TOST - 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	3.89%	3.09%	3.36%	5.50%	2.95%	3.28%	26.28	27.88	25.52	28.72
Weekly	8.21%	8.01%	8.62%	12.60%	6.50%	7.21%	25.37	28.89	23.77	30.83
Monthly	15.62%	16.75%	16.13%	25.86%	13.53%	15.01%	23.65	30.99	20.65	35.48
Quarterly	26.86%	54.02%	37.91%	42.73%	23.43%	26.00%	21.42	34.22	16.94	43.25
Annual	—	—	—	—	46.85%	52.00%	16.94	43.25	10.61	69.10
Option Time Horizon	—	—	—	—	18.02%	20.00%	22.61	32.42	18.88	38.82

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $27.07 | Strike (K): $28.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.6300 (Bid $1.4800 / Ask $1.7800) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 46.85% (CRR binomial tree, American, n=20 steps) | BS IV: 47.40% (European Black-Scholes) | Yahoo IV (Annual): 52.00% → 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 -0.06. Further, an Excess Kurtosis of 3.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.68%	7	0.63%	0.63%
-11.68% to -8.76%	12	1.08%	1.72%
-8.76% to -5.84%	45	4.07%	5.78%
-5.84% to -2.92%	132	11.92%	17.71%
-2.92% to 0.00%	354	31.98%	49.68%
0.00% to 2.92%	365	32.97%	82.66%
2.92% to 5.84%	128	11.56%	94.22%
5.84% to 8.76%	44	3.97%	98.19%
8.76% to 11.68%	7	0.63%	98.83%
Greater than 11.68%	13	1.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.89%	3.90%	76.51%	68.27%
±2σ	-7.79%	7.79%	95.03%	95.45%
±3σ	-11.68%	11.68%	98.19%	99.73%

Descriptive Statistics

Mean	0.001%
Standard Error	0.117%
Median	0.056%
Mode	0.000%
Standard Deviation	3.894%
Sample Variance	15.166%
Kurtosis	3.29
Skewness	-0.06
Range	39.614%
Minimum	-22.843%
Maximum	16.771%
Count	1107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.774%	557	50.32%	1.396%
Negative	-2.860%	540	48.78%	-1.395%
Zero	0.000%	10	0.90%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.79%
20	1 Month	4.87%
60	1 Quarter	3.98%
250	1 Year	4.27%
750	3 Years	4.33%
1,250	5 Years	5.50%
2,500	10 Years	5.50%
5,000	20 Years	5.50%
12,500	50 Years	5.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.77. Further, an Excess Kurtosis of 4.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.97%	0	0.00%	0.00%
-3.97% to -1.65%	0	0.00%	0.00%
-1.65% to 0.67%	0	0.00%	0.00%
0.67% to 2.99%	231	20.85%	20.85%
2.99% to 5.31%	466	42.06%	62.91%
5.31% to 7.63%	212	19.13%	82.04%
7.63% to 9.95%	101	9.12%	91.16%
9.95% to 12.27%	54	4.87%	96.03%
12.27% to 14.58%	26	2.35%	98.38%
Greater than 14.58%	18	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.22%	8.40%	80.14%	68.27%
±2σ	-0.88%	11.49%	95.04%	95.45%
±3σ	-3.97%	14.58%	98.38%	99.73%

Descriptive Statistics

Mean	5.308%
Standard Error	0.093%
Median	4.290%
Mode	2.906%
Standard Deviation	3.092%
Sample Variance	9.563%
Kurtosis	4.38
Skewness	1.77
Range	23.232%
Minimum	0.967%
Maximum	24.199%
Count	1108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.308%	1108	100.00%	5.308%
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 2.25 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.02%	6	0.54%	0.54%
-10.02% to -7.50%	6	0.54%	1.08%
-7.50% to -4.98%	50	4.51%	5.60%
-4.98% to -2.46%	144	13.00%	18.59%
-2.46% to 0.07%	379	34.21%	52.80%
0.07% to 2.59%	318	28.70%	81.50%
2.59% to 5.11%	129	11.64%	93.14%
5.11% to 7.63%	51	4.60%	97.74%
7.63% to 10.16%	18	1.62%	99.37%
Greater than 10.16%	7	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.30%	3.43%	73.92%	68.27%
±2σ	-6.66%	6.79%	94.58%	95.45%
±3σ	-10.02%	10.16%	98.83%	99.73%

