SONO - 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	3.43%	2.62%	2.85%	3.98%	2.73%	3.03%	15.00	15.84	14.59	16.27
Weekly	7.50%	7.03%	7.49%	9.57%	6.01%	6.66%	14.51	16.36	13.67	17.38
Monthly	16.03%	14.82%	15.83%	20.74%	12.51%	13.87%	13.60	17.46	12.00	19.79
Quarterly	29.13%	33.11%	25.73%	37.59%	21.66%	24.02%	12.41	19.14	9.99	23.77
Annual	—	—	—	—	43.32%	48.05%	9.99	23.77	6.48	36.65
Option Time Horizon	—	—	—	—	16.66%	18.48%	13.04	18.20	11.04	21.50

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $15.41 | Strike (K): $17.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.3750 (Bid $0.3000 / Ask $0.4500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 43.32% (CRR binomial tree, American, n=20 steps) | BS IV: 43.60% (European Black-Scholes) | Yahoo IV (Annual): 48.05% → 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 0.23. Further, an Excess Kurtosis of 9.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.26%	11	0.58%	0.58%
-10.26% to -7.68%	11	0.58%	1.16%
-7.68% to -5.11%	64	3.37%	4.53%
-5.11% to -2.53%	225	11.86%	16.39%
-2.53% to 0.05%	648	34.16%	50.55%
0.05% to 2.62%	629	33.16%	83.71%
2.62% to 5.20%	226	11.91%	95.62%
5.20% to 7.77%	51	2.69%	98.31%
7.77% to 10.35%	14	0.74%	99.05%
Greater than 10.35%	18	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.39%	3.48%	79.02%	68.27%
±2σ	-6.82%	6.91%	95.68%	95.45%
±3σ	-10.26%	10.35%	98.47%	99.73%

Descriptive Statistics

Mean	0.046%
Standard Error	0.079%
Median	0.000%
Mode	0.000%
Standard Deviation	3.434%
Sample Variance	11.793%
Kurtosis	9.83
Skewness	0.23
Range	54.787%
Minimum	-24.945%
Maximum	29.842%
Count	1897

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.421%	938	49.45%	1.197%
Negative	-2.312%	945	49.81%	-1.152%
Zero	0.000%	14	0.74%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.29%
20	1 Month	5.88%
60	1 Quarter	4.19%
250	1 Year	4.26%
750	3 Years	3.74%
1,250	5 Years	3.98%
2,500	10 Years	4.48%
5,000	20 Years	4.48%
12,500	50 Years	4.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.98. Further, an Excess Kurtosis of 17.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.52%	0	0.00%	0.00%
-3.52% to -1.56%	0	0.00%	0.00%
-1.56% to 0.41%	0	0.00%	0.00%
0.41% to 2.37%	296	15.60%	15.60%
2.37% to 4.33%	913	48.10%	63.70%
4.33% to 6.29%	406	21.39%	85.09%
6.29% to 8.26%	150	7.90%	92.99%
8.26% to 10.22%	71	3.74%	96.73%
10.22% to 12.18%	31	1.63%	98.37%
Greater than 12.18%	31	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.71%	6.95%	84.30%	68.27%
±2σ	-0.90%	9.57%	95.47%	95.45%
±3σ	-3.52%	12.18%	98.37%	99.73%

Descriptive Statistics

Mean	4.331%
Standard Error	0.060%
Median	3.648%
Mode	3.223%
Standard Deviation	2.617%
Sample Variance	6.851%
Kurtosis	17.63
Skewness	2.98
Range	34.556%
Minimum	0.841%
Maximum	35.397%
Count	1898

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.331%	1898	100.00%	4.331%
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 -0.12. Further, an Excess Kurtosis of 3.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.46%	17	0.90%	0.90%
-8.46% to -6.32%	15	0.79%	1.69%
-6.32% to -4.18%	59	3.11%	4.79%
-4.18% to -2.04%	250	13.17%	17.97%
-2.04% to 0.10%	633	33.35%	51.32%
0.10% to 2.24%	584	30.77%	82.09%
2.24% to 4.38%	229	12.07%	94.15%
4.38% to 6.52%	76	4.00%	98.16%
6.52% to 8.66%	17	0.90%	99.05%
Greater than 8.66%	18	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.75%	2.96%	75.61%	68.27%
±2σ	-5.61%	5.81%	95.05%	95.45%
±3σ	-8.46%	8.67%	98.16%	99.73%

