SOFI - 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	4.62%	3.77%	3.83%	5.96%	3.74%	3.84%	18.32	19.75	17.65	20.50
Weekly	10.06%	9.37%	9.63%	14.37%	8.24%	8.46%	17.52	20.65	16.13	22.43
Monthly	19.31%	18.51%	20.43%	31.67%	17.16%	17.62%	16.02	22.58	13.50	26.81
Quarterly	37.34%	35.62%	38.87%	56.16%	29.71%	30.52%	14.13	25.60	10.50	34.46
Annual	—	—	—	—	59.43%	61.04%	10.50	34.46	5.79	62.43
Option Time Horizon	—	—	—	—	22.86%	23.48%	15.13	23.90	12.04	30.04

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $19.02 | Strike (K): $20.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.3900 (Bid $1.3700 / Ask $1.4100) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 59.43% (CRR binomial tree, American, n=20 steps) | BS IV: 60.16% (European Black-Scholes) | Yahoo IV (Annual): 61.04% → 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 2.04. Further, an Excess Kurtosis of 21.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.73%	3	0.23%	0.23%
-13.73% to -10.26%	10	0.78%	1.01%
-10.26% to -6.80%	45	3.49%	4.50%
-6.80% to -3.33%	171	13.28%	17.78%
-3.33% to 0.14%	441	34.24%	52.02%
0.14% to 3.60%	397	30.82%	82.84%
3.60% to 7.07%	162	12.58%	95.42%
7.07% to 10.53%	33	2.56%	97.98%
10.53% to 14.00%	18	1.40%	99.38%
Greater than 14.00%	8	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.49%	4.76%	77.95%	68.27%
±2σ	-9.11%	9.38%	95.81%	95.45%
±3σ	-13.73%	14.00%	99.15%	99.73%

Descriptive Statistics

Mean	0.136%
Standard Error	0.129%
Median	-0.144%
Mode	0.000%
Standard Deviation	4.621%
Sample Variance	21.351%
Kurtosis	21.13
Skewness	2.04
Range	73.189%
Minimum	-15.268%
Maximum	57.921%
Count	1288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.481%	627	48.68%	1.695%
Negative	-3.083%	651	50.54%	-1.558%
Zero	0.000%	10	0.78%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.72%
20	1 Month	5.40%
60	1 Quarter	4.80%
250	1 Year	5.77%
750	3 Years	5.39%
1,250	5 Years	5.96%
2,500	10 Years	6.10%
5,000	20 Years	6.10%
12,500	50 Years	6.10%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.93. Further, an Excess Kurtosis of 137.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.41%	0	0.00%	0.00%
-5.41% to -2.58%	0	0.00%	0.00%
-2.58% to 0.24%	0	0.00%	0.00%
0.24% to 3.06%	151	11.71%	11.71%
3.06% to 5.89%	664	51.51%	63.23%
5.89% to 8.71%	302	23.43%	86.66%
8.71% to 11.54%	106	8.22%	94.88%
11.54% to 14.36%	43	3.34%	98.22%
14.36% to 17.19%	8	0.62%	98.84%
Greater than 17.19%	15	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.12%	9.66%	88.91%	68.27%
±2σ	-1.64%	13.42%	97.21%	95.45%
±3σ	-5.41%	17.19%	98.84%	99.73%

Descriptive Statistics

Mean	5.890%
Standard Error	0.105%
Median	5.087%
Mode	2.730%
Standard Deviation	3.766%
Sample Variance	14.185%
Kurtosis	137.97
Skewness	7.93
Range	81.073%
Minimum	1.500%
Maximum	82.573%
Count	1289

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.890%	1289	100.00%	5.890%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.50. Further, an Excess Kurtosis of 7.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.27%	6	0.47%	0.47%
-11.27% to -8.40%	13	1.01%	1.47%
-8.40% to -5.53%	40	3.10%	4.58%
-5.53% to -2.65%	195	15.13%	19.71%
-2.65% to 0.22%	414	32.12%	51.82%
0.22% to 3.09%	381	29.56%	81.38%
3.09% to 5.96%	158	12.26%	93.64%
5.96% to 8.84%	58	4.50%	98.14%
8.84% to 11.71%	17	1.32%	99.46%
Greater than 11.71%	7	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.61%	4.05%	74.48%	68.27%
±2σ	-7.44%	7.88%	94.96%	95.45%
±3σ	-11.27%	11.71%	98.99%	99.73%

