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	3.36%	2.47%	2.84%	4.05%	3.26%	3.30%	36.31	38.75	35.14	40.04
Weekly	7.10%	6.18%	6.85%	9.47%	7.18%	7.27%	34.91	40.30	32.49	43.30
Monthly	15.27%	14.53%	15.50%	19.63%	14.95%	15.14%	32.30	43.56	27.82	50.58
Quarterly	31.20%	31.10%	25.05%	35.38%	25.89%	26.22%	28.95	48.60	22.35	62.96
Annual	—	—	—	—	51.79%	52.44%	22.35	62.96	13.31	105.67
Option Time Horizon	—	—	—	—	19.55%	19.79%	30.85	45.61	25.37	55.45

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $37.51 | Strike (K): $40.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.0250 (Bid $1.5500 / Ask $2.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 51.79% (CRR binomial tree, American, n=20 steps) | BS IV: 52.14% (European Black-Scholes) | Yahoo IV (Annual): 52.44% → 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 7.89 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	0.59%	0.59%
-9.99% to -7.47%	15	0.81%	1.40%
-7.47% to -4.95%	74	3.98%	5.38%
-4.95% to -2.42%	247	13.29%	18.67%
-2.42% to 0.10%	564	30.34%	49.00%
0.10% to 2.62%	629	33.84%	82.84%
2.62% to 5.14%	229	12.32%	95.16%
5.14% to 7.67%	66	3.55%	98.71%
7.67% to 10.19%	9	0.48%	99.19%
Greater than 10.19%	15	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.26%	3.46%	76.87%	68.27%
±2σ	-6.63%	6.83%	95.97%	95.45%
±3σ	-9.99%	10.19%	98.60%	99.73%

Descriptive Statistics

Mean	0.099%
Standard Error	0.078%
Median	0.148%
Mode	0.000%
Standard Deviation	3.363%
Sample Variance	11.312%
Kurtosis	7.89
Skewness	0.62
Range	50.339%
Minimum	-18.764%
Maximum	31.575%
Count	1859

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.364%	975	52.45%	1.240%
Negative	-2.425%	875	47.07%	-1.141%
Zero	0.000%	9	0.48%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.09%
20	1 Month	4.11%
60	1 Quarter	3.94%
250	1 Year	3.99%
750	3 Years	3.69%
1,250	5 Years	4.05%
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 19.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.01%	0	0.00%	0.00%
-3.01% to -1.16%	0	0.00%	0.00%
-1.16% to 0.69%	0	0.00%	0.00%
0.69% to 2.54%	323	17.37%	17.37%
2.54% to 4.39%	845	45.43%	62.80%
4.39% to 6.24%	389	20.91%	83.71%
6.24% to 8.09%	180	9.68%	93.39%
8.09% to 9.94%	66	3.55%	96.94%
9.94% to 11.79%	28	1.51%	98.44%
Greater than 11.79%	29	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.92%	6.85%	83.55%	68.27%
±2σ	-0.55%	9.32%	96.45%	95.45%
±3σ	-3.01%	11.79%	98.44%	99.73%

Descriptive Statistics

Mean	4.387%
Standard Error	0.057%
Median	3.736%
Mode	2.429%
Standard Deviation	2.467%
Sample Variance	6.087%
Kurtosis	19.18
Skewness	3.00
Range	33.505%
Minimum	0.978%
Maximum	34.483%
Count	1860

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.387%	1860	100.00%	4.387%
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 5.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.50%	10	0.54%	0.54%
-8.50% to -6.36%	8	0.43%	0.97%
-6.36% to -4.23%	78	4.19%	5.16%
-4.23% to -2.10%	260	13.98%	19.14%
-2.10% to 0.04%	598	32.15%	51.29%
0.04% to 2.17%	552	29.68%	80.97%
2.17% to 4.30%	241	12.96%	93.92%
4.30% to 6.43%	83	4.46%	98.39%
6.43% to 8.57%	20	1.08%	99.46%
Greater than 8.57%	10	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.81%	2.88%	74.52%	68.27%
±2σ	-5.65%	5.72%	95.81%	95.45%
±3σ	-8.50%	8.57%	98.92%	99.73%

