YETI - 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	3.37%	2.48%	2.85%	4.06%	2.75%	3.24%	46.39	49.01	45.13	50.38
Weekly	7.10%	6.21%	6.85%	9.48%	6.05%	7.14%	44.88	50.66	42.24	53.82
Monthly	15.24%	14.61%	15.52%	19.65%	12.60%	14.86%	42.03	54.08	37.06	61.35
Quarterly	30.86%	31.70%	24.73%	34.53%	21.83%	25.74%	38.33	59.31	30.81	73.78
Annual	—	—	—	—	43.66%	51.48%	30.81	73.78	19.91	114.17
Option Time Horizon	—	—	—	—	20.69%	24.40%	38.77	58.64	31.52	72.12

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $47.68 | Strike (K): $50.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.1750 (Bid $2.6500 / Ask $3.7000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 43.66% (CRR binomial tree, American, n=20 steps) | BS IV: 44.19% (European Black-Scholes) | Yahoo IV (Annual): 51.48% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.62. Further, an Excess Kurtosis of 7.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.99%	11	0.60%	0.60%
-9.99% to -7.47%	15	0.82%	1.41%
-7.47% to -4.94%	72	3.92%	5.33%
-4.94% to -2.41%	244	13.28%	18.61%
-2.41% to 0.11%	559	30.41%	49.02%
0.11% to 2.64%	621	33.79%	82.81%
2.64% to 5.16%	229	12.46%	95.27%
5.16% to 7.69%	63	3.43%	98.69%
7.69% to 10.22%	9	0.49%	99.18%
Greater than 10.22%	15	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.26%	3.48%	77.04%	68.27%
±2σ	-6.62%	6.85%	95.92%	95.45%
±3σ	-9.99%	10.22%	98.59%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.079%
Median	0.164%
Mode	0.000%
Standard Deviation	3.368%
Sample Variance	11.346%
Kurtosis	7.92
Skewness	0.62
Range	50.339%
Minimum	-18.764%
Maximum	31.575%
Count	1838

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.372%	967	52.61%	1.248%
Negative	-2.422%	862	46.90%	-1.136%
Zero	0.000%	9	0.49%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.27%
20	1 Month	4.27%
60	1 Quarter	3.58%
250	1 Year	3.97%
750	3 Years	3.67%
1,250	5 Years	4.06%
2,500	10 Years	4.56%
5,000	20 Years	4.56%
12,500	50 Years	4.56%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.00. Further, an Excess Kurtosis of 19.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.03%	0	0.00%	0.00%
-3.03% to -1.18%	0	0.00%	0.00%
-1.18% to 0.68%	0	0.00%	0.00%
0.68% to 2.54%	319	17.35%	17.35%
2.54% to 4.39%	835	45.41%	62.75%
4.39% to 6.25%	386	20.99%	83.74%
6.25% to 8.11%	176	9.57%	93.31%
8.11% to 9.96%	67	3.64%	96.95%
9.96% to 11.82%	27	1.47%	98.42%
Greater than 11.82%	29	1.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.92%	6.87%	83.58%	68.27%
±2σ	-0.56%	9.34%	96.41%	95.45%
±3σ	-3.03%	11.82%	98.42%	99.73%

Descriptive Statistics

Mean	4.392%
Standard Error	0.058%
Median	3.743%
Mode	2.429%
Standard Deviation	2.475%
Sample Variance	6.125%
Kurtosis	19.13
Skewness	3.00
Range	33.505%
Minimum	0.978%
Maximum	34.483%
Count	1839

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.392%	1839	100.00%	4.392%
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 0.45. Further, an Excess Kurtosis of 5.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.52%	10	0.54%	0.54%
-8.52% to -6.38%	8	0.44%	0.98%
-6.38% to -4.24%	77	4.19%	5.17%
-4.24% to -2.11%	258	14.03%	19.20%
-2.11% to 0.03%	590	32.08%	51.28%
0.03% to 2.17%	545	29.64%	80.91%
2.17% to 4.30%	241	13.10%	94.02%
4.30% to 6.44%	81	4.40%	98.42%
6.44% to 8.58%	19	1.03%	99.46%
Greater than 8.58%	10	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.82%	2.88%	74.44%	68.27%
±2σ	-5.67%	5.73%	95.81%	95.45%
±3σ	-8.52%	8.58%	98.91%	99.73%

