.30%
5,000	20 Years	6.27%
12,500	50 Years	6.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.71. Further, an Excess Kurtosis of 12.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.61%	0	0.00%	0.00%
-5.61% to -2.68%	0	0.00%	0.00%
-2.68% to 0.26%	0	0.00%	0.00%
0.26% to 3.19%	825	17.01%	17.01%
3.19% to 6.12%	2241	46.22%	63.23%
6.12% to 9.06%	1028	21.20%	84.43%
9.06% to 11.99%	431	8.89%	93.32%
11.99% to 14.92%	167	3.44%	96.76%
14.92% to 17.86%	68	1.40%	98.16%
Greater than 17.86%	89	1.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.21%	10.04%	84.86%	68.27%
±2σ	-1.70%	13.95%	95.67%	95.45%
±3σ	-5.61%	17.86%	98.16%	99.73%

Descriptive Statistics

Mean	6.124%
Standard Error	0.056%
Median	5.085%
Mode	5.000%
Standard Deviation	3.911%
Sample Variance	15.297%
Kurtosis	12.39
Skewness	2.71
Range	41.729%
Minimum	1.059%
Maximum	42.788%
Count	4849

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.124%	4849	100.00%	6.124%
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 0.18. Further, an Excess Kurtosis of 3.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.02%	37	0.76%	0.76%
-12.02% to -8.95%	49	1.01%	1.77%
-8.95% to -5.88%	168	3.46%	5.24%
-5.88% to -2.80%	594	12.25%	17.49%
-2.80% to 0.27%	1602	33.04%	50.53%
0.27% to 3.34%	1556	32.09%	82.61%
3.34% to 6.41%	573	11.82%	94.43%
6.41% to 9.49%	161	3.32%	97.75%
9.49% to 12.56%	64	1.32%	99.07%
Greater than 12.56%	45	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.83%	4.37%	76.94%	68.27%
±2σ	-7.93%	8.46%	94.62%	95.45%
±3σ	-12.02%	12.56%	98.31%	99.73%

Descriptive Statistics

Mean	0.269%
Standard Error	0.059%
Median	0.227%
Mode	0.000%
Standard Deviation	4.097%
Sample Variance	16.783%
Kurtosis	3.53
Skewness	0.18
Range	48.429%
Minimum	-20.448%
Maximum	27.981%
Count	4849

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.074%	2522	52.01%	1.599%
Negative	-2.832%	2276	46.94%	-1.329%
Zero	0.000%	51	1.05%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.83. Further, an Excess Kurtosis of 3.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.38%	2	0.20%	0.20%
-32.38% to -24.13%	9	0.89%	1.09%
-24.13% to -15.88%	41	4.08%	5.17%
-15.88% to -7.64%	143	14.21%	19.38%
-7.64% to 0.61%	336	33.40%	52.78%
0.61% to 8.86%	298	29.62%	82.41%
8.86% to 17.11%	117	11.63%	94.04%
17.11% to 25.36%	35	3.48%	97.51%
25.36% to 33.61%	13	1.29%	98.81%
Greater than 33.61%	12	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.38%	11.61%	75.55%	68.27%
±2σ	-21.38%	22.61%	94.83%	95.45%
±3σ	-32.38%	33.61%	98.61%	99.73%

Descriptive Statistics

Mean	0.613%
Standard Error	0.347%
Median	0.186%
Mode	0.000%
Standard Deviation	10.998%
Sample Variance	120.945%
Kurtosis	3.53
Skewness	0.83
Range	100.623%
Minimum	-37.200%
Maximum	63.423%
Count	1006

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.417%	512	50.90%	4.284%
Negative	-7.536%	490	48.71%	-3.671%
Zero	0.000%	4	0.40%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.74%
12	1 Quarter	17.85%
52	1 Year	19.55%
156	3 Years	15.18%
260	5 Years	14.37%
520	10 Years	12.63%
1,040	20 Years	14.98%
2,600	50 Years	14.98%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 9.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.38%	0	0.00%	0.00%
-16.38% to -8.21%	0	0.00%	0.00%
-8.21% to -0.04%	0	0.00%	0.00%
-0.04% to 8.13%	164	16.29%	16.29%
8.13% to 16.30%	467	46.38%	62.66%
16.30% to 24.46%	229	22.74%	85.40%
24.46% to 32.63%	80	7.94%	93.35%
32.63% to 40.80%	34	3.38%	96.72%
40.80% to 48.97%	12	1.19%	97.91%
Greater than 48.97%	21	2.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.41%	27.19%	85.00%	68.27%
±2σ	-5.48%	38.08%	95.63%	95.45%
±3σ	-16.38%	48.97%	97.91%	99.73%

