TDOC - 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	3.85%	3.02%	3.42%	5.51%	5.38%	5.46%	4.49	5.00	4.26	5.28
Weekly	8.67%	8.82%	8.86%	12.86%	11.84%	12.03%	4.21	5.34	3.74	6.01
Monthly	15.81%	18.25%	18.21%	26.24%	24.64%	25.03%	3.70	6.06	2.90	7.76
Quarterly	27.78%	34.42%	36.11%	44.16%	42.68%	43.36%	3.09	7.26	2.02	11.13
Annual	—	—	—	—	85.36%	86.72%	2.02	11.13	0.86	26.13
Option Time Horizon	—	—	—	—	32.83%	33.36%	3.41	6.58	2.46	9.14

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $4.74 | Strike (K): $5.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.5300 (Bid $0.5000 / Ask $0.5600) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 85.36% (CRR binomial tree, American, n=20 steps) | BS IV: 86.24% (European Black-Scholes) | Yahoo IV (Annual): 86.72% → 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 -0.20. Further, an Excess Kurtosis of 7.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.54%	12	0.45%	0.45%
-11.54% to -8.66%	21	0.79%	1.23%
-8.66% to -5.77%	95	3.55%	4.79%
-5.77% to -2.88%	390	14.58%	19.36%
-2.88% to 0.01%	824	30.80%	50.17%
0.01% to 2.90%	820	30.65%	80.82%
2.90% to 5.78%	373	13.94%	94.77%
5.78% to 8.67%	87	3.25%	98.02%
8.67% to 11.56%	36	1.35%	99.36%
Greater than 11.56%	17	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.84%	3.86%	74.73%	68.27%
±2σ	-7.69%	7.71%	95.29%	95.45%
±3σ	-11.55%	11.56%	98.92%	99.73%

Descriptive Statistics

Mean	0.008%
Standard Error	0.074%
Median	0.000%
Mode	0.000%
Standard Deviation	3.851%
Sample Variance	14.833%
Kurtosis	7.73
Skewness	-0.20
Range	67.103%
Minimum	-40.150%
Maximum	26.953%
Count	2675

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.808%	1333	49.83%	1.399%
Negative	-2.828%	1316	49.20%	-1.391%
Zero	0.000%	26	0.97%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.14%
20	1 Month	5.76%
60	1 Quarter	4.49%
250	1 Year	5.28%
750	3 Years	5.04%
1,250	5 Years	5.51%
2,500	10 Years	5.29%
5,000	20 Years	5.41%
12,500	50 Years	5.41%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.32. Further, an Excess Kurtosis of 9.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.76%	0	0.00%	0.00%
-3.76% to -1.50%	0	0.00%	0.00%
-1.50% to 0.76%	0	0.00%	0.00%
0.76% to 3.03%	527	19.69%	19.69%
3.03% to 5.29%	1158	43.27%	62.97%
5.29% to 7.55%	546	20.40%	83.37%
7.55% to 9.82%	252	9.42%	92.79%
9.82% to 12.08%	94	3.51%	96.30%
12.08% to 14.34%	53	1.98%	98.28%
Greater than 14.34%	46	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.27%	8.31%	80.64%	68.27%
±2σ	-0.75%	11.33%	95.25%	95.45%
±3σ	-3.76%	14.34%	98.28%	99.73%

Descriptive Statistics

Mean	5.290%
Standard Error	0.058%
Median	4.551%
Mode	3.222%
Standard Deviation	3.018%
Sample Variance	9.109%
Kurtosis	9.74
Skewness	2.32
Range	30.428%
Minimum	1.131%
Maximum	31.559%
Count	2676

