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	4.60%	3.75%	3.81%	5.89%	4.18%	4.24%	16.39	17.82	15.72	18.58
Weekly	10.00%	9.31%	9.58%	14.23%	9.21%	9.34%	15.59	18.74	14.22	20.55
Monthly	19.26%	18.49%	20.41%	31.49%	19.18%	19.44%	14.11	20.71	11.65	25.08
Quarterly	37.62%	34.62%	39.17%	56.61%	33.21%	33.67%	12.26	23.83	8.80	33.21
Annual	—	—	—	—	66.42%	67.33%	8.80	33.21	4.53	64.53
Option Time Horizon	—	—	—	—	25.07%	25.42%	13.30	21.96	10.35	28.22

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $17.09 | Strike (K): $18.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.3900 (Bid $1.3600 / Ask $1.4200) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 66.42% (CRR binomial tree, American, n=20 steps) | BS IV: 67.23% (European Black-Scholes) | Yahoo IV (Annual): 67.33% → 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 21.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.66%	3	0.23%	0.23%
-13.66% to -10.21%	10	0.76%	0.99%
-10.21% to -6.77%	48	3.67%	4.66%
-6.77% to -3.32%	171	13.06%	17.72%
-3.32% to 0.13%	449	34.30%	52.02%
0.13% to 3.57%	402	30.71%	82.73%
3.57% to 7.02%	167	12.76%	95.49%
7.02% to 10.47%	33	2.52%	98.01%
10.47% to 13.91%	18	1.38%	99.39%
Greater than 13.91%	8	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.47%	4.72%	78.07%	68.27%
±2σ	-9.06%	9.32%	95.72%	95.45%
±3σ	-13.66%	13.92%	99.16%	99.73%

Descriptive Statistics

Mean	0.127%
Standard Error	0.127%
Median	-0.171%
Mode	0.000%
Standard Deviation	4.596%
Sample Variance	21.124%
Kurtosis	21.28
Skewness	2.04
Range	73.189%
Minimum	-15.268%
Maximum	57.921%
Count	1309

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.458%	636	48.59%	1.680%
Negative	-3.067%	663	50.65%	-1.553%
Zero	0.000%	10	0.76%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.39%
20	1 Month	5.44%
60	1 Quarter	5.11%
250	1 Year	5.68%
750	3 Years	5.39%
1,250	5 Years	5.89%
2,500	10 Years	6.09%
5,000	20 Years	6.09%
12,500	50 Years	6.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.94. Further, an Excess Kurtosis of 138.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.35%	0	0.00%	0.00%
-5.35% to -2.54%	0	0.00%	0.00%
-2.54% to 0.26%	0	0.00%	0.00%
0.26% to 3.07%	152	11.60%	11.60%
3.07% to 5.88%	677	51.68%	63.28%
5.88% to 8.69%	306	23.36%	86.64%
8.69% to 11.50%	109	8.32%	94.96%
11.50% to 14.31%	42	3.21%	98.17%
14.31% to 17.12%	9	0.69%	98.85%
Greater than 17.12%	15	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.14%	9.63%	88.55%	68.27%
±2σ	-1.61%	13.37%	97.25%	95.45%
±3σ	-5.35%	17.12%	98.85%	99.73%

Descriptive Statistics

Mean	5.881%
Standard Error	0.103%
Median	5.083%
Mode	2.730%
Standard Deviation	3.745%
Sample Variance	14.025%
Kurtosis	138.96
Skewness	7.94
Range	81.073%
Minimum	1.500%
Maximum	82.573%
Count	1310