Descriptive Statistics

Mean	0.031%
Standard Error	0.066%
Median	0.000%
Mode	0.000%
Standard Deviation	2.849%
Sample Variance	8.115%
Kurtosis	5.55
Skewness	0.45
Range	41.171%
Minimum	-15.395%
Maximum	25.776%
Count	1839

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.158%	905	49.21%	1.062%
Negative	-2.068%	917	49.86%	-1.031%
Zero	0.000%	17	0.92%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.65. Further, an Excess Kurtosis of 3.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.76%	2	0.52%	0.52%
-20.76% to -15.44%	3	0.79%	1.31%
-15.44% to -10.11%	16	4.19%	5.50%
-10.11% to -4.78%	54	14.14%	19.63%
-4.78% to 0.54%	124	32.46%	52.09%
0.54% to 5.87%	117	30.63%	82.72%
5.87% to 11.20%	45	11.78%	94.50%
11.20% to 16.52%	15	3.93%	98.43%
16.52% to 21.85%	2	0.52%	98.95%
Greater than 21.85%	4	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.56%	7.64%	74.87%	68.27%
±2σ	-13.66%	14.75%	95.55%	95.45%
±3σ	-20.76%	21.85%	98.43%	99.73%

Descriptive Statistics

Mean	0.542%
Standard Error	0.363%
Median	0.310%
Mode	-5.539%
Standard Deviation	7.102%
Sample Variance	50.441%
Kurtosis	3.81
Skewness	0.65
Range	62.773%
Minimum	-22.391%
Maximum	40.382%
Count	382

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.498%	199	52.09%	2.864%
Negative	-4.873%	182	47.64%	-2.322%
Zero	0.000%	1	0.26%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.66%
12	1 Quarter	7.45%
52	1 Year	8.92%
156	3 Years	8.54%
260	5 Years	9.48%
520	10 Years	10.64%
1,040	20 Years	10.64%
2,600	50 Years	10.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.17. Further, an Excess Kurtosis of 7.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.40%	0	0.00%	0.00%
-7.40% to -2.74%	0	0.00%	0.00%
-2.74% to 1.91%	0	0.00%	0.00%
1.91% to 6.57%	76	19.84%	19.84%
6.57% to 11.23%	163	42.56%	62.40%
11.23% to 15.88%	79	20.63%	83.03%
15.88% to 20.54%	37	9.66%	92.69%
20.54% to 25.19%	14	3.66%	96.34%
25.19% to 29.85%	6	1.57%	97.91%
Greater than 29.85%	8	2.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.02%	17.43%	80.94%	68.27%
±2σ	-1.19%	23.64%	95.30%	95.45%
±3σ	-7.40%	29.85%	97.91%	99.73%

Descriptive Statistics

Mean	11.226%
Standard Error	0.317%
Median	9.714%
Mode	6.152%
Standard Deviation	6.208%
Sample Variance	38.535%
Kurtosis	7.33
Skewness	2.17
Range	47.237%
Minimum	2.996%
Maximum	50.233%
Count	383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.226%	383	100.00%	11.226%
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 0.47. Further, an Excess Kurtosis of 3.00 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.42%	2	0.52%	0.52%
-20.42% to -15.28%	3	0.78%	1.31%
-15.28% to -10.15%	16	4.18%	5.48%
-10.15% to -5.01%	50	13.05%	18.54%
-5.01% to 0.13%	129	33.68%	52.22%
0.13% to 5.26%	117	30.55%	82.77%
5.26% to 10.40%	45	11.75%	94.52%
10.40% to 15.54%	11	2.87%	97.39%
15.54% to 20.67%	6	1.57%	98.96%
Greater than 20.67%	4	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.72%	6.98%	74.67%	68.27%
±2σ	-13.57%	13.82%	95.56%	95.45%
±3σ	-20.42%	20.67%	98.43%	99.73%