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.290%	2676	100.00%	5.290%
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 0.15. Further, an Excess Kurtosis of 2.75 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.15%	15	0.56%	0.56%
-10.15% to -7.59%	29	1.08%	1.64%
-7.59% to -5.03%	110	4.11%	5.75%
-5.03% to -2.47%	369	13.79%	19.54%
-2.47% to 0.09%	832	31.09%	50.64%
0.09% to 2.65%	809	30.23%	80.87%
2.65% to 5.21%	351	13.12%	93.98%
5.21% to 7.77%	114	4.26%	98.24%
7.77% to 10.34%	33	1.23%	99.48%
Greater than 10.34%	14	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.33%	3.50%	73.77%	68.27%
±2σ	-6.74%	6.92%	94.81%	95.45%
±3σ	-10.16%	10.34%	98.92%	99.73%

Descriptive Statistics

Mean	0.090%
Standard Error	0.066%
Median	0.025%
Mode	0.000%
Standard Deviation	3.415%
Sample Variance	11.660%
Kurtosis	2.75
Skewness	0.15
Range	39.226%
Minimum	-16.008%
Maximum	23.218%
Count	2676

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.611%	1345	50.26%	1.312%
Negative	-2.523%	1296	48.43%	-1.222%
Zero	0.000%	35	1.31%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of 3.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.96%	2	0.36%	0.36%
-25.96% to -19.45%	6	1.08%	1.44%
-19.45% to -12.95%	26	4.68%	6.13%
-12.95% to -6.44%	74	13.33%	19.46%
-6.44% to 0.06%	172	30.99%	50.45%
0.06% to 6.57%	176	31.71%	82.16%
6.57% to 13.07%	72	12.97%	95.14%
13.07% to 19.58%	15	2.70%	97.84%
19.58% to 26.09%	5	0.90%	98.74%
Greater than 26.09%	7	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.61%	8.74%	75.14%	68.27%
±2σ	-17.28%	17.41%	94.59%	95.45%
±3σ	-25.96%	26.09%	98.38%	99.73%

Descriptive Statistics

Mean	0.064%
Standard Error	0.368%
Median	0.000%
Mode	0.000%
Standard Deviation	8.674%
Sample Variance	75.245%
Kurtosis	3.03
Skewness	0.36
Range	82.102%
Minimum	-38.672%
Maximum	43.430%
Count	555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.404%	275	49.55%	3.173%
Negative	-6.229%	277	49.91%	-3.109%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.87%
12	1 Quarter	9.86%
52	1 Year	12.11%
156	3 Years	11.72%
260	5 Years	12.86%
520	10 Years	12.24%
1,040	20 Years	12.55%
2,600	50 Years	12.55%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.82. Further, an Excess Kurtosis of 29.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.83%	0	0.00%	0.00%
-12.83% to -6.21%	0	0.00%	0.00%
-6.21% to 0.41%	0	0.00%	0.00%
0.41% to 7.03%	90	16.19%	16.19%
7.03% to 13.64%	261	46.94%	63.13%
13.64% to 20.26%	134	24.10%	87.23%
20.26% to 26.88%	35	6.29%	93.53%
26.88% to 33.50%	18	3.24%	96.76%
33.50% to 40.12%	9	1.62%	98.38%
Greater than 40.12%	9	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.82%	22.47%	85.97%	68.27%
±2σ	-4.00%	31.29%	95.50%	95.45%
±3σ	-12.83%	40.12%	98.38%	99.73%

Descriptive Statistics

Mean	13.644%
Standard Error	0.374%
Median	11.702%
Mode	7.438%
Standard Deviation	8.824%
Sample Variance	77.870%
Kurtosis	29.57
Skewness	3.82
Range	107.897%
Minimum	2.781%
Maximum	110.678%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.644%	556	100.00%	13.644%
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 0.98. Further, an Excess Kurtosis of 4.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.76%	3	0.54%	0.54%
-25.76% to -19.11%	3	0.54%	1.08%
-19.11% to -12.47%	15	2.70%	3.78%
-12.47% to -5.82%	84	15.11%	18.88%
-5.82% to 0.82%	192	34.53%	53.42%
0.82% to 7.47%	166	29.86%	83.27%
7.47% to 14.12%	56	10.07%	93.35%
14.12% to 20.76%	20	3.60%	96.94%
20.76% to 27.41%	14	2.52%	99.46%
Greater than 27.41%	3	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.04%	9.68%	76.44%	68.27%
±2σ	-16.90%	18.55%	94.78%	95.45%
±3σ	-25.76%	27.41%	98.92%	99.73%