Descriptive Statistics

Mean	16.295%
Standard Error	0.343%
Median	13.285%
Mode	4.716%
Standard Deviation	10.890%
Sample Variance	118.588%
Kurtosis	9.71
Skewness	2.52
Range	90.141%
Minimum	2.464%
Maximum	92.605%
Count	1007

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.295%	1007	100.00%	16.295%
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 2.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.52%	7	0.70%	0.70%
-31.52% to -23.44%	8	0.79%	1.49%
-23.44% to -15.36%	32	3.18%	4.67%
-15.36% to -7.28%	143	14.20%	18.87%
-7.28% to 0.80%	353	35.05%	53.92%
0.80% to 8.88%	284	28.20%	82.13%
8.88% to 16.96%	114	11.32%	93.45%
16.96% to 25.04%	41	4.07%	97.52%
25.04% to 33.12%	16	1.59%	99.11%
Greater than 33.12%	9	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.97%	11.58%	75.57%	68.27%
±2σ	-20.75%	22.35%	94.24%	95.45%
±3σ	-31.52%	33.12%	98.41%	99.73%

Descriptive Statistics

Mean	0.802%
Standard Error	0.340%
Median	0.000%
Mode	-8.728%
Standard Deviation	10.774%
Sample Variance	116.089%
Kurtosis	2.55
Skewness	0.51
Range	90.972%
Minimum	-37.596%
Maximum	53.376%
Count	1007

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.641%	503	49.95%	4.316%
Negative	-7.050%	502	49.85%	-3.514%
Zero	0.000%	2	0.20%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.92. Further, an Excess Kurtosis of 1.89 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.02%	0	0.00%	0.00%
-64.02% to -47.40%	1	0.43%	0.43%
-47.40% to -30.77%	5	2.16%	2.60%
-30.77% to -14.15%	45	19.48%	22.08%
-14.15% to 2.47%	76	32.90%	54.98%
2.47% to 19.09%	60	25.97%	80.95%
19.09% to 35.72%	27	11.69%	92.64%
35.72% to 52.34%	12	5.19%	97.84%
52.34% to 68.96%	3	1.30%	99.13%
Greater than 68.96%	2	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.69%	24.64%	72.73%	68.27%
±2σ	-41.86%	46.80%	95.24%	95.45%
±3σ	-64.02%	68.96%	99.13%	99.73%

Descriptive Statistics

Mean	2.472%
Standard Error	1.458%
Median	0.000%
Mode	-50.435%
Standard Deviation	22.164%
Sample Variance	491.243%
Kurtosis	1.89
Skewness	0.92
Range	152.420%
Minimum	-50.435%
Maximum	101.985%
Count	231

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.312%	115	49.78%	9.614%
Negative	-14.347%	115	49.78%	-7.143%
Zero	0.000%	1	0.43%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	26.32%
12	1 Year	36.51%
36	3 Years	29.85%
60	5 Years	28.76%
120	10 Years	26.43%
240	20 Years	32.38%
600	50 Years	32.38%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.00. Further, an Excess Kurtosis of 40.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.55%	0	0.00%	0.00%
-46.55% to -24.92%	0	0.00%	0.00%
-24.92% to -3.30%	0	0.00%	0.00%
-3.30% to 18.33%	29	12.50%	12.50%
18.33% to 39.95%	121	52.16%	64.66%
39.95% to 61.58%	56	24.14%	88.79%
61.58% to 83.20%	12	5.17%	93.97%
83.20% to 104.83%	9	3.88%	97.84%
104.83% to 126.45%	3	1.29%	99.14%
Greater than 126.45%	2	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.12%	68.79%	90.52%	68.27%
±2σ	-17.71%	97.62%	96.98%	95.45%
±3σ	-46.55%	126.45%	99.14%	99.73%

Descriptive Statistics

Mean	39.953%
Standard Error	1.893%
Median	35.052%
Mode	28.846%
Standard Deviation	28.833%
Sample Variance	831.356%
Kurtosis	40.23
Skewness	5.00
Range	307.657%
Minimum	10.028%
Maximum	317.685%
Count	232