Descriptive Statistics

Mean	0.218%
Standard Error	0.107%
Median	0.063%
Mode	0.000%
Standard Deviation	3.830%
Sample Variance	14.667%
Kurtosis	7.49
Skewness	-0.50
Range	55.455%
Minimum	-36.259%
Maximum	19.196%
Count	1289

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.015%	648	50.27%	1.516%
Negative	-2.711%	617	47.87%	-1.298%
Zero	0.000%	24	1.86%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.97. Further, an Excess Kurtosis of 3.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.52%	0	0.00%	0.00%
-29.52% to -21.98%	0	0.00%	0.00%
-21.98% to -14.44%	18	6.72%	6.72%
-14.44% to -6.90%	36	13.43%	20.15%
-6.90% to 0.65%	86	32.09%	52.24%
0.65% to 8.19%	84	31.34%	83.58%
8.19% to 15.73%	27	10.07%	93.66%
15.73% to 23.27%	9	3.36%	97.01%
23.27% to 30.81%	6	2.24%	99.25%
Greater than 30.81%	2	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.41%	10.70%	75.37%	68.27%
±2σ	-19.47%	20.76%	94.78%	95.45%
±3σ	-29.52%	30.81%	99.25%	99.73%

Descriptive Statistics

Mean	0.646%
Standard Error	0.614%
Median	0.214%
Mode	0.000%
Standard Deviation	10.056%
Sample Variance	101.129%
Kurtosis	3.45
Skewness	0.97
Range	76.639%
Minimum	-20.983%
Maximum	55.656%
Count	268

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.838%	135	50.37%	3.948%
Negative	-6.861%	129	48.13%	-3.302%
Zero	0.000%	4	1.49%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.88%
12	1 Quarter	10.34%
52	1 Year	13.22%
156	3 Years	13.17%
260	5 Years	14.37%
520	10 Years	14.80%
1,040	20 Years	14.80%
2,600	50 Years	14.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.56. Further, an Excess Kurtosis of 12.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.07%	0	0.00%	0.00%
-12.07% to -5.05%	0	0.00%	0.00%
-5.05% to 1.98%	0	0.00%	0.00%
1.98% to 9.00%	48	17.84%	17.84%
9.00% to 16.02%	124	46.10%	63.94%
16.02% to 23.05%	48	17.84%	81.78%
23.05% to 30.07%	30	11.15%	92.94%
30.07% to 37.10%	13	4.83%	97.77%
37.10% to 44.12%	1	0.37%	98.14%
Greater than 44.12%	5	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.66%	25.39%	80.30%	68.27%
±2σ	-2.71%	34.76%	96.65%	95.45%
±3σ	-12.07%	44.12%	98.14%	99.73%

Descriptive Statistics

Mean	16.024%
Standard Error	0.571%
Median	13.801%
Mode	14.451%
Standard Deviation	9.366%
Sample Variance	87.724%
Kurtosis	12.42
Skewness	2.56
Range	82.000%
Minimum	3.029%
Maximum	85.029%
Count	269

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.024%	269	100.00%	16.024%
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 0.08. Further, an Excess Kurtosis of 0.72 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.44%	1	0.37%	0.37%
-28.44% to -21.22%	2	0.74%	1.12%
-21.22% to -14.00%	11	4.09%	5.20%
-14.00% to -6.78%	38	14.13%	19.33%
-6.78% to 0.44%	85	31.60%	50.93%
0.44% to 7.66%	75	27.88%	78.81%
7.66% to 14.88%	34	12.64%	91.45%
14.88% to 22.10%	17	6.32%	97.77%
22.10% to 29.32%	6	2.23%	100.00%
Greater than 29.32%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.19%	10.07%	73.61%	68.27%
±2σ	-18.81%	19.69%	93.68%	95.45%
±3σ	-28.44%	29.32%	99.63%	99.73%

