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	4.70%	3.91%	4.10%	5.97%	5.40%	5.40%	12.01	13.38	11.38	14.13
Weekly	11.03%	10.94%	10.88%	14.37%	11.88%	11.88%	11.26	14.28	10.00	16.08
Monthly	22.21%	28.76%	22.09%	29.04%	24.74%	24.72%	9.90	16.24	7.73	20.80
Quarterly	38.68%	58.14%	41.06%	48.97%	42.84%	42.82%	8.26	19.46	5.38	29.87
Annual	—	—	—	—	85.69%	85.64%	5.38	29.87	2.28	70.37
Option Time Horizon	—	—	—	—	32.34%	32.33%	9.18	17.52	6.64	24.21

Calculation Notes: Computed at 2026-03-23T16:40 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $12.68 | Strike (K): $13.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.5250 (Bid $1.4500 / Ask $1.6000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 85.69% (CRR binomial tree, American, n=20 steps) | BS IV: 85.82% (European Black-Scholes) | Yahoo IV (Annual): 85.64% → 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 0.43. Further, an Excess Kurtosis of 4.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.98%	35	0.72%	0.72%
-13.98% to -10.46%	51	1.05%	1.77%
-10.46% to -6.94%	154	3.16%	4.93%
-6.94% to -3.42%	546	11.21%	16.14%
-3.42% to 0.10%	1713	35.18%	51.32%
0.10% to 3.63%	1563	32.10%	83.43%
3.63% to 7.15%	528	10.84%	94.27%
7.15% to 10.67%	159	3.27%	97.54%
10.67% to 14.19%	64	1.31%	98.85%
Greater than 14.19%	56	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.59%	4.80%	78.11%	68.27%
±2σ	-9.29%	9.50%	94.45%	95.45%
±3σ	-13.98%	14.19%	98.11%	99.73%

Descriptive Statistics

Mean	0.105%
Standard Error	0.067%
Median	0.000%
Mode	0.000%
Standard Deviation	4.696%
Sample Variance	22.051%
Kurtosis	4.58
Skewness	0.43
Range	60.428%
Minimum	-26.944%
Maximum	33.484%
Count	4869

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.418%	2406	49.41%	1.689%
Negative	-3.193%	2415	49.60%	-1.584%
Zero	0.000%	48	0.99%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	14.17%
20	1 Month	8.58%
60	1 Quarter	7.88%
250	1 Year	8.28%
750	3 Years	6.29%
1,250	5 Years	5.97%
2,500	10 Years	5.34%
5,000	20 Years	6.28%
12,500	50 Years	6.28%

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 -5.59%	0	0.00%	0.00%
-5.59% to -2.67%	0	0.00%	0.00%
-2.67% to 0.27%	0	0.00%	0.00%
0.27% to 3.20%	828	17.00%	17.00%
3.20% to 6.13%	2249	46.18%	63.18%
6.13% to 9.06%	1035	21.25%	84.44%
9.06% to 11.99%	432	8.87%	93.31%
11.99% to 14.92%	168	3.45%	96.76%
14.92% to 17.85%	68	1.40%	98.15%
Greater than 17.85%	90	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.22%	10.03%	84.83%	68.27%
±2σ	-1.69%	13.94%	95.69%	95.45%
±3σ	-5.59%	17.85%	98.17%	99.73%

Descriptive Statistics

Mean	6.126%
Standard Error	0.056%
Median	5.088%
Mode	5.000%
Standard Deviation	3.907%
Sample Variance	15.265%
Kurtosis	12.39
Skewness	2.71
Range	41.729%
Minimum	1.059%
Maximum	42.788%
Count	4870

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.126%	4870	100.00%	6.126%
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 3.52 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 -5.87%	169	3.47%	5.24%
-5.87% to -2.80%	596	12.24%	17.47%
-2.80% to 0.27%	1612	33.10%	50.57%
0.27% to 3.34%	1561	32.05%	82.63%
3.34% to 6.42%	574	11.79%	94.41%
6.42% to 9.49%	161	3.31%	97.72%
9.49% to 12.56%	66	1.36%	99.08%
Greater than 12.56%	45	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.83%	4.37%	76.94%	68.27%
±2σ	-7.92%	8.47%	94.60%	95.45%
±3σ	-12.02%	12.56%	98.32%	99.73%