Descriptive Statistics

Mean	0.126%
Standard Error	0.350%
Median	-0.282%
Mode	-2.423%
Standard Deviation	6.849%
Sample Variance	46.912%
Kurtosis	3.00
Skewness	0.47
Range	60.182%
Minimum	-28.154%
Maximum	32.028%
Count	383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.216%	186	48.56%	2.533%
Negative	-4.679%	197	51.44%	-2.407%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of 0.40 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.33%	0	0.00%	0.00%
-43.33% to -31.90%	2	2.27%	2.27%
-31.90% to -20.47%	3	3.41%	5.68%
-20.47% to -9.04%	12	13.64%	19.32%
-9.04% to 2.38%	25	28.41%	47.73%
2.38% to 13.81%	24	27.27%	75.00%
13.81% to 25.24%	16	18.18%	93.18%
25.24% to 36.67%	3	3.41%	96.59%
36.67% to 48.10%	3	3.41%	100.00%
Greater than 48.10%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.86%	17.62%	70.45%	68.27%
±2σ	-28.09%	32.86%	93.18%	95.45%
±3σ	-43.33%	48.10%	100.00%	99.73%

Descriptive Statistics

Mean	2.384%
Standard Error	1.625%
Median	2.585%
Mode	-35.471%
Standard Deviation	15.239%
Sample Variance	232.241%
Kurtosis	0.40
Skewness	0.23
Range	76.916%
Minimum	-35.471%
Maximum	41.445%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.182%	48	54.55%	7.190%
Negative	-10.573%	40	45.45%	-4.806%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	15.34%
12	1 Year	18.25%
36	3 Years	17.74%
60	5 Years	19.65%
120	10 Years	23.18%
240	20 Years	23.18%
600	50 Years	23.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.48. Further, an Excess Kurtosis of 9.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.32%	0	0.00%	0.00%
-17.32% to -6.37%	0	0.00%	0.00%
-6.37% to 4.59%	0	0.00%	0.00%
4.59% to 15.55%	15	16.85%	16.85%
15.55% to 26.51%	41	46.07%	62.92%
26.51% to 37.47%	16	17.98%	80.90%
37.47% to 48.42%	10	11.24%	92.13%
48.42% to 59.38%	5	5.62%	97.75%
59.38% to 70.34%	0	0.00%	97.75%
Greater than 70.34%	2	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.90%	41.12%	87.64%	68.27%
±2σ	-2.71%	55.73%	97.75%	95.45%
±3σ	-17.32%	70.34%	97.75%	99.73%

Descriptive Statistics

Mean	26.508%
Standard Error	1.549%
Median	22.154%
Mode	9.315%
Standard Deviation	14.611%
Sample Variance	213.495%
Kurtosis	9.18
Skewness	2.48
Range	94.023%
Minimum	9.315%
Maximum	103.338%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.508%	89	100.00%	26.508%
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 0.86. Further, an Excess Kurtosis of 1.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.40%	0	0.00%	0.00%
-46.40% to -34.76%	0	0.00%	0.00%
-34.76% to -23.12%	4	4.49%	4.49%
-23.12% to -11.47%	17	19.10%	23.60%
-11.47% to 0.17%	28	31.46%	55.06%
0.17% to 11.81%	23	25.84%	80.90%
11.81% to 23.45%	11	12.36%	93.26%
23.45% to 35.10%	3	3.37%	96.63%
35.10% to 46.74%	1	1.12%	97.75%
Greater than 46.74%	2	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.35%	15.69%	71.91%	68.27%
±2σ	-30.88%	31.21%	95.51%	95.45%
±3σ	-46.40%	46.74%	97.75%	99.73%