Descriptive Statistics

Mean	0.440%
Standard Error	0.587%
Median	0.278%
Mode	-2.230%
Standard Deviation	9.627%
Sample Variance	92.676%
Kurtosis	0.72
Skewness	0.08
Range	63.351%
Minimum	-36.019%
Maximum	27.332%
Count	269

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.597%	137	50.93%	3.869%
Negative	-7.041%	131	48.70%	-3.429%
Zero	0.000%	1	0.37%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -56.65%	0	0.00%	0.00%
-56.65% to -42.17%	0	0.00%	0.00%
-42.17% to -27.69%	2	3.28%	3.28%
-27.69% to -13.21%	11	18.03%	21.31%
-13.21% to 1.27%	22	36.07%	57.38%
1.27% to 15.76%	14	22.95%	80.33%
15.76% to 30.24%	6	9.84%	90.16%
30.24% to 44.72%	4	6.56%	96.72%
44.72% to 59.20%	2	3.28%	100.00%
Greater than 59.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.04%	20.58%	70.49%	68.27%
±2σ	-37.34%	39.89%	95.08%	95.45%
±3σ	-56.65%	59.20%	100.00%	99.73%

Descriptive Statistics

Mean	1.274%
Standard Error	2.472%
Median	-4.203%
Mode	-35.238%
Standard Deviation	19.309%
Sample Variance	372.824%
Kurtosis	0.08
Skewness	0.67
Range	85.563%
Minimum	-35.238%
Maximum	50.325%
Count	61

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.540%	27	44.26%	8.206%
Negative	-12.436%	34	55.74%	-6.932%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.68%
12	1 Year	30.55%
36	3 Years	30.02%
60	5 Years	31.67%
120	10 Years	31.88%
240	20 Years	31.88%
600	50 Years	31.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.92. Further, an Excess Kurtosis of 7.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.75%	0	0.00%	0.00%
-15.75% to -1.86%	0	0.00%	0.00%
-1.86% to 12.02%	0	0.00%	0.00%
12.02% to 25.90%	11	17.74%	17.74%
25.90% to 39.79%	26	41.94%	59.68%
39.79% to 53.67%	13	20.97%	80.65%
53.67% to 67.55%	7	11.29%	91.94%
67.55% to 81.44%	4	6.45%	98.39%
81.44% to 95.32%	0	0.00%	98.39%
Greater than 95.32%	1	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.28%	58.30%	75.81%	68.27%
±2σ	2.77%	76.81%	98.39%	95.45%
±3σ	-15.75%	95.32%	98.39%	99.73%

Descriptive Statistics

Mean	39.787%
Standard Error	2.351%
Median	37.020%
Mode	12.903%
Standard Deviation	18.511%
Sample Variance	342.649%
Kurtosis	7.37
Skewness	1.92
Range	115.656%
Minimum	12.903%
Maximum	128.559%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.787%	62	100.00%	39.787%
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 0.05. Further, an Excess Kurtosis of 0.04 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.28%	0	0.00%	0.00%
-59.28% to -43.96%	1	1.61%	1.61%
-43.96% to -28.63%	3	4.84%	6.45%
-28.63% to -13.31%	10	16.13%	22.58%
-13.31% to 2.02%	15	24.19%	46.77%
2.02% to 17.35%	19	30.65%	77.42%
17.35% to 32.67%	10	16.13%	93.55%
32.67% to 48.00%	3	4.84%	98.39%
48.00% to 63.33%	1	1.61%	100.00%
Greater than 63.33%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.41%	22.45%	66.13%	68.27%
±2σ	-38.85%	42.89%	96.77%	95.45%
±3σ	-59.28%	63.32%	100.00%	99.73%