Descriptive Statistics

Mean	0.035%
Standard Error	0.066%
Median	0.000%
Mode	0.000%
Standard Deviation	2.844%
Sample Variance	8.090%
Kurtosis	5.53
Skewness	0.45
Range	41.171%
Minimum	-15.395%
Maximum	25.776%
Count	1860

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.157%	917	49.30%	1.063%
Negative	-2.065%	926	49.78%	-1.028%
Zero	0.000%	17	0.91%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.66. Further, an Excess Kurtosis of 3.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.83%	2	0.52%	0.52%
-20.83% to -15.50%	3	0.78%	1.30%
-15.50% to -10.18%	15	3.89%	5.18%
-10.18% to -4.85%	56	14.51%	19.69%
-4.85% to 0.48%	124	32.12%	51.81%
0.48% to 5.80%	120	31.09%	82.90%
5.80% to 11.13%	45	11.66%	94.56%
11.13% to 16.46%	15	3.89%	98.45%
16.46% to 21.78%	2	0.52%	98.96%
Greater than 21.78%	4	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.62%	7.58%	75.13%	68.27%
±2σ	-13.73%	14.68%	95.60%	95.45%
±3σ	-20.83%	21.78%	98.45%	99.73%

Descriptive Statistics

Mean	0.477%
Standard Error	0.361%
Median	0.291%
Mode	-5.539%
Standard Deviation	7.102%
Sample Variance	50.440%
Kurtosis	3.78
Skewness	0.66
Range	62.773%
Minimum	-22.391%
Maximum	40.382%
Count	386

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.479%	200	51.81%	2.839%
Negative	-4.929%	185	47.93%	-2.362%
Zero	0.000%	1	0.26%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.84%
12	1 Quarter	9.02%
52	1 Year	9.11%
156	3 Years	8.64%
260	5 Years	9.47%
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 7.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.31%	0	0.00%	0.00%
-7.31% to -2.68%	0	0.00%	0.00%
-2.68% to 1.96%	0	0.00%	0.00%
1.96% to 6.60%	77	19.90%	19.90%
6.60% to 11.23%	165	42.64%	62.53%
11.23% to 15.87%	79	20.41%	82.95%
15.87% to 20.51%	38	9.82%	92.76%
20.51% to 25.14%	14	3.62%	96.38%
25.14% to 29.78%	6	1.55%	97.93%
Greater than 29.78%	8	2.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.05%	17.41%	80.88%	68.27%
±2σ	-1.13%	23.60%	95.09%	95.45%
±3σ	-7.31%	29.78%	97.93%	99.73%

Descriptive Statistics

Mean	11.233%
Standard Error	0.314%
Median	9.744%
Mode	6.152%
Standard Deviation	6.182%
Sample Variance	38.219%
Kurtosis	7.38
Skewness	2.17
Range	47.237%
Minimum	2.996%
Maximum	50.233%
Count	387

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.233%	387	100.00%	11.233%
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 0.46. Further, an Excess Kurtosis of 2.93 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.37%	3	0.78%	0.78%
-20.37% to -15.23%	2	0.52%	1.29%
-15.23% to -10.09%	16	4.13%	5.43%
-10.09% to -4.96%	51	13.18%	18.60%
-4.96% to 0.18%	130	33.59%	52.20%
0.18% to 5.32%	117	30.23%	82.43%
5.32% to 10.46%	48	12.40%	94.83%
10.46% to 15.60%	10	2.58%	97.42%
15.60% to 20.74%	6	1.55%	98.97%
Greater than 20.74%	4	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.67%	7.04%	74.42%	68.27%
±2σ	-13.52%	13.89%	95.61%	95.45%
±3σ	-20.37%	20.74%	98.19%	99.73%