Descriptive Statistics

Mean	0.271%
Standard Error	0.059%
Median	0.224%
Mode	0.000%
Standard Deviation	4.097%
Sample Variance	16.786%
Kurtosis	3.52
Skewness	0.18
Range	48.429%
Minimum	-20.448%
Maximum	27.981%
Count	4870

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.078%	2531	51.97%	1.600%
Negative	-2.829%	2288	46.98%	-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 0.80. Further, an Excess Kurtosis of 3.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.53%	2	0.20%	0.20%
-32.53% to -24.25%	10	0.99%	1.19%
-24.25% to -15.98%	40	3.96%	5.15%
-15.98% to -7.70%	140	13.86%	19.01%
-7.70% to 0.57%	339	33.56%	52.57%
0.57% to 8.85%	302	29.90%	82.48%
8.85% to 17.12%	117	11.58%	94.06%
17.12% to 25.40%	35	3.47%	97.52%
25.40% to 33.67%	13	1.29%	98.81%
Greater than 33.67%	12	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.46%	11.61%	75.74%	68.27%
±2σ	-21.50%	22.64%	94.75%	95.45%
±3σ	-32.53%	33.68%	98.61%	99.73%

Descriptive Statistics

Mean	0.573%
Standard Error	0.347%
Median	0.175%
Mode	0.000%
Standard Deviation	11.034%
Sample Variance	121.741%
Kurtosis	3.49
Skewness	0.80
Range	100.623%
Minimum	-37.200%
Maximum	63.423%
Count	1010

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.422%	513	50.79%	4.278%
Negative	-7.589%	493	48.81%	-3.704%
Zero	0.000%	4	0.40%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	21.89%
12	1 Quarter	18.55%
52	1 Year	20.21%
156	3 Years	15.38%
260	5 Years	14.37%
520	10 Years	12.70%
1,040	20 Years	15.00%
2,600	50 Years	15.00%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.50. Further, an Excess Kurtosis of 9.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.47%	0	0.00%	0.00%
-16.47% to -8.27%	0	0.00%	0.00%
-8.27% to -0.07%	0	0.00%	0.00%
-0.07% to 8.14%	164	16.22%	16.22%
8.14% to 16.34%	470	46.49%	62.71%
16.34% to 24.54%	230	22.75%	85.46%
24.54% to 32.75%	78	7.72%	93.18%
32.75% to 40.95%	35	3.46%	96.64%
40.95% to 49.15%	12	1.19%	97.82%
Greater than 49.15%	22	2.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.40%	27.28%	84.97%	68.27%
±2σ	-5.54%	38.22%	95.55%	95.45%
±3σ	-16.47%	49.15%	97.82%	99.73%

Descriptive Statistics

Mean	16.340%
Standard Error	0.344%
Median	13.293%
Mode	4.716%
Standard Deviation	10.938%
Sample Variance	119.647%
Kurtosis	9.50
Skewness	2.50
Range	90.141%
Minimum	2.464%
Maximum	92.605%
Count	1011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.340%	1011	100.00%	16.340%
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 0.57. Further, an Excess Kurtosis of 2.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.78%	7	0.69%	0.69%
-31.78% to -23.62%	8	0.79%	1.48%
-23.62% to -15.46%	31	3.07%	4.55%
-15.46% to -7.30%	143	14.14%	18.69%
-7.30% to 0.86%	357	35.31%	54.01%
0.86% to 9.01%	287	28.39%	82.39%
9.01% to 17.17%	111	10.98%	93.37%
17.17% to 25.33%	42	4.15%	97.53%
25.33% to 33.49%	15	1.48%	99.01%
Greater than 33.49%	10	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.02%	11.73%	75.96%	68.27%
±2σ	-20.90%	22.61%	94.16%	95.45%
±3σ	-31.78%	33.49%	98.32%	99.73%