Descriptive Statistics

Mean	0.823%
Standard Error	0.376%
Median	0.150%
Mode	0.000%
Standard Deviation	8.861%
Sample Variance	78.525%
Kurtosis	4.95
Skewness	0.98
Range	89.691%
Minimum	-28.356%
Maximum	61.335%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.990%	286	51.44%	3.596%
Negative	-5.773%	267	48.02%	-2.772%
Zero	0.000%	3	0.54%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.04. Further, an Excess Kurtosis of 0.16 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -47.61%	1	0.79%	0.79%
-47.61% to -35.76%	0	0.00%	0.79%
-35.76% to -23.91%	5	3.94%	4.72%
-23.91% to -12.05%	26	20.47%	25.20%
-12.05% to -0.20%	32	25.20%	50.39%
-0.20% to 11.66%	34	26.77%	77.17%
11.66% to 23.51%	18	14.17%	91.34%
23.51% to 35.37%	10	7.87%	99.21%
35.37% to 47.22%	1	0.79%	100.00%
Greater than 47.22%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.00%	15.61%	68.50%	68.27%
±2σ	-31.81%	31.42%	96.06%	95.45%
±3σ	-47.61%	47.22%	99.21%	99.73%

Descriptive Statistics

Mean	-0.196%
Standard Error	1.403%
Median	-0.302%
Mode	-53.196%
Standard Deviation	15.806%
Sample Variance	249.823%
Kurtosis	0.16
Skewness	0.04
Range	93.353%
Minimum	-53.196%
Maximum	40.157%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.009%	61	48.03%	6.248%
Negative	-12.591%	65	51.18%	-6.444%
Zero	0.000%	1	0.79%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.30%
12	1 Year	22.90%
36	3 Years	24.42%
60	5 Years	26.24%
120	10 Years	26.14%
240	20 Years	26.61%
600	50 Years	26.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.67. Further, an Excess Kurtosis of 24.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.61%	0	0.00%	0.00%
-22.61% to -8.93%	0	0.00%	0.00%
-8.93% to 4.76%	0	0.00%	0.00%
4.76% to 18.44%	27	21.09%	21.09%
18.44% to 32.12%	47	36.72%	57.81%
32.12% to 45.81%	36	28.12%	85.94%
45.81% to 59.49%	13	10.16%	96.09%
59.49% to 73.18%	4	3.12%	99.22%
73.18% to 86.86%	0	0.00%	99.22%
Greater than 86.86%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.88%	50.37%	83.59%	68.27%
±2σ	-4.37%	68.62%	96.88%	95.45%
±3σ	-22.61%	86.86%	99.22%	99.73%

Descriptive Statistics

Mean	32.125%
Standard Error	1.613%
Median	29.444%
Mode	9.714%
Standard Deviation	18.246%
Sample Variance	332.908%
Kurtosis	24.57
Skewness	3.67
Range	159.851%
Minimum	9.714%
Maximum	169.565%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.125%	128	100.00%	32.125%
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 2.01. Further, an Excess Kurtosis of 10.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.76%	0	0.00%	0.00%
-51.76% to -38.10%	0	0.00%	0.00%
-38.10% to -24.45%	2	1.56%	1.56%
-24.45% to -10.79%	24	18.75%	20.31%
-10.79% to 2.86%	44	34.38%	54.69%
2.86% to 16.51%	34	26.56%	81.25%
16.51% to 30.17%	20	15.62%	96.88%
30.17% to 43.82%	1	0.78%	97.66%
43.82% to 57.48%	2	1.56%	99.22%
Greater than 57.48%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.35%	21.06%	75.78%	68.27%
±2σ	-33.55%	39.27%	97.66%	95.45%
±3σ	-51.76%	57.48%	99.22%	99.73%