Descriptive Statistics

Mean	0.184%
Standard Error	0.348%
Median	-0.229%
Mode	-2.423%
Standard Deviation	6.852%
Sample Variance	46.951%
Kurtosis	2.93
Skewness	0.46
Range	60.182%
Minimum	-28.154%
Maximum	32.028%
Count	387

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.260%	189	48.84%	2.569%
Negative	-4.661%	198	51.16%	-2.385%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.27. Further, an Excess Kurtosis of 0.37 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.70%	0	0.00%	0.00%
-43.70% to -32.25%	2	2.25%	2.25%
-32.25% to -20.80%	3	3.37%	5.62%
-20.80% to -9.35%	13	14.61%	20.22%
-9.35% to 2.10%	26	29.21%	49.44%
2.10% to 13.55%	23	25.84%	75.28%
13.55% to 25.00%	16	17.98%	93.26%
25.00% to 36.45%	3	3.37%	96.63%
36.45% to 47.91%	3	3.37%	100.00%
Greater than 47.91%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.17%	17.37%	70.79%	68.27%
±2σ	-28.44%	32.64%	93.26%	95.45%
±3σ	-43.70%	47.91%	100.00%	99.73%

Descriptive Statistics

Mean	2.101%
Standard Error	1.618%
Median	2.441%
Mode	-35.471%
Standard Deviation	15.268%
Sample Variance	233.117%
Kurtosis	0.37
Skewness	0.27
Range	76.916%
Minimum	-35.471%
Maximum	41.445%
Count	89

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.371%	47	52.81%	7.061%
Negative	-10.511%	42	47.19%	-4.960%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	18.13%
12	1 Year	18.86%
36	3 Years	18.05%
60	5 Years	19.63%
120	10 Years	23.16%
240	20 Years	23.16%
600	50 Years	23.16%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.49. 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 -17.09%	0	0.00%	0.00%
-17.09% to -6.19%	0	0.00%	0.00%
-6.19% to 4.71%	0	0.00%	0.00%
4.71% to 15.60%	15	16.67%	16.67%
15.60% to 26.50%	42	46.67%	63.33%
26.50% to 37.40%	16	17.78%	81.11%
37.40% to 48.29%	10	11.11%	92.22%
48.29% to 59.19%	5	5.56%	97.78%
59.19% to 70.09%	0	0.00%	97.78%
Greater than 70.09%	2	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.97%	41.03%	87.78%	68.27%
±2σ	-2.56%	55.56%	97.78%	95.45%
±3σ	-17.09%	70.09%	97.78%	99.73%

Descriptive Statistics

Mean	26.499%
Standard Error	1.532%
Median	22.282%
Mode	9.315%
Standard Deviation	14.529%
Sample Variance	211.104%
Kurtosis	9.31
Skewness	2.49
Range	94.023%
Minimum	9.315%
Maximum	103.338%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.499%	90	100.00%	26.499%
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 0.81. Further, an Excess Kurtosis of 1.83 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.09%	0	0.00%	0.00%
-46.09% to -34.46%	0	0.00%	0.00%
-34.46% to -22.84%	4	4.44%	4.44%
-22.84% to -11.21%	17	18.89%	23.33%
-11.21% to 0.41%	27	30.00%	53.33%
0.41% to 12.04%	24	26.67%	80.00%
12.04% to 23.66%	13	14.44%	94.44%
23.66% to 35.29%	2	2.22%	96.67%
35.29% to 46.91%	1	1.11%	97.78%
Greater than 46.91%	2	2.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.09%	15.91%	72.22%	68.27%
±2σ	-30.59%	31.41%	95.56%	95.45%
±3σ	-46.09%	46.91%	97.78%	99.73%

