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	3.88%	3.08%	3.36%	5.49%	4.34%	4.36%	26.21	28.59	25.10	29.86
Weekly	8.21%	7.95%	8.62%	12.61%	9.56%	9.61%	24.88	30.12	22.61	33.14
Monthly	15.46%	16.68%	15.98%	25.78%	19.90%	20.00%	22.43	33.40	18.39	40.76
Quarterly	26.83%	53.75%	37.90%	43.01%	34.47%	34.64%	19.39	38.64	13.74	54.55
Annual	—	—	—	—	68.95%	69.29%	13.74	54.55	6.89	108.70
Option Time Horizon	—	—	—	—	26.02%	26.15%	21.10	35.51	16.27	46.07

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $27.38 | Strike (K): $28.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.6350 (Bid $2.3600 / Ask $2.9100) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 68.95% (CRR binomial tree, American, n=20 steps) | BS IV: 69.15% (European Black-Scholes) | Yahoo IV (Annual): 69.29% → 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 -11.63%	7	0.62%	0.62%
-11.63% to -8.72%	12	1.06%	1.68%
-8.72% to -5.82%	46	4.08%	5.76%
-5.82% to -2.91%	133	11.79%	17.55%
-2.91% to 0.00%	362	32.09%	49.65%
0.00% to 2.91%	372	32.98%	82.62%
2.91% to 5.82%	132	11.70%	94.33%
5.82% to 8.73%	44	3.90%	98.23%
8.73% to 11.64%	7	0.62%	98.85%
Greater than 11.64%	13	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.88%	3.88%	76.51%	68.27%
±2σ	-7.75%	7.76%	95.04%	95.45%
±3σ	-11.63%	11.64%	98.23%	99.73%

Descriptive Statistics

Mean	0.003%
Standard Error	0.115%
Median	0.057%
Mode	0.000%
Standard Deviation	3.879%
Sample Variance	15.043%
Kurtosis	3.29
Skewness	-0.06
Range	39.614%
Minimum	-22.843%
Maximum	16.771%
Count	1128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.764%	568	50.35%	1.392%
Negative	-2.854%	549	48.67%	-1.389%
Zero	0.000%	11	0.97%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.71%
20	1 Month	4.90%
60	1 Quarter	4.59%
250	1 Year	4.24%
750	3 Years	4.34%
1,250	5 Years	5.49%
2,500	10 Years	5.49%
5,000	20 Years	5.49%
12,500	50 Years	5.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.78. Further, an Excess Kurtosis of 4.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.92%	0	0.00%	0.00%
-3.92% to -1.62%	0	0.00%	0.00%
-1.62% to 0.69%	0	0.00%	0.00%
0.69% to 3.00%	235	20.81%	20.81%
3.00% to 5.30%	475	42.07%	62.89%
5.30% to 7.61%	218	19.31%	82.20%
7.61% to 9.91%	102	9.03%	91.23%
9.91% to 12.22%	55	4.87%	96.10%
12.22% to 14.53%	26	2.30%	98.41%
Greater than 14.53%	18	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.23%	8.38%	80.16%	68.27%
±2σ	-0.85%	11.45%	95.04%	95.45%
±3σ	-3.92%	14.53%	98.41%	99.73%

Descriptive Statistics

Mean	5.302%
Standard Error	0.092%
Median	4.288%
Mode	2.906%
Standard Deviation	3.075%
Sample Variance	9.458%
Kurtosis	4.44
Skewness	1.78
Range	23.232%
Minimum	0.967%
Maximum	24.199%
Count	1129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.302%	1129	100.00%	5.302%
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 2.23 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	0.53%	0.53%
-10.02% to -7.50%	7	0.62%	1.15%
-7.50% to -4.98%	50	4.43%	5.58%
-4.98% to -2.46%	148	13.11%	18.69%
-2.46% to 0.05%	381	33.75%	52.44%
0.05% to 2.57%	330	29.23%	81.67%
2.57% to 5.09%	128	11.34%	93.00%
5.09% to 7.61%	54	4.78%	97.79%
7.61% to 10.12%	18	1.59%	99.38%
Greater than 10.12%	7	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.30%	3.41%	74.14%	68.27%
±2σ	-6.66%	6.77%	94.60%	95.45%
±3σ	-10.02%	10.13%	98.85%	99.73%