Descriptive Statistics

Mean	0.067%
Standard Error	0.101%
Median	-0.072%
Mode	0.000%
Standard Deviation	3.363%
Sample Variance	11.309%
Kurtosis	2.25
Skewness	0.12
Range	34.068%
Minimum	-17.331%
Maximum	16.737%
Count	1108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.625%	535	48.28%	1.267%
Negative	-2.359%	564	50.90%	-1.201%
Zero	0.000%	9	0.81%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.00. Further, an Excess Kurtosis of 1.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.61%	1	0.43%	0.43%
-24.61% to -18.45%	4	1.74%	2.17%
-18.45% to -12.29%	9	3.91%	6.09%
-12.29% to -6.13%	28	12.17%	18.26%
-6.13% to 0.03%	75	32.61%	50.87%
0.03% to 6.19%	69	30.00%	80.87%
6.19% to 12.36%	29	12.61%	93.48%
12.36% to 18.52%	9	3.91%	97.39%
18.52% to 24.68%	4	1.74%	99.13%
Greater than 24.68%	2	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.18%	8.25%	73.48%	68.27%
±2σ	-16.40%	16.46%	94.78%	95.45%
±3σ	-24.61%	24.68%	98.70%	99.73%

Descriptive Statistics

Mean	0.033%
Standard Error	0.542%
Median	-0.066%
Mode	-8.175%
Standard Deviation	8.215%
Sample Variance	67.480%
Kurtosis	1.26
Skewness	0.00
Range	54.222%
Minimum	-29.057%
Maximum	25.165%
Count	230

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.189%	113	49.13%	3.041%
Negative	-5.963%	116	50.44%	-3.007%
Zero	0.000%	1	0.43%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.95%
12	1 Quarter	8.52%
52	1 Year	9.45%
156	3 Years	9.95%
260	5 Years	12.60%
520	10 Years	12.60%
1,040	20 Years	12.60%
2,600	50 Years	12.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.60. 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 -10.43%	0	0.00%	0.00%
-10.43% to -4.42%	0	0.00%	0.00%
-4.42% to 1.59%	0	0.00%	0.00%
1.59% to 7.60%	52	22.51%	22.51%
7.60% to 13.61%	96	41.56%	64.07%
13.61% to 19.62%	39	16.88%	80.95%
19.62% to 25.63%	21	9.09%	90.04%
25.63% to 31.64%	14	6.06%	96.10%
31.64% to 37.65%	5	2.16%	98.27%
Greater than 37.65%	4	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.60%	21.63%	78.35%	68.27%
±2σ	-2.41%	29.64%	96.10%	95.45%
±3σ	-10.43%	37.65%	98.27%	99.73%

Descriptive Statistics

Mean	13.614%
Standard Error	0.527%
Median	10.985%
Mode	11.069%
Standard Deviation	8.013%
Sample Variance	64.201%
Kurtosis	2.93
Skewness	1.60
Range	44.817%
Minimum	3.930%
Maximum	48.747%
Count	231

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.614%	231	100.00%	13.614%
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 0.88. Further, an Excess Kurtosis of 2.77 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.19%	0	0.00%	0.00%
-25.19% to -18.72%	1	0.43%	0.43%
-18.72% to -12.26%	9	3.90%	4.33%
-12.26% to -5.79%	33	14.29%	18.61%
-5.79% to 0.68%	83	35.93%	54.55%
0.68% to 7.14%	66	28.57%	83.12%
7.14% to 13.61%	23	9.96%	93.07%
13.61% to 20.07%	8	3.46%	96.54%
20.07% to 26.54%	6	2.60%	99.13%
Greater than 26.54%	2	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.95%	9.30%	74.89%	68.27%
±2σ	-16.57%	17.92%	93.07%	95.45%
±3σ	-25.19%	26.54%	99.13%	99.73%

