VRTX - 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	3.47%	2.96%	3.06%	2.35%	2.27%	2.55%	466.17	487.87	455.69	499.10
Weekly	7.64%	7.63%	7.49%	5.32%	5.01%	5.61%	453.61	501.39	431.45	527.14
Monthly	14.99%	17.45%	14.98%	11.22%	10.42%	11.67%	429.69	529.30	387.15	587.45
Quarterly	24.42%	31.30%	22.27%	19.53%	18.06%	20.21%	398.12	571.27	332.35	684.31
Annual	—	—	—	—	36.11%	40.42%	332.35	684.31	231.62	981.93
Option Time Horizon	—	—	—	—	13.89%	15.55%	415.06	547.96	361.23	629.61

Calculation Notes: Computed at 2026-02-22T14:18 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $476.90 | Strike (K): $480.00 (first OTM call ≥ spot) | Observed Mid-Price: $26.1000 (Bid $23.8000 / Ask $28.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 36.11% (CRR binomial tree, American, n=20 steps) | BS IV: 35.99% (European Black-Scholes) | Yahoo IV (Annual): 40.42% → 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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.54. Further, an Excess Kurtosis of 26.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.29%	42	0.48%	0.48%
-10.29% to -7.69%	78	0.90%	1.38%
-7.69% to -5.09%	277	3.19%	4.57%
-5.09% to -2.49%	950	10.93%	15.49%
-2.49% to 0.11%	3291	37.85%	53.34%
0.11% to 2.71%	2771	31.87%	85.21%
2.71% to 5.31%	845	9.72%	94.93%
5.31% to 7.92%	275	3.16%	98.09%
7.92% to 10.52%	86	0.99%	99.08%
Greater than 10.52%	80	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.36%	3.58%	79.77%	68.27%
±2σ	-6.82%	7.05%	95.35%	95.45%
±3σ	-10.29%	10.52%	98.60%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.037%
Median	0.000%
Mode	0.000%
Standard Deviation	3.468%
Sample Variance	12.030%
Kurtosis	26.79
Skewness	1.54
Range	98.666%
Minimum	-36.759%
Maximum	61.907%
Count	8695

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.467%	4211	48.43%	1.195%
Negative	-2.263%	4159	47.83%	-1.082%
Zero	0.000%	325	3.74%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.96%
20	1 Month	2.92%
60	1 Quarter	2.57%
250	1 Year	2.61%
750	3 Years	2.27%
1,250	5 Years	2.35%
2,500	10 Years	2.70%
5,000	20 Years	3.35%
12,500	50 Years	4.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.12. Further, an Excess Kurtosis of 7.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.47%	0	0.00%	0.00%
-4.47% to -2.25%	0	0.00%	0.00%
-2.25% to -0.03%	0	0.00%	0.00%
-0.03% to 2.19%	1790	20.58%	20.58%
2.19% to 4.41%	3628	41.72%	62.30%
4.41% to 6.63%	1784	20.52%	82.82%
6.63% to 8.84%	828	9.52%	92.34%
8.84% to 11.06%	345	3.97%	96.31%
11.06% to 13.28%	163	1.87%	98.18%
Greater than 13.28%	158	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.45%	7.37%	82.36%	68.27%
±2σ	-1.51%	10.32%	95.48%	95.45%
±3σ	-4.47%	13.28%	98.18%	99.73%

Descriptive Statistics

Mean	4.407%
Standard Error	0.032%
Median	3.564%
Mode	5.128%
Standard Deviation	2.958%
Sample Variance	8.750%
Kurtosis	7.62
Skewness	2.12
Range	32.459%
Minimum	0.605%
Maximum	33.064%
Count	8696

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.407%	8696	100.00%	4.407%
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 0.17. Further, an Excess Kurtosis of 3.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.12%	58	0.67%	0.67%
-9.12% to -6.83%	113	1.30%	1.97%
-6.83% to -4.54%	335	3.85%	5.82%
-4.54% to -2.24%	969	11.14%	16.96%
-2.24% to 0.05%	3092	35.56%	52.52%
0.05% to 2.34%	2645	30.42%	82.93%
2.34% to 4.64%	956	10.99%	93.93%
4.64% to 6.93%	342	3.93%	97.86%
6.93% to 9.22%	116	1.33%	99.20%
Greater than 9.22%	70	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.01%	3.11%	76.35%	68.27%
±2σ	-6.06%	6.17%	94.05%	95.45%
±3σ	-9.12%	9.22%	98.53%	99.73%