Descriptive Statistics

Mean	0.054%
Standard Error	0.100%
Median	-0.085%
Mode	0.000%
Standard Deviation	3.357%
Sample Variance	11.268%
Kurtosis	2.23
Skewness	0.12
Range	34.068%
Minimum	-17.331%
Maximum	16.737%
Count	1129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.614%	544	48.18%	1.260%
Negative	-2.362%	576	51.02%	-1.205%
Zero	0.000%	9	0.80%	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 1.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.58%	1	0.43%	0.43%
-24.58% to -18.42%	4	1.71%	2.14%
-18.42% to -12.27%	9	3.85%	5.98%
-12.27% to -6.11%	29	12.39%	18.38%
-6.11% to 0.04%	76	32.48%	50.85%
0.04% to 6.20%	69	29.49%	80.34%
6.20% to 12.36%	31	13.25%	93.59%
12.36% to 18.51%	9	3.85%	97.44%
18.51% to 24.66%	4	1.71%	99.15%
Greater than 24.66%	2	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.16%	8.25%	72.22%	68.27%
±2σ	-16.37%	16.46%	94.87%	95.45%
±3σ	-24.58%	24.67%	98.72%	99.73%

Descriptive Statistics

Mean	0.044%
Standard Error	0.537%
Median	-0.066%
Mode	-8.175%
Standard Deviation	8.207%
Sample Variance	67.361%
Kurtosis	1.22
Skewness	0.00
Range	54.222%
Minimum	-29.057%
Maximum	25.165%
Count	234

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.229%	115	49.15%	3.061%
Negative	-5.983%	118	50.43%	-3.017%
Zero	0.000%	1	0.43%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.45%
12	1 Quarter	10.71%
52	1 Year	9.68%
156	3 Years	10.03%
260	5 Years	12.61%
520	10 Years	12.61%
1,040	20 Years	12.61%
2,600	50 Years	12.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.61. Further, an Excess Kurtosis of 3.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.23%	0	0.00%	0.00%
-10.23% to -4.27%	0	0.00%	0.00%
-4.27% to 1.69%	0	0.00%	0.00%
1.69% to 7.66%	52	22.13%	22.13%
7.66% to 13.62%	97	41.28%	63.40%
13.62% to 19.58%	42	17.87%	81.28%
19.58% to 25.54%	21	8.94%	90.21%
25.54% to 31.50%	14	5.96%	96.17%
31.50% to 37.46%	5	2.13%	98.30%
Greater than 37.46%	4	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.67%	21.57%	77.87%	68.27%
±2σ	-2.28%	29.52%	96.17%	95.45%
±3σ	-10.23%	37.46%	98.30%	99.73%

Descriptive Statistics

Mean	13.617%
Standard Error	0.519%
Median	11.062%
Mode	11.069%
Standard Deviation	7.949%
Sample Variance	63.192%
Kurtosis	3.02
Skewness	1.61
Range	44.817%
Minimum	3.930%
Maximum	48.747%
Count	235

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.617%	235	100.00%	13.617%
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 2.70 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.22%	0	0.00%	0.00%
-25.22% to -18.75%	1	0.43%	0.43%
-18.75% to -12.28%	9	3.83%	4.26%
-12.28% to -5.82%	35	14.89%	19.15%
-5.82% to 0.65%	83	35.32%	54.47%
0.65% to 7.11%	67	28.51%	82.98%
7.11% to 13.58%	24	10.21%	93.19%
13.58% to 20.04%	8	3.40%	96.60%
20.04% to 26.51%	6	2.55%	99.15%
Greater than 26.51%	2	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.97%	9.27%	74.04%	68.27%
±2σ	-16.60%	17.89%	93.19%	95.45%
±3σ	-25.22%	26.51%	99.15%	99.73%