Descriptive Statistics

Mean	0.676%
Standard Error	0.567%
Median	0.083%
Mode	-0.363%
Standard Deviation	8.622%
Sample Variance	74.337%
Kurtosis	2.77
Skewness	0.88
Range	60.785%
Minimum	-20.843%
Maximum	39.942%
Count	231

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.711%	117	50.65%	3.399%
Negative	-5.519%	114	49.35%	-2.724%
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 0.54. Further, an Excess Kurtosis of 0.35 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.84%	0	0.00%	0.00%
-46.84% to -35.12%	0	0.00%	0.00%
-35.12% to -23.41%	2	3.77%	3.77%
-23.41% to -11.70%	13	24.53%	28.30%
-11.70% to 0.02%	13	24.53%	52.83%
0.02% to 11.73%	14	26.42%	79.25%
11.73% to 23.44%	6	11.32%	90.57%
23.44% to 35.16%	4	7.55%	98.11%
35.16% to 46.87%	1	1.89%	100.00%
Greater than 46.87%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.60%	15.63%	73.58%	68.27%
±2σ	-31.22%	31.25%	94.34%	95.45%
±3σ	-46.84%	46.87%	100.00%	99.73%

Descriptive Statistics

Mean	0.017%
Standard Error	2.145%
Median	-1.797%
Mode	-34.082%
Standard Deviation	15.618%
Sample Variance	243.928%
Kurtosis	0.35
Skewness	0.54
Range	79.070%
Minimum	-34.082%
Maximum	44.988%
Count	53

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.169%	25	47.17%	6.212%
Negative	-11.726%	28	52.83%	-6.195%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.23%
12	1 Year	18.93%
36	3 Years	21.02%
60	5 Years	25.86%
120	10 Years	25.86%
240	20 Years	25.86%
600	50 Years	25.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.96. Further, an Excess Kurtosis of 4.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.52%	0	0.00%	0.00%
-19.52% to -6.96%	0	0.00%	0.00%
-6.96% to 5.60%	0	0.00%	0.00%
5.60% to 18.16%	8	14.81%	14.81%
18.16% to 30.73%	25	46.30%	61.11%
30.73% to 43.29%	13	24.07%	85.19%
43.29% to 55.85%	4	7.41%	92.59%
55.85% to 68.42%	1	1.85%	94.44%
68.42% to 80.98%	1	1.85%	96.30%
Greater than 80.98%	2	3.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.98%	47.48%	85.19%	68.27%
±2σ	-2.77%	64.23%	92.59%	95.45%
±3σ	-19.52%	80.98%	96.30%	99.73%

Descriptive Statistics

Mean	30.728%
Standard Error	2.280%
Median	24.631%
Mode	11.399%
Standard Deviation	16.751%
Sample Variance	280.593%
Kurtosis	4.21
Skewness	1.96
Range	78.505%
Minimum	11.399%
Maximum	89.904%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.728%	54	100.00%	30.728%
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 0.48. Further, an Excess Kurtosis of 0.58 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.55%	0	0.00%	0.00%
-45.55% to -33.45%	0	0.00%	0.00%
-33.45% to -21.36%	3	5.56%	5.56%
-21.36% to -9.26%	9	16.67%	22.22%
-9.26% to 2.83%	18	33.33%	55.56%
2.83% to 14.93%	8	14.81%	70.37%
14.93% to 27.02%	13	24.07%	94.44%
27.02% to 39.12%	2	3.70%	98.15%
39.12% to 51.21%	0	0.00%	98.15%
Greater than 51.21%	1	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.29%	18.96%	70.37%	68.27%
±2σ	-29.42%	35.09%	94.44%	95.45%
±3σ	-45.55%	51.21%	98.15%	99.73%