Descriptive Statistics

Mean	0.103%
Standard Error	0.066%
Median	0.052%
Mode	0.000%
Standard Deviation	2.854%
Sample Variance	8.147%
Kurtosis	3.72
Skewness	-0.12
Range	32.889%
Minimum	-19.638%
Maximum	13.251%
Count	1898

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.173%	951	50.10%	1.089%
Negative	-2.027%	923	48.63%	-0.986%
Zero	0.000%	24	1.26%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 2.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.26%	4	1.02%	1.02%
-22.26% to -16.64%	1	0.25%	1.27%
-16.64% to -11.02%	17	4.31%	5.58%
-11.02% to -5.40%	44	11.17%	16.75%
-5.40% to 0.23%	138	35.03%	51.78%
0.23% to 5.85%	119	30.20%	81.98%
5.85% to 11.47%	47	11.93%	93.91%
11.47% to 17.09%	15	3.81%	97.72%
17.09% to 22.71%	7	1.78%	99.49%
Greater than 22.71%	2	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.27%	7.72%	76.90%	68.27%
±2σ	-14.77%	15.21%	93.91%	95.45%
±3σ	-22.26%	22.71%	98.48%	99.73%

Descriptive Statistics

Mean	0.225%
Standard Error	0.378%
Median	-0.164%
Mode	-7.465%
Standard Deviation	7.495%
Sample Variance	56.171%
Kurtosis	2.69
Skewness	0.08
Range	63.630%
Minimum	-28.663%
Maximum	34.967%
Count	394

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.791%	193	48.98%	2.837%
Negative	-5.172%	199	50.51%	-2.612%
Zero	0.000%	2	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.57%
12	1 Quarter	9.16%
52	1 Year	10.32%
156	3 Years	9.10%
260	5 Years	9.57%
520	10 Years	10.56%
1,040	20 Years	10.56%
2,600	50 Years	10.56%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.16. Further, an Excess Kurtosis of 6.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.81%	0	0.00%	0.00%
-9.81% to -4.54%	0	0.00%	0.00%
-4.54% to 0.73%	0	0.00%	0.00%
0.73% to 6.00%	70	17.72%	17.72%
6.00% to 11.27%	188	47.59%	65.32%
11.27% to 16.54%	72	18.23%	83.54%
16.54% to 21.81%	35	8.86%	92.41%
21.81% to 27.08%	15	3.80%	96.20%
27.08% to 32.35%	6	1.52%	97.72%
Greater than 32.35%	9	2.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.24%	18.30%	82.53%	68.27%
±2σ	-2.78%	25.33%	95.70%	95.45%
±3σ	-9.81%	32.36%	97.72%	99.73%

Descriptive Statistics

Mean	11.271%
Standard Error	0.354%
Median	8.866%
Mode	3.096%
Standard Deviation	7.028%
Sample Variance	49.395%
Kurtosis	6.70
Skewness	2.16
Range	49.091%
Minimum	3.069%
Maximum	52.160%
Count	395

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.271%	395	100.00%	11.271%
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 4.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.22%	1	0.25%	0.25%
-22.22% to -16.60%	3	0.76%	1.01%
-16.60% to -10.99%	17	4.30%	5.32%
-10.99% to -5.37%	49	12.41%	17.72%
-5.37% to 0.25%	136	34.43%	52.15%
0.25% to 5.86%	122	30.89%	83.04%
5.86% to 11.48%	43	10.89%	93.92%
11.48% to 17.09%	15	3.80%	97.72%
17.09% to 22.71%	5	1.27%	98.99%
Greater than 22.71%	4	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.24%	7.73%	77.22%	68.27%
±2σ	-14.73%	15.22%	95.44%	95.45%
±3σ	-22.22%	22.71%	98.73%	99.73%