Descriptive Statistics

Mean	0.647%
Standard Error	0.562%
Median	0.083%
Mode	-0.363%
Standard Deviation	8.621%
Sample Variance	74.330%
Kurtosis	2.70
Skewness	0.86
Range	60.785%
Minimum	-20.843%
Maximum	39.942%
Count	235

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.723%	119	50.64%	3.404%
Negative	-5.586%	116	49.36%	-2.757%
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 0.42 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.33%	0	0.00%	0.00%
-46.33% to -34.74%	0	0.00%	0.00%
-34.74% to -23.14%	2	3.70%	3.70%
-23.14% to -11.55%	14	25.93%	29.63%
-11.55% to 0.04%	12	22.22%	51.85%
0.04% to 11.64%	15	27.78%	79.63%
11.64% to 23.23%	6	11.11%	90.74%
23.23% to 34.82%	4	7.41%	98.15%
34.82% to 46.42%	1	1.85%	100.00%
Greater than 46.42%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.42%	15.50%	72.22%	68.27%
±2σ	-30.87%	30.96%	94.44%	95.45%
±3σ	-46.33%	46.42%	100.00%	99.73%

Descriptive Statistics

Mean	0.043%
Standard Error	2.104%
Median	-1.405%
Mode	-34.082%
Standard Deviation	15.458%
Sample Variance	238.965%
Kurtosis	0.42
Skewness	0.54
Range	79.070%
Minimum	-34.082%
Maximum	44.988%
Count	54

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.688%	26	48.15%	6.109%
Negative	-11.698%	28	51.85%	-6.066%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.73%
12	1 Year	19.26%
36	3 Years	21.10%
60	5 Years	25.78%
120	10 Years	25.78%
240	20 Years	25.78%
600	50 Years	25.78%

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 4.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.43%	0	0.00%	0.00%
-19.43% to -6.92%	0	0.00%	0.00%
-6.92% to 5.59%	0	0.00%	0.00%
5.59% to 18.11%	9	16.36%	16.36%
18.11% to 30.62%	23	41.82%	58.18%
30.62% to 43.13%	14	25.45%	83.64%
43.13% to 55.64%	5	9.09%	92.73%
55.64% to 68.15%	1	1.82%	94.55%
68.15% to 80.66%	1	1.82%	96.36%
Greater than 80.66%	2	3.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.94%	47.30%	85.45%	68.27%
±2σ	-2.75%	63.98%	92.73%	95.45%
±3σ	-19.43%	80.66%	96.36%	99.73%

Descriptive Statistics

Mean	30.617%
Standard Error	2.249%
Median	25.096%
Mode	11.399%
Standard Deviation	16.682%
Sample Variance	278.273%
Kurtosis	4.25
Skewness	1.96
Range	78.505%
Minimum	11.399%
Maximum	89.904%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.617%	55	100.00%	30.617%
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 0.50. Further, an Excess Kurtosis of 0.66 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.23%	0	0.00%	0.00%
-45.23% to -33.25%	0	0.00%	0.00%
-33.25% to -21.26%	3	5.45%	5.45%
-21.26% to -9.28%	9	16.36%	21.82%
-9.28% to 2.71%	19	34.55%	56.36%
2.71% to 14.70%	9	16.36%	72.73%
14.70% to 26.68%	12	21.82%	94.55%
26.68% to 38.67%	2	3.64%	98.18%
38.67% to 50.65%	0	0.00%	98.18%
Greater than 50.65%	1	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.27%	18.69%	69.09%	68.27%
±2σ	-29.25%	34.67%	94.55%	95.45%
±3σ	-45.23%	50.65%	98.18%	99.73%