Descriptive Statistics

Mean	0.415%
Standard Error	1.634%
Median	-1.175%
Mode	-33.140%
Standard Deviation	15.500%
Sample Variance	240.254%
Kurtosis	1.83
Skewness	0.81
Range	88.673%
Minimum	-33.140%
Maximum	55.533%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.992%	42	46.67%	6.063%
Negative	-10.589%	48	53.33%	-5.647%
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 1.53. Further, an Excess Kurtosis of 3.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.92%	0	0.00%	0.00%
-86.92% to -63.52%	0	0.00%	0.00%
-63.52% to -40.12%	0	0.00%	0.00%
-40.12% to -16.72%	7	23.33%	23.33%
-16.72% to 6.68%	11	36.67%	60.00%
6.68% to 30.08%	7	23.33%	83.33%
30.08% to 53.48%	3	10.00%	93.33%
53.48% to 76.88%	0	0.00%	93.33%
76.88% to 100.27%	1	3.33%	96.67%
Greater than 100.27%	1	3.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.52%	37.88%	80.00%	68.27%
±2σ	-55.72%	69.08%	93.33%	95.45%
±3σ	-86.92%	100.27%	96.67%	99.73%

Descriptive Statistics

Mean	6.677%
Standard Error	5.696%
Median	2.743%
Mode	-36.813%
Standard Deviation	31.199%
Sample Variance	973.358%
Kurtosis	3.39
Skewness	1.53
Range	146.572%
Minimum	-36.813%
Maximum	109.759%
Count	30

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.776%	17	56.67%	14.040%
Negative	-16.990%	13	43.33%	-7.362%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	38.25%
12	3 Years	33.73%
20	5 Years	35.38%
40	10 Years	42.33%
80	20 Years	42.33%
200	50 Years	42.33%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.67. Further, an Excess Kurtosis of 2.81 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.54%	0	0.00%	0.00%
-40.54% to -17.22%	0	0.00%	0.00%
-17.22% to 6.10%	0	0.00%	0.00%
6.10% to 29.42%	6	19.35%	19.35%
29.42% to 52.75%	15	48.39%	67.74%
52.75% to 76.07%	5	16.13%	83.87%
76.07% to 99.39%	3	9.68%	93.55%
99.39% to 122.71%	0	0.00%	93.55%
122.71% to 146.03%	1	3.23%	96.77%
Greater than 146.03%	1	3.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.65%	83.84%	83.87%	68.27%
±2σ	-9.45%	114.94%	93.55%	95.45%
±3σ	-40.54%	146.03%	96.77%	99.73%

Descriptive Statistics

Mean	52.746%
Standard Error	5.585%
Median	43.532%
Mode	19.357%
Standard Deviation	31.096%
Sample Variance	966.944%
Kurtosis	2.81
Skewness	1.67
Range	133.326%
Minimum	19.357%
Maximum	152.683%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.746%	31	100.00%	52.746%
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 0.25. Further, an Excess Kurtosis of 0.32 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.56%	0	0.00%	0.00%
-74.56% to -55.78%	0	0.00%	0.00%
-55.78% to -37.00%	2	6.45%	6.45%
-37.00% to -18.21%	5	16.13%	22.58%
-18.21% to 0.57%	11	35.48%	58.06%
0.57% to 19.36%	6	19.35%	77.42%
19.36% to 38.14%	5	16.13%	93.55%
38.14% to 56.92%	1	3.23%	96.77%
56.92% to 75.71%	1	3.23%	100.00%
Greater than 75.71%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.47%	25.62%	74.19%	68.27%
±2σ	-49.52%	50.66%	93.55%	95.45%
±3σ	-74.56%	75.71%	100.00%	99.73%

Descriptive Statistics

Mean	0.572%
Standard Error	4.498%
Median	-0.917%
Mode	-52.354%
Standard Deviation	25.045%
Sample Variance	627.229%
Kurtosis	0.32
Skewness	0.25
Range	110.552%
Minimum	-52.354%
Maximum	58.198%
Count	31

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.852%	13	41.94%	9.583%
Negative	-15.519%	18	58.06%	-9.011%
Zero	0.000%	0	0.00%	0.000%

YETI Deep Analytical Report