Descriptive Statistics

Mean	0.169%
Standard Error	1.645%
Median	-1.750%
Mode	-33.140%
Standard Deviation	15.523%
Sample Variance	240.949%
Kurtosis	1.91
Skewness	0.86
Range	88.673%
Minimum	-33.140%
Maximum	55.533%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.183%	40	44.94%	5.925%
Negative	-10.454%	49	55.06%	-5.756%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.52. Further, an Excess Kurtosis of 3.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.15%	0	0.00%	0.00%
-85.15% to -62.01%	0	0.00%	0.00%
-62.01% to -38.87%	0	0.00%	0.00%
-38.87% to -15.72%	6	20.00%	20.00%
-15.72% to 7.42%	13	43.33%	63.33%
7.42% to 30.56%	6	20.00%	83.33%
30.56% to 53.70%	3	10.00%	93.33%
53.70% to 76.84%	0	0.00%	93.33%
76.84% to 99.99%	1	3.33%	96.67%
Greater than 99.99%	1	3.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.44%	38.27%	76.67%	68.27%
±2σ	-54.29%	69.13%	93.33%	95.45%
±3σ	-85.15%	99.99%	96.67%	99.73%

Descriptive Statistics

Mean	7.419%
Standard Error	5.633%
Median	3.649%
Mode	-36.813%
Standard Deviation	30.856%
Sample Variance	952.088%
Kurtosis	3.51
Skewness	1.52
Range	146.572%
Minimum	-36.813%
Maximum	109.759%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.639%	18	60.00%	14.183%
Negative	-16.911%	12	40.00%	-6.764%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.98%
12	3 Years	32.31%
20	5 Years	34.53%
40	10 Years	41.76%
80	20 Years	41.76%
200	50 Years	41.76%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.62. Further, an Excess Kurtosis of 2.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.19%	0	0.00%	0.00%
-43.19% to -19.41%	0	0.00%	0.00%
-19.41% to 4.36%	0	0.00%	0.00%
4.36% to 28.13%	7	22.58%	22.58%
28.13% to 51.90%	13	41.94%	64.52%
51.90% to 75.67%	6	19.35%	83.87%
75.67% to 99.44%	3	9.68%	93.55%
99.44% to 123.21%	0	0.00%	93.55%
123.21% to 146.99%	1	3.23%	96.77%
Greater than 146.99%	1	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	20.20%	83.59%	77.42%	68.27%
±2σ	-11.49%	115.29%	93.55%	95.45%
±3σ	-43.19%	146.99%	96.77%	99.73%

Descriptive Statistics

Mean	51.900%
Standard Error	5.693%
Median	40.995%
Mode	17.674%
Standard Deviation	31.695%
Sample Variance	1004.582%
Kurtosis	2.61
Skewness	1.62
Range	135.009%
Minimum	17.674%
Maximum	152.683%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	51.900%	31	100.00%	51.900%
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 0.34. Further, an Excess Kurtosis of 0.52 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.47%	0	0.00%	0.00%
-74.47% to -55.92%	0	0.00%	0.00%
-55.92% to -37.37%	2	6.45%	6.45%
-37.37% to -18.82%	5	16.13%	22.58%
-18.82% to -0.27%	11	35.48%	58.06%
-0.27% to 18.28%	7	22.58%	80.65%
18.28% to 36.83%	4	12.90%	93.55%
36.83% to 55.39%	1	3.23%	96.77%
55.39% to 73.94%	1	3.23%	100.00%
Greater than 73.94%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.00%	24.47%	70.97%	68.27%
±2σ	-49.74%	49.20%	90.32%	95.45%
±3σ	-74.47%	73.94%	100.00%	99.73%

Descriptive Statistics

Mean	-0.268%
Standard Error	4.443%
Median	-3.070%
Mode	-52.354%
Standard Deviation	24.735%
Sample Variance	611.820%
Kurtosis	0.52
Skewness	0.34
Range	110.552%
Minimum	-52.354%
Maximum	58.198%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.919%	12	38.71%	8.872%
Negative	-14.912%	19	61.29%	-9.140%
Zero	0.000%	0	0.00%	0.000%

YETI Deep Analytical Report