Descriptive Statistics

Mean	0.856%
Standard Error	0.342%
Median	0.000%
Mode	-8.728%
Standard Deviation	10.878%
Sample Variance	118.323%
Kurtosis	2.68
Skewness	0.57
Range	90.972%
Minimum	-37.596%
Maximum	53.376%
Count	1011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.741%	505	49.95%	4.366%
Negative	-7.042%	504	49.85%	-3.511%
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 0.93. Further, an Excess Kurtosis of 1.87 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.36%	0	0.00%	0.00%
-64.36% to -47.70%	1	0.43%	0.43%
-47.70% to -31.03%	5	2.16%	2.59%
-31.03% to -14.37%	44	18.97%	21.55%
-14.37% to 2.29%	78	33.62%	55.17%
2.29% to 18.95%	60	25.86%	81.03%
18.95% to 35.61%	27	11.64%	92.67%
35.61% to 52.27%	12	5.17%	97.84%
52.27% to 68.93%	3	1.29%	99.14%
Greater than 68.93%	2	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.93%	24.50%	72.41%	68.27%
±2σ	-42.14%	46.72%	94.83%	95.45%
±3σ	-64.36%	68.93%	99.14%	99.73%

Descriptive Statistics

Mean	2.288%
Standard Error	1.458%
Median	-0.888%
Mode	-50.435%
Standard Deviation	22.215%
Sample Variance	493.493%
Kurtosis	1.87
Skewness	0.93
Range	152.420%
Minimum	-50.435%
Maximum	101.985%
Count	232

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.439%	114	49.14%	9.552%
Negative	-14.404%	117	50.43%	-7.264%
Zero	0.000%	1	0.43%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	32.20%
12	1 Year	38.40%
36	3 Years	30.47%
60	5 Years	29.04%
120	10 Years	26.61%
240	20 Years	32.43%
600	50 Years	32.43%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.24%	0	0.00%	0.00%
-46.24% to -24.67%	0	0.00%	0.00%
-24.67% to -3.10%	0	0.00%	0.00%
-3.10% to 18.47%	30	12.88%	12.88%
18.47% to 40.04%	121	51.93%	64.81%
40.04% to 61.62%	57	24.46%	89.27%
61.62% to 83.19%	11	4.72%	93.99%
83.19% to 104.76%	9	3.86%	97.85%
104.76% to 126.33%	3	1.29%	99.14%
Greater than 126.33%	2	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.28%	68.80%	90.56%	68.27%
±2σ	-17.48%	97.57%	97.00%	95.45%
±3σ	-46.24%	126.33%	99.14%	99.73%

Descriptive Statistics

Mean	40.044%
Standard Error	1.884%
Median	35.061%
Mode	28.846%
Standard Deviation	28.761%
Sample Variance	827.207%
Kurtosis	40.41
Skewness	5.00
Range	307.657%
Minimum	10.028%
Maximum	317.685%
Count	233

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	40.044%	233	100.00%	40.044%
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 0.94. Further, an Excess Kurtosis of 3.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.57%	0	0.00%	0.00%
-63.57% to -47.00%	1	0.43%	0.43%
-47.00% to -30.43%	10	4.29%	4.72%
-30.43% to -13.86%	42	18.03%	22.75%
-13.86% to 2.71%	65	27.90%	50.64%
2.71% to 19.29%	70	30.04%	80.69%
19.29% to 35.86%	34	14.59%	95.28%
35.86% to 52.43%	6	2.58%	97.85%
52.43% to 69.00%	2	0.86%	98.71%
Greater than 69.00%	3	1.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.38%	24.81%	71.24%	68.27%
±2σ	-41.47%	46.91%	96.57%	95.45%
±3σ	-63.57%	69.00%	98.71%	99.73%

