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%	5.49%	5.38%	5.39%	5.12	5.70	4.85	6.02
Weekly	8.66%	8.81%	8.86%	12.81%	11.84%	11.86%	4.80	6.08	4.27	6.85
Monthly	15.71%	18.18%	18.12%	26.17%	24.64%	24.70%	4.22	6.92	3.30	8.85
Quarterly	27.71%	34.18%	36.12%	44.63%	42.68%	42.77%	3.53	8.28	2.30	12.69
Annual	—	—	—	—	85.36%	85.55%	2.30	12.69	0.98	29.80
Option Time Horizon	—	—	—	—	32.22%	32.29%	3.92	7.46	2.84	10.30

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $5.41 | Strike (K): $6.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.4850 (Bid $0.4300 / Ask $0.5400) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 85.36% (CRR binomial tree, American, n=20 steps) | BS IV: 85.98% (European Black-Scholes) | Yahoo IV (Annual): 85.55% → 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 -0.17. Further, an Excess Kurtosis of 7.72 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 -8.65%	21	0.78%	1.22%
-8.65% to -5.77%	95	3.52%	4.75%
-5.77% to -2.88%	393	14.58%	19.32%
-2.88% to 0.01%	833	30.90%	50.22%
0.01% to 2.90%	827	30.68%	80.90%
2.90% to 5.79%	376	13.95%	94.84%
5.79% to 8.68%	85	3.15%	98.00%
8.68% to 11.57%	36	1.34%	99.33%
Greater than 11.57%	18	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.84%	3.87%	74.70%	68.27%
±2σ	-7.69%	7.72%	95.29%	95.45%
±3σ	-11.55%	11.57%	98.89%	99.73%

Descriptive Statistics

Mean	0.014%
Standard Error	0.074%
Median	0.000%
Mode	0.000%
Standard Deviation	3.853%
Sample Variance	14.848%
Kurtosis	7.72
Skewness	-0.17
Range	67.103%
Minimum	-40.150%
Maximum	26.953%
Count	2696

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.814%	1343	49.81%	1.402%
Negative	-2.820%	1327	49.22%	-1.388%
Zero	0.000%	26	0.96%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.54%
20	1 Month	5.42%
60	1 Quarter	5.15%
250	1 Year	5.19%
750	3 Years	5.06%
1,250	5 Years	5.49%
2,500	10 Years	5.28%
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 9.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.77%	0	0.00%	0.00%
-3.77% to -1.50%	0	0.00%	0.00%
-1.50% to 0.76%	0	0.00%	0.00%
0.76% to 3.03%	529	19.61%	19.61%
3.03% to 5.29%	1172	43.46%	63.07%
5.29% to 7.55%	549	20.36%	83.43%
7.55% to 9.82%	252	9.34%	92.77%
9.82% to 12.08%	95	3.52%	96.29%
12.08% to 14.34%	53	1.97%	98.26%
Greater than 14.34%	47	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.27%	8.31%	80.72%	68.27%
±2σ	-0.75%	11.32%	95.25%	95.45%
±3σ	-3.76%	14.34%	98.26%	99.73%

Descriptive Statistics

Mean	5.289%
Standard Error	0.058%
Median	4.549%
Mode	3.222%
Standard Deviation	3.018%
Sample Variance	9.106%
Kurtosis	9.71
Skewness	2.32
Range	30.428%
Minimum	1.131%
Maximum	31.559%
Count	2697

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.289%	2697	100.00%	5.289%
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 -10.16%	16	0.59%	0.59%
-10.16% to -7.60%	29	1.08%	1.67%
-7.60% to -5.04%	111	4.12%	5.78%
-5.04% to -2.48%	369	13.68%	19.47%
-2.48% to 0.09%	840	31.15%	50.61%
0.09% to 2.65%	818	30.33%	80.94%
2.65% to 5.21%	352	13.05%	93.99%
5.21% to 7.77%	114	4.23%	98.22%
7.77% to 10.33%	34	1.26%	99.48%
Greater than 10.33%	14	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.33%	3.50%	73.82%	68.27%
±2σ	-6.75%	6.92%	94.77%	95.45%
±3σ	-10.16%	10.33%	98.89%	99.73%