Descriptive Statistics

Mean	0.051%
Standard Error	0.033%
Median	0.000%
Mode	0.000%
Standard Deviation	3.058%
Sample Variance	9.352%
Kurtosis	3.54
Skewness	0.17
Range	40.043%
Minimum	-19.355%
Maximum	20.688%
Count	8696

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.281%	4192	48.21%	1.100%
Negative	-2.179%	4186	48.14%	-1.049%
Zero	0.000%	318	3.66%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.76. Further, an Excess Kurtosis of 5.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.38%	9	0.50%	0.50%
-22.38% to -16.65%	20	1.11%	1.61%
-16.65% to -10.92%	55	3.05%	4.66%
-10.92% to -5.19%	210	11.64%	16.30%
-5.19% to 0.54%	671	37.20%	53.49%
0.54% to 6.27%	567	31.43%	84.92%
6.27% to 12.00%	162	8.98%	93.90%
12.00% to 17.73%	60	3.33%	97.23%
17.73% to 23.47%	28	1.55%	98.78%
Greater than 23.47%	22	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.10%	8.18%	80.10%	68.27%
±2σ	-14.74%	15.82%	94.24%	95.45%
±3σ	-22.38%	23.47%	98.28%	99.73%

Descriptive Statistics

Mean	0.543%
Standard Error	0.180%
Median	0.116%
Mode	0.000%
Standard Deviation	7.641%
Sample Variance	58.378%
Kurtosis	5.91
Skewness	0.76
Range	90.266%
Minimum	-37.972%
Maximum	52.294%
Count	1804

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.641%	915	50.72%	2.861%
Negative	-4.898%	854	47.34%	-2.319%
Zero	0.000%	35	1.94%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.44%
12	1 Quarter	6.20%
52	1 Year	5.83%
156	3 Years	5.17%
260	5 Years	5.32%
520	10 Years	6.07%
1,040	20 Years	7.73%
2,600	50 Years	9.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.61. Further, an Excess Kurtosis of 11.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.32%	0	0.00%	0.00%
-12.32% to -6.59%	0	0.00%	0.00%
-6.59% to -0.87%	0	0.00%	0.00%
-0.87% to 4.86%	316	17.51%	17.51%
4.86% to 10.58%	836	46.32%	63.82%
10.58% to 16.31%	387	21.44%	85.26%
16.31% to 22.03%	130	7.20%	92.47%
22.03% to 27.76%	67	3.71%	96.18%
27.76% to 33.48%	38	2.11%	98.28%
Greater than 33.48%	31	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.95%	18.22%	85.43%	68.27%
±2σ	-4.68%	25.85%	95.12%	95.45%
±3σ	-12.32%	33.48%	98.28%	99.73%

Descriptive Statistics

Mean	10.583%
Standard Error	0.180%
Median	8.462%
Mode	10.000%
Standard Deviation	7.633%
Sample Variance	58.268%
Kurtosis	11.72
Skewness	2.61
Range	81.103%
Minimum	1.619%
Maximum	82.722%
Count	1805

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.583%	1805	100.00%	10.583%
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 1.07. Further, an Excess Kurtosis of 8.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.40%	9	0.50%	0.50%
-22.40% to -16.78%	17	0.94%	1.44%
-16.78% to -11.16%	67	3.71%	5.15%
-11.16% to -5.54%	192	10.64%	15.79%
-5.54% to 0.07%	650	36.01%	51.80%
0.07% to 5.69%	596	33.02%	84.82%
5.69% to 11.31%	179	9.92%	94.74%
11.31% to 16.93%	56	3.10%	97.84%
16.93% to 22.55%	24	1.33%	99.17%
Greater than 22.55%	15	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.42%	7.57%	79.83%	68.27%
±2σ	-14.91%	15.06%	94.40%	95.45%
±3σ	-22.40%	22.55%	98.67%	99.73%

Descriptive Statistics

Mean	0.074%
Standard Error	0.176%
Median	-0.023%
Mode	0.000%
Standard Deviation	7.492%
Sample Variance	56.130%
Kurtosis	8.64
Skewness	1.07
Range	96.331%
Minimum	-33.930%
Maximum	62.401%
Count	1805