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.881%	1310	100.00%	5.881%
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 7.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.23%	6	0.46%	0.46%
-11.23% to -8.37%	13	0.99%	1.45%
-8.37% to -5.51%	41	3.13%	4.58%
-5.51% to -2.65%	199	15.19%	19.77%
-2.65% to 0.21%	418	31.91%	51.68%
0.21% to 3.07%	388	29.62%	81.30%
3.07% to 5.93%	163	12.44%	93.74%
5.93% to 8.79%	58	4.43%	98.17%
8.79% to 11.65%	17	1.30%	99.47%
Greater than 11.65%	7	0.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.60%	4.02%	74.66%	68.27%
±2σ	-7.42%	7.84%	94.96%	95.45%
±3σ	-11.23%	11.65%	99.01%	99.73%

Descriptive Statistics

Mean	0.211%
Standard Error	0.105%
Median	0.066%
Mode	0.000%
Standard Deviation	3.813%
Sample Variance	14.543%
Kurtosis	7.50
Skewness	-0.50
Range	55.455%
Minimum	-36.259%
Maximum	19.196%
Count	1310

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.991%	660	50.38%	1.507%
Negative	-2.711%	626	47.79%	-1.295%
Zero	0.000%	24	1.83%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.99. 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 -29.40%	0	0.00%	0.00%
-29.40% to -21.90%	0	0.00%	0.00%
-21.90% to -14.40%	20	7.35%	7.35%
-14.40% to -6.90%	35	12.87%	20.22%
-6.90% to 0.60%	87	31.99%	52.21%
0.60% to 8.10%	86	31.62%	83.82%
8.10% to 15.60%	26	9.56%	93.38%
15.60% to 23.10%	10	3.68%	97.06%
23.10% to 30.60%	6	2.21%	99.26%
Greater than 30.60%	2	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.40%	10.60%	75.74%	68.27%
±2σ	-19.40%	20.60%	94.49%	95.45%
±3σ	-29.40%	30.60%	99.26%	99.73%

Descriptive Statistics

Mean	0.600%
Standard Error	0.606%
Median	0.214%
Mode	0.000%
Standard Deviation	10.001%
Sample Variance	100.027%
Kurtosis	3.52
Skewness	0.99
Range	76.639%
Minimum	-20.983%
Maximum	55.656%
Count	272

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.746%	137	50.37%	3.902%
Negative	-6.855%	131	48.16%	-3.302%
Zero	0.000%	4	1.47%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.96%
12	1 Quarter	11.78%
52	1 Year	12.97%
156	3 Years	13.09%
260	5 Years	14.23%
520	10 Years	14.76%
1,040	20 Years	14.76%
2,600	50 Years	14.76%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.58. Further, an Excess Kurtosis of 12.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.94%	0	0.00%	0.00%
-11.94% to -4.96%	0	0.00%	0.00%
-4.96% to 2.02%	0	0.00%	0.00%
2.02% to 9.00%	48	17.58%	17.58%
9.00% to 15.98%	126	46.15%	63.74%
15.98% to 22.96%	50	18.32%	82.05%
22.96% to 29.94%	30	10.99%	93.04%
29.94% to 36.92%	13	4.76%	97.80%
36.92% to 43.91%	1	0.37%	98.17%
Greater than 43.91%	5	1.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.67%	25.29%	80.59%	68.27%
±2σ	-2.63%	34.60%	96.70%	95.45%
±3σ	-11.94%	43.91%	98.17%	99.73%

Descriptive Statistics

Mean	15.981%
Standard Error	0.563%
Median	13.801%
Mode	8.901%
Standard Deviation	9.308%
Sample Variance	86.636%
Kurtosis	12.62
Skewness	2.58
Range	82.000%
Minimum	3.029%
Maximum	85.029%
Count	273

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.981%	273	100.00%	15.981%
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 0.74 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.27%	1	0.37%	0.37%
-28.27% to -21.08%	2	0.73%	1.10%
-21.08% to -13.90%	11	4.03%	5.13%
-13.90% to -6.72%	40	14.65%	19.78%
-6.72% to 0.47%	85	31.14%	50.92%
0.47% to 7.65%	77	28.21%	79.12%
7.65% to 14.83%	33	12.09%	91.21%
14.83% to 22.02%	18	6.59%	97.80%
22.02% to 29.20%	6	2.20%	100.00%
Greater than 29.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.11%	10.04%	73.63%	68.27%
±2σ	-18.69%	19.62%	93.77%	95.45%
±3σ	-28.27%	29.20%	99.63%	99.73%