Descriptive Statistics

Mean	0.086%
Standard Error	0.066%
Median	0.029%
Mode	0.000%
Standard Deviation	3.416%
Sample Variance	11.667%
Kurtosis	2.75
Skewness	0.15
Range	39.226%
Minimum	-16.008%
Maximum	23.218%
Count	2697

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.604%	1356	50.28%	1.309%
Negative	-2.526%	1306	48.42%	-1.223%
Zero	0.000%	35	1.30%	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 -25.90%	2	0.36%	0.36%
-25.90% to -19.40%	6	1.07%	1.43%
-19.40% to -12.90%	26	4.65%	6.08%
-12.90% to -6.41%	74	13.24%	19.32%
-6.41% to 0.09%	173	30.95%	50.27%
0.09% to 6.59%	178	31.84%	82.11%
6.59% to 13.08%	72	12.88%	94.99%
13.08% to 19.58%	16	2.86%	97.85%
19.58% to 26.08%	5	0.89%	98.75%
Greater than 26.08%	7	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.57%	8.75%	75.13%	68.27%
±2σ	-17.23%	17.41%	94.45%	95.45%
±3σ	-25.90%	26.08%	98.39%	99.73%

Descriptive Statistics

Mean	0.090%
Standard Error	0.366%
Median	0.000%
Mode	0.000%
Standard Deviation	8.662%
Sample Variance	75.032%
Kurtosis	3.03
Skewness	0.36
Range	82.102%
Minimum	-38.672%
Maximum	43.430%
Count	559

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.394%	278	49.73%	3.180%
Negative	-6.214%	278	49.73%	-3.090%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.21%
12	1 Quarter	12.13%
52	1 Year	12.01%
156	3 Years	11.82%
260	5 Years	12.81%
520	10 Years	12.25%
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 29.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.78%	0	0.00%	0.00%
-12.78% to -6.17%	0	0.00%	0.00%
-6.17% to 0.43%	0	0.00%	0.00%
0.43% to 7.04%	90	16.07%	16.07%
7.04% to 13.65%	263	46.96%	63.04%
13.65% to 20.25%	135	24.11%	87.14%
20.25% to 26.86%	36	6.43%	93.57%
26.86% to 33.47%	18	3.21%	96.79%
33.47% to 40.07%	9	1.61%	98.39%
Greater than 40.07%	9	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.84%	22.45%	85.89%	68.27%
±2σ	-3.97%	31.26%	95.54%	95.45%
±3σ	-12.78%	40.07%	98.39%	99.73%

Descriptive Statistics

Mean	13.647%
Standard Error	0.372%
Median	11.702%
Mode	7.438%
Standard Deviation	8.808%
Sample Variance	77.578%
Kurtosis	29.58
Skewness	3.82
Range	107.897%
Minimum	2.781%
Maximum	110.678%
Count	560

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.647%	560	100.00%	13.647%
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 4.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.77%	3	0.54%	0.54%
-25.77% to -19.13%	3	0.54%	1.07%
-19.13% to -12.48%	15	2.68%	3.75%
-12.48% to -5.83%	86	15.36%	19.11%
-5.83% to 0.81%	192	34.29%	53.39%
0.81% to 7.46%	167	29.82%	83.21%
7.46% to 14.11%	57	10.18%	93.39%
14.11% to 20.75%	20	3.57%	96.96%
20.75% to 27.40%	14	2.50%	99.46%
Greater than 27.40%	3	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.05%	9.68%	76.25%	68.27%
±2σ	-16.91%	18.54%	94.82%	95.45%
±3σ	-25.77%	27.40%	98.93%	99.73%