Descriptive Statistics

Mean	2.859%
Standard Error	1.609%
Median	0.554%
Mode	-28.402%
Standard Deviation	18.206%
Sample Variance	331.464%
Kurtosis	10.54
Skewness	2.01
Range	144.190%
Minimum	-28.402%
Maximum	115.788%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.130%	68	53.12%	8.038%
Negative	-11.049%	60	46.88%	-5.179%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.01. 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 -83.59%	0	0.00%	0.00%
-83.59% to -62.76%	0	0.00%	0.00%
-62.76% to -41.92%	3	6.98%	6.98%
-41.92% to -21.08%	7	16.28%	23.26%
-21.08% to -0.24%	11	25.58%	48.84%
-0.24% to 20.60%	13	30.23%	79.07%
20.60% to 41.43%	6	13.95%	93.02%
41.43% to 62.27%	3	6.98%	100.00%
62.27% to 83.11%	0	0.00%	100.00%
Greater than 83.11%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.03%	27.54%	65.12%	68.27%
±2σ	-55.81%	55.33%	95.35%	95.45%
±3σ	-83.59%	83.11%	100.00%	99.73%

Descriptive Statistics

Mean	-0.242%
Standard Error	4.237%
Median	0.278%
Mode	-55.990%
Standard Deviation	27.784%
Sample Variance	771.943%
Kurtosis	-0.58
Skewness	0.01
Range	117.813%
Minimum	-55.990%
Maximum	61.823%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.035%	22	51.16%	11.274%
Negative	-23.581%	21	48.84%	-11.516%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	34.10%
12	3 Years	43.27%
20	5 Years	44.16%
40	10 Years	45.66%
80	20 Years	46.28%
200	50 Years	46.28%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.55. Further, an Excess Kurtosis of 2.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.90%	0	0.00%	0.00%
-39.90% to -14.08%	0	0.00%	0.00%
-14.08% to 11.74%	0	0.00%	0.00%
11.74% to 37.55%	9	20.45%	20.45%
37.55% to 63.37%	21	47.73%	68.18%
63.37% to 89.19%	6	13.64%	81.82%
89.19% to 115.01%	3	6.82%	88.64%
115.01% to 140.83%	4	9.09%	97.73%
140.83% to 166.65%	0	0.00%	97.73%
Greater than 166.65%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	28.95%	97.80%	79.55%	68.27%
±2σ	-5.48%	132.22%	93.18%	95.45%
±3σ	-39.90%	166.65%	97.73%	99.73%

Descriptive Statistics

Mean	63.373%
Standard Error	5.190%
Median	49.875%
Mode	26.818%
Standard Deviation	34.425%
Sample Variance	1185.101%
Kurtosis	2.35
Skewness	1.55
Range	154.330%
Minimum	26.818%
Maximum	181.148%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	63.373%	44	100.00%	63.373%
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 1.45. Further, an Excess Kurtosis of 2.36 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -99.42%	0	0.00%	0.00%
-99.42% to -72.33%	0	0.00%	0.00%
-72.33% to -45.25%	0	0.00%	0.00%
-45.25% to -18.17%	8	18.18%	18.18%
-18.17% to 8.91%	19	43.18%	61.36%
8.91% to 35.99%	9	20.45%	81.82%
35.99% to 63.07%	5	11.36%	93.18%
63.07% to 90.16%	1	2.27%	95.45%
90.16% to 117.24%	1	2.27%	97.73%
Greater than 117.24%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.20%	45.02%	75.00%	68.27%
±2σ	-63.31%	81.13%	95.45%	95.45%
±3σ	-99.42%	117.24%	97.73%	99.73%

Descriptive Statistics

Mean	8.910%
Standard Error	5.444%
Median	-1.090%
Mode	-37.609%
Standard Deviation	36.109%
Sample Variance	1303.868%
Kurtosis	2.36
Skewness	1.45
Range	170.636%
Minimum	-37.609%
Maximum	133.027%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.737%	21	47.73%	17.533%
Negative	-16.497%	23	52.27%	-8.623%
Zero	0.000%	0	0.00%	0.000%

TDOC Deep Analytical Report