Descriptive Statistics

Mean	0.466%
Standard Error	0.580%
Median	0.278%
Mode	-2.230%
Standard Deviation	9.578%
Sample Variance	91.747%
Kurtosis	0.74
Skewness	0.08
Range	63.351%
Minimum	-36.019%
Maximum	27.332%
Count	273

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.596%	139	50.92%	3.868%
Negative	-6.982%	133	48.72%	-3.401%
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 0.11 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -56.66%	0	0.00%	0.00%
-56.66% to -42.22%	0	0.00%	0.00%
-42.22% to -27.77%	2	3.23%	3.23%
-27.77% to -13.33%	11	17.74%	20.97%
-13.33% to 1.11%	23	37.10%	58.06%
1.11% to 15.55%	14	22.58%	80.65%
15.55% to 29.99%	6	9.68%	90.32%
29.99% to 44.44%	4	6.45%	96.77%
44.44% to 58.88%	2	3.23%	100.00%
Greater than 58.88%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.15%	20.37%	69.35%	68.27%
±2σ	-37.40%	39.62%	95.16%	95.45%
±3σ	-56.66%	58.88%	100.00%	99.73%

Descriptive Statistics

Mean	1.110%
Standard Error	2.445%
Median	-3.824%
Mode	-35.238%
Standard Deviation	19.256%
Sample Variance	370.784%
Kurtosis	0.11
Skewness	0.67
Range	85.563%
Minimum	-35.238%
Maximum	50.325%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.540%	27	43.55%	8.074%
Negative	-12.336%	35	56.45%	-6.964%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.23%
12	1 Year	30.14%
36	3 Years	29.87%
60	5 Years	31.49%
120	10 Years	31.73%
240	20 Years	31.73%
600	50 Years	31.73%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.91. Further, an Excess Kurtosis of 7.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.89%	0	0.00%	0.00%
-15.89% to -2.02%	0	0.00%	0.00%
-2.02% to 11.85%	0	0.00%	0.00%
11.85% to 25.71%	12	19.05%	19.05%
25.71% to 39.58%	26	41.27%	60.32%
39.58% to 53.45%	12	19.05%	79.37%
53.45% to 67.32%	8	12.70%	92.06%
67.32% to 81.19%	4	6.35%	98.41%
81.19% to 95.06%	0	0.00%	98.41%
Greater than 95.06%	1	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.09%	58.08%	73.02%	68.27%
±2σ	2.60%	76.57%	98.41%	95.45%
±3σ	-15.89%	95.06%	98.41%	99.73%

Descriptive Statistics

Mean	39.584%
Standard Error	2.330%
Median	36.667%
Mode	12.903%
Standard Deviation	18.493%
Sample Variance	341.980%
Kurtosis	7.34
Skewness	1.91
Range	115.656%
Minimum	12.903%
Maximum	128.559%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.584%	63	100.00%	39.584%
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 0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.10%	0	0.00%	0.00%
-59.10% to -43.80%	1	1.59%	1.59%
-43.80% to -28.49%	3	4.76%	6.35%
-28.49% to -13.19%	10	15.87%	22.22%
-13.19% to 2.12%	16	25.40%	47.62%
2.12% to 17.43%	19	30.16%	77.78%
17.43% to 32.73%	10	15.87%	93.65%
32.73% to 48.04%	3	4.76%	98.41%
48.04% to 63.34%	1	1.59%	100.00%
Greater than 63.34%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.29%	22.53%	63.49%	68.27%
±2σ	-38.70%	42.94%	96.83%	95.45%
±3σ	-59.10%	63.34%	100.00%	99.73%