Descriptive Statistics

Mean	0.814%
Standard Error	0.374%
Median	0.150%
Mode	0.000%
Standard Deviation	8.862%
Sample Variance	78.529%
Kurtosis	4.91
Skewness	0.98
Range	89.691%
Minimum	-28.356%
Maximum	61.335%
Count	560

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.966%	289	51.61%	3.595%
Negative	-5.812%	268	47.86%	-2.781%
Zero	0.000%	3	0.54%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.03. Further, an Excess Kurtosis of 0.21 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -47.22%	1	0.78%	0.78%
-47.22% to -35.44%	0	0.00%	0.78%
-35.44% to -23.66%	5	3.91%	4.69%
-23.66% to -11.88%	25	19.53%	24.22%
-11.88% to -0.09%	33	25.78%	50.00%
-0.09% to 11.69%	35	27.34%	77.34%
11.69% to 23.47%	18	14.06%	91.41%
23.47% to 35.25%	10	7.81%	99.22%
35.25% to 47.03%	1	0.78%	100.00%
Greater than 47.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.80%	15.61%	68.75%	68.27%
±2σ	-31.51%	31.32%	96.09%	95.45%
±3σ	-47.22%	47.03%	99.22%	99.73%

Descriptive Statistics

Mean	-0.094%
Standard Error	1.388%
Median	-0.163%
Mode	-53.196%
Standard Deviation	15.708%
Sample Variance	246.732%
Kurtosis	0.21
Skewness	0.03
Range	93.353%
Minimum	-53.196%
Maximum	40.157%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.853%	62	48.44%	6.226%
Negative	-12.445%	65	50.78%	-6.320%
Zero	0.000%	1	0.78%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.94%
12	1 Year	22.92%
36	3 Years	24.62%
60	5 Years	26.17%
120	10 Years	26.04%
240	20 Years	26.59%
600	50 Years	26.59%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.69. Further, an Excess Kurtosis of 24.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.48%	0	0.00%	0.00%
-22.48% to -8.85%	0	0.00%	0.00%
-8.85% to 4.79%	0	0.00%	0.00%
4.79% to 18.43%	27	20.93%	20.93%
18.43% to 32.07%	48	37.21%	58.14%
32.07% to 45.71%	35	27.13%	85.27%
45.71% to 59.35%	14	10.85%	96.12%
59.35% to 72.99%	4	3.10%	99.22%
72.99% to 86.62%	0	0.00%	99.22%
Greater than 86.62%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.89%	50.25%	83.72%	68.27%
±2σ	-4.30%	68.44%	96.90%	95.45%
±3σ	-22.48%	86.62%	99.22%	99.73%

Descriptive Statistics

Mean	32.070%
Standard Error	1.601%
Median	29.357%
Mode	9.714%
Standard Deviation	18.185%
Sample Variance	330.695%
Kurtosis	24.76
Skewness	3.69
Range	159.851%
Minimum	9.714%
Maximum	169.565%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.070%	129	100.00%	32.070%
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 2.05. Further, an Excess Kurtosis of 10.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.67%	0	0.00%	0.00%
-51.67% to -38.08%	0	0.00%	0.00%
-38.08% to -24.49%	2	1.55%	1.55%
-24.49% to -10.89%	24	18.60%	20.16%
-10.89% to 2.70%	45	34.88%	55.04%
2.70% to 16.29%	33	25.58%	80.62%
16.29% to 29.89%	21	16.28%	96.90%
29.89% to 43.48%	1	0.78%	97.67%
43.48% to 57.07%	2	1.55%	99.22%
Greater than 57.07%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.42%	20.82%	75.19%	68.27%
±2σ	-33.55%	38.95%	97.67%	95.45%
±3σ	-51.67%	57.07%	99.22%	99.73%