Descriptive Statistics

Mean	2.710%
Standard Error	2.155%
Median	1.294%
Mode	-30.799%
Standard Deviation	15.981%
Sample Variance	255.403%
Kurtosis	0.66
Skewness	0.50
Range	83.334%
Minimum	-30.799%
Maximum	52.535%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.518%	29	52.73%	7.655%
Negative	-10.460%	26	47.27%	-4.945%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.16. Further, an Excess Kurtosis of -0.50 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.30%	0	0.00%	0.00%
-80.30% to -60.18%	0	0.00%	0.00%
-60.18% to -40.06%	1	5.56%	5.56%
-40.06% to -19.94%	2	11.11%	16.67%
-19.94% to 0.18%	6	33.33%	50.00%
0.18% to 20.30%	4	22.22%	72.22%
20.30% to 40.42%	5	27.78%	100.00%
40.42% to 60.54%	0	0.00%	100.00%
60.54% to 80.66%	0	0.00%	100.00%
Greater than 80.66%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.65%	27.01%	66.67%	68.27%
±2σ	-53.47%	53.84%	94.44%	95.45%
±3σ	-80.30%	80.66%	100.00%	99.73%

Descriptive Statistics

Mean	0.181%
Standard Error	6.323%
Median	-5.320%
Mode	-57.009%
Standard Deviation	26.827%
Sample Variance	719.684%
Kurtosis	-0.50
Skewness	-0.16
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	-22.265%	9	50.00%	-11.132%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	30.82%
12	3 Years	37.27%
20	5 Years	43.01%
40	10 Years	43.01%
80	20 Years	43.01%
200	50 Years	43.01%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.80. Further, an Excess Kurtosis of 15.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -100.38%	0	0.00%	0.00%
-100.38% to -60.07%	0	0.00%	0.00%
-60.07% to -19.75%	0	0.00%	0.00%
-19.75% to 20.56%	0	0.00%	0.00%
20.56% to 60.88%	15	78.95%	78.95%
60.88% to 101.19%	3	15.79%	94.74%
101.19% to 141.50%	0	0.00%	94.74%
141.50% to 181.82%	0	0.00%	94.74%
181.82% to 222.13%	0	0.00%	94.74%
Greater than 222.13%	1	5.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.12%	114.63%	94.74%	68.27%
±2σ	-46.63%	168.38%	94.74%	95.45%
±3σ	-100.38%	222.13%	94.74%	99.73%

Descriptive Statistics

Mean	60.875%
Standard Error	12.332%
Median	45.460%
Mode	29.134%
Standard Deviation	53.752%
Sample Variance	2889.304%
Kurtosis	15.49
Skewness	3.80
Range	244.424%
Minimum	29.134%
Maximum	273.558%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	60.875%	19	100.00%	60.875%
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 2.20. Further, an Excess Kurtosis of 7.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.92%	0	0.00%	0.00%
-103.92% to -75.49%	0	0.00%	0.00%
-75.49% to -47.07%	0	0.00%	0.00%
-47.07% to -18.64%	4	21.05%	21.05%
-18.64% to 9.78%	5	26.32%	47.37%
9.78% to 38.21%	9	47.37%	94.74%
38.21% to 66.63%	0	0.00%	94.74%
66.63% to 95.06%	0	0.00%	94.74%
95.06% to 123.48%	0	0.00%	94.74%
Greater than 123.48%	1	5.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.12%	47.68%	89.47%	68.27%
±2σ	-66.02%	85.58%	94.74%	95.45%
±3σ	-103.92%	123.48%	94.74%	99.73%

Descriptive Statistics

Mean	9.782%
Standard Error	8.695%
Median	10.287%
Mode	-28.655%
Standard Deviation	37.900%
Sample Variance	1436.415%
Kurtosis	7.05
Skewness	2.20
Range	167.029%
Minimum	-28.655%
Maximum	138.374%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.034%	11	57.90%	17.967%
Negative	-19.440%	8	42.10%	-8.185%
Zero	0.000%	0	0.00%	0.000%

TOST Deep Analytical Report