Descriptive Statistics

Mean	0.246%
Standard Error	0.377%
Median	0.046%
Mode	-9.770%
Standard Deviation	7.488%
Sample Variance	56.078%
Kurtosis	4.75
Skewness	0.94
Range	64.549%
Minimum	-23.184%
Maximum	41.365%
Count	395

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.581%	198	50.13%	2.798%
Negative	-5.116%	197	49.87%	-2.552%
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 0.74. Further, an Excess Kurtosis of 1.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -47.12%	0	0.00%	0.00%
-47.12% to -35.10%	0	0.00%	0.00%
-35.10% to -23.08%	3	3.33%	3.33%
-23.08% to -11.06%	17	18.89%	22.22%
-11.06% to 0.96%	29	32.22%	54.44%
0.96% to 12.98%	27	30.00%	84.44%
12.98% to 25.00%	8	8.89%	93.33%
25.00% to 37.02%	3	3.33%	96.67%
37.02% to 49.05%	2	2.22%	98.89%
Greater than 49.05%	1	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.07%	16.99%	71.11%	68.27%
±2σ	-31.09%	33.02%	92.22%	95.45%
±3σ	-47.12%	49.05%	98.89%	99.73%

Descriptive Statistics

Mean	0.962%
Standard Error	1.690%
Median	-0.194%
Mode	-31.976%
Standard Deviation	16.028%
Sample Variance	256.907%
Kurtosis	1.17
Skewness	0.74
Range	84.305%
Minimum	-31.976%
Maximum	52.329%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.520%	44	48.89%	6.610%
Negative	-11.296%	45	50.00%	-5.648%
Zero	0.000%	1	1.11%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.66%
12	1 Year	22.24%
36	3 Years	20.25%
60	5 Years	20.74%
120	10 Years	23.46%
240	20 Years	23.46%
600	50 Years	23.46%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.32. Further, an Excess Kurtosis of 1.43 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.13%	0	0.00%	0.00%
-17.13% to -6.01%	0	0.00%	0.00%
-6.01% to 5.11%	0	0.00%	0.00%
5.11% to 16.23%	24	26.37%	26.37%
16.23% to 27.35%	30	32.97%	59.34%
27.35% to 38.46%	21	23.08%	82.42%
38.46% to 49.58%	5	5.49%	87.91%
49.58% to 60.70%	7	7.69%	95.60%
60.70% to 71.82%	3	3.30%	98.90%
Greater than 71.82%	1	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.52%	42.17%	76.92%	68.27%
±2σ	-2.30%	56.99%	93.41%	95.45%
±3σ	-17.13%	71.82%	98.90%	99.73%

Descriptive Statistics

Mean	27.346%
Standard Error	1.554%
Median	23.098%
Mode	9.520%
Standard Deviation	14.824%
Sample Variance	219.763%
Kurtosis	1.43
Skewness	1.32
Range	70.723%
Minimum	9.520%
Maximum	80.243%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.346%	91	100.00%	27.346%
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 0.31. Further, an Excess Kurtosis of 0.29 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.12%	0	0.00%	0.00%
-46.12% to -34.25%	0	0.00%	0.00%
-34.25% to -22.37%	6	6.59%	6.59%
-22.37% to -10.50%	12	13.19%	19.78%
-10.50% to 1.37%	29	31.87%	51.65%
1.37% to 13.24%	25	27.47%	79.12%
13.24% to 25.11%	14	15.38%	94.51%
25.11% to 36.98%	2	2.20%	96.70%
36.98% to 48.86%	3	3.30%	100.00%
Greater than 48.86%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.46%	17.20%	70.33%	68.27%
±2σ	-30.29%	33.03%	94.51%	95.45%
±3σ	-46.12%	48.86%	100.00%	99.73%