Descriptive Statistics

Mean	2.120%
Standard Error	2.571%
Median	3.525%
Mode	-49.920%
Standard Deviation	20.408%
Sample Variance	416.473%
Kurtosis	0.03
Skewness	0.05
Range	104.659%
Minimum	-49.920%
Maximum	54.739%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.007%	34	53.97%	9.178%
Negative	-15.334%	29	46.03%	-7.059%
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 -0.17 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.56%	0	0.00%	0.00%
-108.56% to -80.35%	0	0.00%	0.00%
-80.35% to -52.13%	0	0.00%	0.00%
-52.13% to -23.92%	5	23.81%	23.81%
-23.92% to 4.30%	8	38.10%	61.90%
4.30% to 32.51%	4	19.05%	80.95%
32.51% to 60.73%	2	9.52%	90.48%
60.73% to 88.94%	2	9.52%	100.00%
88.94% to 117.16%	0	0.00%	100.00%
Greater than 117.16%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.32%	41.92%	71.43%	68.27%
±2σ	-70.94%	79.54%	90.48%	95.45%
±3σ	-108.56%	117.16%	100.00%	99.73%

Descriptive Statistics

Mean	4.298%
Standard Error	8.209%
Median	-9.176%
Mode	-50.962%
Standard Deviation	37.620%
Sample Variance	1415.238%
Kurtosis	-0.17
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	-24.583%	11	52.38%	-12.877%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	54.90%
12	3 Years	57.25%
20	5 Years	56.61%
40	10 Years	56.70%
80	20 Years	56.70%
200	50 Years	56.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.74. 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 -22.63%	0	0.00%	0.00%
-22.63% to 3.34%	0	0.00%	0.00%
3.34% to 29.30%	0	0.00%	0.00%
29.30% to 55.27%	4	18.18%	18.18%
55.27% to 81.24%	10	45.45%	63.64%
81.24% to 107.21%	3	13.64%	77.27%
107.21% to 133.18%	3	13.64%	90.91%
133.18% to 159.14%	1	4.55%	95.45%
159.14% to 185.11%	1	4.55%	100.00%
Greater than 185.11%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	46.62%	115.86%	68.18%	68.27%
±2σ	11.99%	150.49%	95.45%	95.45%
±3σ	-22.63%	185.11%	100.00%	99.73%

Descriptive Statistics

Mean	81.240%
Standard Error	7.382%
Median	70.036%
Mode	31.057%
Standard Deviation	34.624%
Sample Variance	1198.837%
Kurtosis	-0.08
Skewness	0.74
Range	131.864%
Minimum	31.057%
Maximum	162.921%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	81.240%	22	100.00%	81.240%
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 0.74. Further, an Excess Kurtosis of 0.59 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -111.39%	0	0.00%	0.00%
-111.39% to -82.01%	0	0.00%	0.00%
-82.01% to -52.64%	0	0.00%	0.00%
-52.64% to -23.26%	6	27.27%	27.27%
-23.26% to 6.12%	5	22.73%	50.00%
6.12% to 35.49%	7	31.82%	81.82%
35.49% to 64.87%	3	13.64%	95.45%
64.87% to 94.25%	0	0.00%	95.45%
94.25% to 123.62%	1	4.55%	100.00%
Greater than 123.62%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.05%	45.29%	68.18%	68.27%
±2σ	-72.22%	84.45%	95.45%	95.45%
±3σ	-111.39%	123.62%	100.00%	99.73%

Descriptive Statistics

Mean	6.117%
Standard Error	8.351%
Median	3.838%
Mode	-49.920%
Standard Deviation	39.169%
Sample Variance	1534.177%
Kurtosis	0.59
Skewness	0.74
Range	157.142%
Minimum	-49.920%
Maximum	107.222%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.802%	11	50.00%	18.401%
Negative	-24.567%	11	50.00%	-12.283%
Zero	0.000%	0	0.00%	0.000%

SOFI Deep Analytical Report