Descriptive Statistics

Mean	2.715%
Standard Error	1.447%
Median	2.311%
Mode	8.451%
Standard Deviation	22.095%
Sample Variance	488.176%
Kurtosis	3.02
Skewness	0.94
Range	161.575%
Minimum	-49.282%
Maximum	112.293%
Count	233

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.949%	120	51.50%	9.759%
Negative	-14.655%	112	48.07%	-7.045%
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 3.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -109.68%	0	0.00%	0.00%
-109.68% to -80.67%	0	0.00%	0.00%
-80.67% to -51.66%	2	2.60%	2.60%
-51.66% to -22.65%	12	15.58%	18.18%
-22.65% to 6.36%	35	45.45%	63.64%
6.36% to 35.37%	15	19.48%	83.12%
35.37% to 64.38%	6	7.79%	90.91%
64.38% to 93.39%	5	6.49%	97.40%
93.39% to 122.40%	1	1.30%	98.70%
Greater than 122.40%	1	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.32%	45.04%	75.32%	68.27%
±2σ	-71.00%	83.72%	97.40%	95.45%
±3σ	-109.68%	122.40%	98.70%	99.73%

Descriptive Statistics

Mean	6.361%
Standard Error	4.408%
Median	-2.401%
Mode	-66.354%
Standard Deviation	38.679%
Sample Variance	1496.050%
Kurtosis	3.17
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	35.011%	37	48.05%	16.823%
Negative	-20.140%	40	51.95%	-10.462%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	70.74%
12	3 Years	53.58%
20	5 Years	48.97%
40	10 Years	46.92%
80	20 Years	58.81%
200	50 Years	58.81%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.69. Further, an Excess Kurtosis of 9.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -92.31%	0	0.00%	0.00%
-92.31% to -48.71%	0	0.00%	0.00%
-48.71% to -5.10%	0	0.00%	0.00%
-5.10% to 38.50%	12	15.38%	15.38%
38.50% to 82.11%	40	51.28%	66.67%
82.11% to 125.71%	15	19.23%	85.90%
125.71% to 169.31%	6	7.69%	93.59%
169.31% to 212.92%	2	2.56%	96.15%
212.92% to 256.52%	1	1.28%	97.44%
Greater than 256.52%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.97%	140.25%	85.90%	68.27%
±2σ	-34.17%	198.38%	94.87%	95.45%
±3σ	-92.31%	256.52%	97.44%	99.73%

Descriptive Statistics

Mean	82.106%
Standard Error	6.583%
Median	70.406%
Mode	20.755%
Standard Deviation	58.139%
Sample Variance	3380.097%
Kurtosis	9.31
Skewness	2.69
Range	340.912%
Minimum	20.755%
Maximum	361.667%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	82.106%	78	100.00%	82.106%
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 1.99. Further, an Excess Kurtosis of 7.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.95%	0	0.00%	0.00%
-115.95% to -85.16%	0	0.00%	0.00%
-85.16% to -54.36%	1	1.28%	1.28%
-54.36% to -23.57%	13	16.67%	17.95%
-23.57% to 7.22%	28	35.90%	53.85%
7.22% to 38.02%	24	30.77%	84.62%
38.02% to 68.81%	8	10.26%	94.87%
68.81% to 99.61%	2	2.56%	97.44%
99.61% to 130.40%	0	0.00%	97.44%
Greater than 130.40%	2	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.83%	48.28%	78.21%	68.27%
±2σ	-74.89%	89.34%	97.44%	95.45%
±3σ	-115.95%	130.40%	97.44%	99.73%

Descriptive Statistics

Mean	7.224%
Standard Error	4.649%
Median	2.942%
Mode	8.230%
Standard Deviation	41.059%
Sample Variance	1685.849%
Kurtosis	7.22
Skewness	1.99
Range	261.994%
Minimum	-62.407%
Maximum	199.587%
Count	78

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.044%	44	56.41%	17.512%
Negative	-23.602%	34	43.59%	-10.288%
Zero	0.000%	0	0.00%	0.000%

CSIQ Deep Analytical Report