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.953%	232	100.00%	39.953%
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 0.96. Further, an Excess Kurtosis of 3.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.63%	0	0.00%	0.00%
-63.63% to -47.09%	1	0.43%	0.43%
-47.09% to -30.55%	10	4.31%	4.74%
-30.55% to -14.01%	41	17.67%	22.41%
-14.01% to 2.53%	67	28.88%	51.29%
2.53% to 19.07%	69	29.74%	81.03%
19.07% to 35.61%	33	14.22%	95.26%
35.61% to 52.15%	6	2.59%	97.84%
52.15% to 68.69%	2	0.86%	98.71%
Greater than 68.69%	3	1.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.52%	24.58%	71.55%	68.27%
±2σ	-41.58%	46.64%	96.55%	95.45%
±3σ	-63.63%	68.69%	98.71%	99.73%

Descriptive Statistics

Mean	2.529%
Standard Error	1.448%
Median	0.466%
Mode	8.451%
Standard Deviation	22.053%
Sample Variance	486.330%
Kurtosis	3.11
Skewness	0.96
Range	161.575%
Minimum	-49.282%
Maximum	112.293%
Count	232

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.923%	118	50.86%	9.625%
Negative	-14.569%	113	48.71%	-7.096%
Zero	0.000%	1	0.43%	0.000%

Close-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 3.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.36%	0	0.00%	0.00%
-108.36% to -79.56%	0	0.00%	0.00%
-79.56% to -50.75%	2	2.60%	2.60%
-50.75% to -21.95%	12	15.58%	18.18%
-21.95% to 6.86%	36	46.75%	64.94%
6.86% to 35.66%	14	18.18%	83.12%
35.66% to 64.47%	6	7.79%	90.91%
64.47% to 93.27%	5	6.49%	97.40%
93.27% to 122.08%	1	1.30%	98.70%
Greater than 122.08%	1	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.55%	45.26%	76.62%	68.27%
±2σ	-69.96%	83.67%	97.40%	95.45%
±3σ	-108.36%	122.08%	98.70%	99.73%

Descriptive Statistics

Mean	6.857%
Standard Error	4.377%
Median	-1.679%
Mode	-66.354%
Standard Deviation	38.407%
Sample Variance	1475.124%
Kurtosis	3.26
Skewness	1.39
Range	229.054%
Minimum	-66.354%
Maximum	162.700%
Count	77

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.216%	38	49.35%	16.886%
Negative	-19.802%	39	50.65%	-10.030%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	63.07%
12	3 Years	51.02%
20	5 Years	47.44%
40	10 Years	46.15%
80	20 Years	58.41%
200	50 Years	58.41%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -94.24%	0	0.00%	0.00%
-94.24% to -50.34%	0	0.00%	0.00%
-50.34% to -6.43%	0	0.00%	0.00%
-6.43% to 37.48%	11	14.10%	14.10%
37.48% to 81.39%	41	52.56%	66.67%
81.39% to 125.30%	15	19.23%	85.90%
125.30% to 169.21%	6	7.69%	93.59%
169.21% to 213.12%	2	2.56%	96.15%
213.12% to 257.03%	1	1.28%	97.44%
Greater than 257.03%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.85%	139.94%	84.62%	68.27%
±2σ	-35.70%	198.48%	94.87%	95.45%
±3σ	-94.24%	257.03%	97.44%	99.73%

Descriptive Statistics

Mean	81.391%
Standard Error	6.629%
Median	68.481%
Mode	20.755%
Standard Deviation	58.545%
Sample Variance	3427.514%
Kurtosis	9.12
Skewness	2.66
Range	340.912%
Minimum	20.755%
Maximum	361.667%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	81.391%	78	100.00%	81.391%
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 2.06. Further, an Excess Kurtosis of 7.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.86%	0	0.00%	0.00%
-115.86% to -85.26%	0	0.00%	0.00%
-85.26% to -54.67%	1	1.28%	1.28%
-54.67% to -24.07%	13	16.67%	17.95%
-24.07% to 6.53%	29	37.18%	55.13%
6.53% to 37.12%	24	30.77%	85.90%
37.12% to 67.72%	7	8.97%	94.87%
67.72% to 98.32%	2	2.56%	97.44%
98.32% to 128.92%	0	0.00%	97.44%
Greater than 128.92%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.27%	47.32%	79.49%	68.27%
±2σ	-75.06%	88.12%	97.44%	95.45%
±3σ	-115.86%	128.92%	97.44%	99.73%

Descriptive Statistics

Mean	6.528%
Standard Error	4.619%
Median	2.243%
Mode	8.230%
Standard Deviation	40.796%
Sample Variance	1664.276%
Kurtosis	7.62
Skewness	2.06
Range	261.994%
Minimum	-62.407%
Maximum	199.587%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.619%	43	55.13%	16.880%
Negative	-23.070%	35	44.87%	-10.352%
Zero	0.000%	0	0.00%	0.000%

CSIQ Deep Analytical Report