Descriptive Statistics

Mean	2.832%
Standard Error	2.195%
Median	1.424%
Mode	-30.799%
Standard Deviation	16.127%
Sample Variance	260.094%
Kurtosis	0.58
Skewness	0.48
Range	83.334%
Minimum	-30.799%
Maximum	52.535%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.553%	29	53.70%	7.816%
Negative	-10.763%	25	46.30%	-4.983%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.15. 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 -80.49%	0	0.00%	0.00%
-80.49% to -60.34%	0	0.00%	0.00%
-60.34% to -40.19%	1	5.56%	5.56%
-40.19% to -20.04%	2	11.11%	16.67%
-20.04% to 0.11%	6	33.33%	50.00%
0.11% to 20.25%	4	22.22%	72.22%
20.25% to 40.40%	5	27.78%	100.00%
40.40% to 60.55%	0	0.00%	100.00%
60.55% to 80.70%	0	0.00%	100.00%
Greater than 80.70%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.76%	26.97%	66.67%	68.27%
±2σ	-53.62%	53.83%	94.44%	95.45%
±3σ	-80.49%	80.70%	100.00%	99.73%

Descriptive Statistics

Mean	0.106%
Standard Error	6.332%
Median	-5.995%
Mode	-57.009%
Standard Deviation	26.864%
Sample Variance	721.662%
Kurtosis	-0.52
Skewness	-0.15
Range	95.244%
Minimum	-57.009%
Maximum	38.235%
Count	18

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.626%	9	50.00%	11.313%
Negative	-22.415%	9	50.00%	-11.208%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	29.57%
12	3 Years	36.85%
20	5 Years	42.73%
40	10 Years	42.73%
80	20 Years	42.73%
200	50 Years	42.73%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.76. Further, an Excess Kurtosis of 15.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -101.60%	0	0.00%	0.00%
-101.60% to -61.09%	0	0.00%	0.00%
-61.09% to -20.57%	0	0.00%	0.00%
-20.57% to 19.94%	0	0.00%	0.00%
19.94% to 60.46%	15	78.95%	78.95%
60.46% to 100.97%	3	15.79%	94.74%
100.97% to 141.48%	0	0.00%	94.74%
141.48% to 182.00%	0	0.00%	94.74%
182.00% to 222.51%	0	0.00%	94.74%
Greater than 222.51%	1	5.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.44%	114.47%	94.74%	68.27%
±2σ	-47.58%	168.49%	94.74%	95.45%
±3σ	-101.60%	222.51%	94.74%	99.73%

Descriptive Statistics

Mean	60.456%
Standard Error	12.393%
Median	45.460%
Mode	24.161%
Standard Deviation	54.019%
Sample Variance	2918.051%
Kurtosis	15.28
Skewness	3.76
Range	249.397%
Minimum	24.161%
Maximum	273.558%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	60.456%	19	100.00%	60.456%
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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.19. Further, an Excess Kurtosis of 7.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.86%	0	0.00%	0.00%
-103.86% to -75.43%	0	0.00%	0.00%
-75.43% to -46.99%	0	0.00%	0.00%
-46.99% to -18.56%	4	21.05%	21.05%
-18.56% to 9.87%	5	26.32%	47.37%
9.87% to 38.31%	9	47.37%	94.74%
38.31% to 66.74%	0	0.00%	94.74%
66.74% to 95.18%	0	0.00%	94.74%
95.18% to 123.61%	0	0.00%	94.74%
Greater than 123.61%	1	5.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.04%	47.79%	89.47%	68.27%
±2σ	-65.95%	85.70%	94.74%	95.45%
±3σ	-103.86%	123.61%	94.74%	99.73%

Descriptive Statistics

Mean	9.874%
Standard Error	8.698%
Median	10.287%
Mode	-28.655%
Standard Deviation	37.913%
Sample Variance	1437.379%
Kurtosis	7.01
Skewness	2.19
Range	167.029%
Minimum	-28.655%
Maximum	138.374%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.194%	11	57.90%	18.060%
Negative	-19.440%	8	42.10%	-8.185%
Zero	0.000%	0	0.00%	0.000%

TOST Deep Analytical Report