Descriptive Statistics

Mean	2.020%
Standard Error	2.595%
Median	4.163%
Mode	-49.920%
Standard Deviation	20.435%
Sample Variance	417.589%
Kurtosis	0.04
Skewness	0.05
Range	104.659%
Minimum	-49.920%
Maximum	54.739%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.760%	34	54.84%	9.191%
Negative	-15.880%	28	45.16%	-7.172%
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 0.73. Further, an Excess Kurtosis of -0.13 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -107.35%	0	0.00%	0.00%
-107.35% to -79.34%	0	0.00%	0.00%
-79.34% to -51.33%	0	0.00%	0.00%
-51.33% to -23.32%	4	19.05%	19.05%
-23.32% to 4.69%	9	42.86%	61.90%
4.69% to 32.70%	4	19.05%	80.95%
32.70% to 60.70%	2	9.52%	90.48%
60.70% to 88.71%	2	9.52%	100.00%
88.71% to 116.72%	0	0.00%	100.00%
Greater than 116.72%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.66%	42.03%	71.43%	68.27%
±2σ	-70.00%	79.38%	90.48%	95.45%
±3σ	-107.35%	116.72%	100.00%	99.73%

Descriptive Statistics

Mean	4.687%
Standard Error	8.149%
Median	-9.176%
Mode	-50.962%
Standard Deviation	37.345%
Sample Variance	1394.637%
Kurtosis	-0.13
Skewness	0.73
Range	134.750%
Minimum	-50.962%
Maximum	83.788%
Count	21

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.067%	10	47.62%	17.175%
Negative	-23.840%	11	52.38%	-12.488%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	52.64%
12	3 Years	56.50%
20	5 Years	56.16%
40	10 Years	56.27%
80	20 Years	56.27%
200	50 Years	56.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.63. Further, an Excess Kurtosis of -0.12 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.32%	0	0.00%	0.00%
-26.32% to 0.40%	0	0.00%	0.00%
0.40% to 27.11%	1	4.55%	4.55%
27.11% to 53.82%	3	13.64%	18.18%
53.82% to 80.53%	10	45.45%	63.64%
80.53% to 107.24%	3	13.64%	77.27%
107.24% to 133.96%	3	13.64%	90.91%
133.96% to 160.67%	1	4.55%	95.45%
160.67% to 187.38%	1	4.55%	100.00%
Greater than 187.38%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	44.92%	116.15%	68.18%	68.27%
±2σ	9.30%	151.76%	95.45%	95.45%
±3σ	-26.32%	187.38%	100.00%	99.73%

Descriptive Statistics

Mean	80.532%
Standard Error	7.593%
Median	70.036%
Mode	26.168%
Standard Deviation	35.616%
Sample Variance	1268.469%
Kurtosis	-0.12
Skewness	0.63
Range	136.753%
Minimum	26.168%
Maximum	162.921%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	80.532%	22	100.00%	80.532%
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 0.79. Further, an Excess Kurtosis of 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -111.08%	0	0.00%	0.00%
-111.08% to -81.93%	0	0.00%	0.00%
-81.93% to -52.77%	0	0.00%	0.00%
-52.77% to -23.62%	6	27.27%	27.27%
-23.62% to 5.53%	5	22.73%	50.00%
5.53% to 34.69%	7	31.82%	81.82%
34.69% to 63.84%	2	9.09%	90.91%
63.84% to 92.99%	1	4.55%	95.45%
92.99% to 122.15%	1	4.55%	100.00%
Greater than 122.15%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.34%	44.40%	68.18%	68.27%
±2σ	-72.21%	83.28%	95.45%	95.45%
±3σ	-111.08%	122.15%	100.00%	99.73%

Descriptive Statistics

Mean	5.533%
Standard Error	8.287%
Median	3.838%
Mode	-49.920%
Standard Deviation	38.871%
Sample Variance	1510.949%
Kurtosis	0.77
Skewness	0.79
Range	157.142%
Minimum	-49.920%
Maximum	107.222%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.632%	11	50.00%	17.816%
Negative	-24.567%	11	50.00%	-12.283%
Zero	0.000%	0	0.00%	0.000%

SOFI Deep Analytical Report