Descriptive Statistics

Mean	1.369%
Standard Error	1.659%
Median	0.521%
Mode	-34.038%
Standard Deviation	15.829%
Sample Variance	250.563%
Kurtosis	0.29
Skewness	0.31
Range	79.324%
Minimum	-34.038%
Maximum	45.286%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.716%	46	50.55%	6.933%
Negative	-11.253%	45	49.45%	-5.565%
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 0.99. Further, an Excess Kurtosis of 0.47 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -83.20%	0	0.00%	0.00%
-83.20% to -61.35%	0	0.00%	0.00%
-61.35% to -39.50%	0	0.00%	0.00%
-39.50% to -17.65%	7	23.33%	23.33%
-17.65% to 4.20%	10	33.33%	56.67%
4.20% to 26.05%	8	26.67%	83.33%
26.05% to 47.90%	1	3.33%	86.67%
47.90% to 69.75%	3	10.00%	96.67%
69.75% to 91.61%	1	3.33%	100.00%
Greater than 91.61%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.93%	33.34%	70.00%	68.27%
±2σ	-54.06%	62.47%	96.67%	95.45%
±3σ	-83.20%	91.61%	100.00%	99.73%

Descriptive Statistics

Mean	4.203%
Standard Error	5.319%
Median	-2.694%
Mode	-37.106%
Standard Deviation	29.134%
Sample Variance	848.790%
Kurtosis	0.47
Skewness	0.99
Range	116.216%
Minimum	-37.106%
Maximum	79.110%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.990%	13	43.33%	12.996%
Negative	-15.516%	17	56.67%	-8.792%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	42.10%
12	3 Years	40.80%
20	5 Years	37.59%
40	10 Years	44.07%
80	20 Years	44.07%
200	50 Years	44.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.09. Further, an Excess Kurtosis of 0.96 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.58%	0	0.00%	0.00%
-41.58% to -16.75%	0	0.00%	0.00%
-16.75% to 8.08%	0	0.00%	0.00%
8.08% to 32.91%	9	29.03%	29.03%
32.91% to 57.74%	9	29.03%	58.06%
57.74% to 82.57%	7	22.58%	80.65%
82.57% to 107.40%	4	12.90%	93.55%
107.40% to 132.24%	1	3.23%	96.77%
132.24% to 157.07%	1	3.23%	100.00%
Greater than 157.07%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.63%	90.85%	70.97%	68.27%
±2σ	-8.47%	123.96%	96.77%	95.45%
±3σ	-41.58%	157.07%	100.00%	99.73%

Descriptive Statistics

Mean	57.742%
Standard Error	5.946%
Median	42.581%
Mode	21.192%
Standard Deviation	33.108%
Sample Variance	1096.156%
Kurtosis	0.96
Skewness	1.09
Range	135.343%
Minimum	21.192%
Maximum	156.535%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	57.742%	31	100.00%	57.742%
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 0.00. Further, an Excess Kurtosis of -0.45 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -73.69%	0	0.00%	0.00%
-73.69% to -54.39%	0	0.00%	0.00%
-54.39% to -35.09%	3	9.68%	9.68%
-35.09% to -15.80%	3	9.68%	19.35%
-15.80% to 3.50%	10	32.26%	51.61%
3.50% to 22.79%	7	22.58%	74.19%
22.79% to 42.09%	6	19.35%	93.55%
42.09% to 61.39%	2	6.45%	100.00%
61.39% to 80.68%	0	0.00%	100.00%
Greater than 80.68%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.23%	29.23%	67.74%	68.27%
±2σ	-47.96%	54.95%	96.77%	95.45%
±3σ	-73.69%	80.68%	100.00%	99.73%

Descriptive Statistics

Mean	3.498%
Standard Error	4.621%
Median	3.166%
Mode	-43.901%
Standard Deviation	25.728%
Sample Variance	661.932%
Kurtosis	-0.45
Skewness	0.00
Range	101.879%
Minimum	-43.901%
Maximum	57.978%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.919%	18	58.06%	12.147%
Negative	-20.623%	13	41.94%	-8.648%
Zero	0.000%	0	0.00%	0.000%

SONO Deep Analytical Report