Descriptive Statistics

Mean	2.700%
Standard Error	1.596%
Median	0.303%
Mode	-28.402%
Standard Deviation	18.124%
Sample Variance	328.480%
Kurtosis	10.75
Skewness	2.05
Range	144.190%
Minimum	-28.402%
Maximum	115.788%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.963%	68	52.71%	7.887%
Negative	-10.971%	61	47.29%	-5.188%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.02. Further, an Excess Kurtosis of -0.56 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -83.08%	0	0.00%	0.00%
-83.08% to -62.30%	0	0.00%	0.00%
-62.30% to -41.51%	3	6.98%	6.98%
-41.51% to -20.73%	7	16.28%	23.26%
-20.73% to 0.05%	11	25.58%	48.84%
0.05% to 20.84%	13	30.23%	79.07%
20.84% to 41.62%	6	13.95%	93.02%
41.62% to 62.41%	3	6.98%	100.00%
62.41% to 83.19%	0	0.00%	100.00%
Greater than 83.19%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.66%	27.77%	65.12%	68.27%
±2σ	-55.37%	55.48%	95.35%	95.45%
±3σ	-83.08%	83.19%	100.00%	99.73%

Descriptive Statistics

Mean	0.054%
Standard Error	4.226%
Median	0.278%
Mode	-55.990%
Standard Deviation	27.712%
Sample Variance	767.961%
Kurtosis	-0.56
Skewness	-0.02
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	-22.974%	21	48.84%	-11.220%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	36.46%
12	3 Years	44.05%
20	5 Years	44.63%
40	10 Years	45.89%
80	20 Years	46.50%
200	50 Years	46.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.58. Further, an Excess Kurtosis of 2.43 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.91%	0	0.00%	0.00%
-38.91% to -13.28%	0	0.00%	0.00%
-13.28% to 12.36%	0	0.00%	0.00%
12.36% to 38.00%	9	20.45%	20.45%
38.00% to 63.64%	21	47.73%	68.18%
63.64% to 89.27%	6	13.64%	81.82%
89.27% to 114.91%	3	6.82%	88.64%
114.91% to 140.55%	4	9.09%	97.73%
140.55% to 166.19%	0	0.00%	97.73%
Greater than 166.19%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	29.45%	97.82%	81.82%	68.27%
±2σ	-4.73%	132.00%	93.18%	95.45%
±3σ	-38.91%	166.19%	97.73%	99.73%

Descriptive Statistics

Mean	63.636%
Standard Error	5.153%
Median	49.875%
Mode	27.808%
Standard Deviation	34.183%
Sample Variance	1168.447%
Kurtosis	2.43
Skewness	1.58
Range	153.340%
Minimum	27.808%
Maximum	181.148%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	63.636%	44	100.00%	63.636%
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 1.48. Further, an Excess Kurtosis of 2.41 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -99.80%	0	0.00%	0.00%
-99.80% to -72.70%	0	0.00%	0.00%
-72.70% to -45.61%	0	0.00%	0.00%
-45.61% to -18.52%	8	18.18%	18.18%
-18.52% to 8.58%	20	45.45%	63.64%
8.58% to 35.67%	8	18.18%	81.82%
35.67% to 62.77%	5	11.36%	93.18%
62.77% to 89.86%	1	2.27%	95.45%
89.86% to 116.95%	1	2.27%	97.73%
Greater than 116.95%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.55%	44.70%	75.00%	68.27%
±2σ	-63.67%	80.83%	95.45%	95.45%
±3σ	-99.80%	116.95%	97.73%	99.73%

Descriptive Statistics

Mean	8.578%
Standard Error	5.446%
Median	-1.090%
Mode	-37.609%
Standard Deviation	36.125%
Sample Variance	1305.030%
Kurtosis	2.41
Skewness	1.48
Range	170.636%
Minimum	-37.609%
Maximum	133.027%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	37.857%	20	45.45%	17.208%
Negative	-15.821%	24	54.55%	-8.630%
Zero	0.000%	0	0.00%	0.000%

TDOC Deep Analytical Report