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.311%	874	48.42%	2.572%
Negative	-4.992%	903	50.03%	-2.497%
Zero	0.000%	28	1.55%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 3.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.76%	1	0.24%	0.24%
-42.76% to -31.52%	3	0.72%	0.96%
-31.52% to -20.28%	18	4.34%	5.30%
-20.28% to -9.04%	51	12.29%	17.59%
-9.04% to 2.20%	144	34.70%	52.29%
2.20% to 13.44%	125	30.12%	82.41%
13.44% to 24.68%	45	10.84%	93.25%
24.68% to 35.92%	17	4.10%	97.35%
35.92% to 47.16%	7	1.69%	99.04%
Greater than 47.16%	4	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.79%	17.19%	74.22%	68.27%
±2σ	-27.78%	32.18%	95.90%	95.45%
±3σ	-42.76%	47.16%	98.80%	99.73%

Descriptive Statistics

Mean	2.200%
Standard Error	0.736%
Median	1.410%
Mode	6.667%
Standard Deviation	14.988%
Sample Variance	224.639%
Kurtosis	3.21
Skewness	0.78
Range	128.232%
Minimum	-51.098%
Maximum	77.134%
Count	415

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.947%	227	54.70%	6.535%
Negative	-9.621%	187	45.06%	-4.335%
Zero	0.000%	1	0.24%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.99%
12	1 Year	11.66%
36	3 Years	11.14%
60	5 Years	11.22%
120	10 Years	12.83%
240	20 Years	16.27%
600	50 Years	21.37%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.47. Further, an Excess Kurtosis of 9.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.82%	0	0.00%	0.00%
-27.82% to -14.73%	0	0.00%	0.00%
-14.73% to -1.64%	0	0.00%	0.00%
-1.64% to 11.45%	67	16.11%	16.11%
11.45% to 24.54%	200	48.08%	64.18%
24.54% to 37.63%	91	21.88%	86.06%
37.63% to 50.72%	23	5.53%	91.59%
50.72% to 63.81%	19	4.57%	96.15%
63.81% to 76.90%	7	1.68%	97.84%
Greater than 76.90%	9	2.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.08%	41.99%	85.82%	68.27%
±2σ	-10.37%	59.45%	95.67%	95.45%
±3σ	-27.83%	76.90%	97.84%	99.73%

Descriptive Statistics

Mean	24.537%
Standard Error	0.856%
Median	19.565%
Mode	16.667%
Standard Deviation	17.454%
Sample Variance	304.633%
Kurtosis	9.57
Skewness	2.47
Range	146.254%
Minimum	2.778%
Maximum	149.032%
Count	416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.537%	416	100.00%	24.537%
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 1.33. Further, an Excess Kurtosis of 7.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.88%	0	0.00%	0.00%
-44.88% to -33.65%	3	0.72%	0.72%
-33.65% to -22.41%	14	3.37%	4.09%
-22.41% to -11.18%	58	13.94%	18.03%
-11.18% to 0.06%	155	37.26%	55.29%
0.06% to 11.29%	121	29.09%	84.38%
11.29% to 22.52%	36	8.65%	93.03%
22.52% to 33.76%	21	5.05%	98.08%
33.76% to 44.99%	4	0.96%	99.04%
Greater than 44.99%	4	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.92%	15.03%	75.00%	68.27%
±2σ	-29.90%	30.01%	95.91%	95.45%
±3σ	-44.88%	44.99%	99.04%	99.73%

Descriptive Statistics

Mean	0.055%
Standard Error	0.734%
Median	-1.404%
Mode	-3.125%
Standard Deviation	14.979%
Sample Variance	224.381%
Kurtosis	7.19
Skewness	1.33
Range	150.012%
Minimum	-43.804%
Maximum	106.208%
Count	416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.899%	186	44.71%	5.320%
Negative	-9.606%	228	54.81%	-5.265%
Zero	0.000%	2	0.48%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 1.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.22%	0	0.00%	0.00%
-67.22% to -48.90%	0	0.00%	0.00%
-48.90% to -30.58%	6	4.32%	4.32%
-30.58% to -12.26%	23	16.55%	20.86%
-12.26% to 6.06%	47	33.81%	54.68%
6.06% to 24.37%	36	25.90%	80.58%
24.37% to 42.69%	17	12.23%	92.81%
42.69% to 61.01%	4	2.88%	95.68%
61.01% to 79.33%	4	2.88%	98.56%
Greater than 79.33%	2	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.37%	30.48%	74.10%	68.27%
±2σ	-42.79%	54.90%	94.96%	95.45%
±3σ	-67.22%	79.33%	98.56%	99.73%

Descriptive Statistics

Mean	6.056%
Standard Error	2.072%
Median	3.558%
Mode	-42.715%
Standard Deviation	24.424%
Sample Variance	596.527%
Kurtosis	1.35
Skewness	0.86
Range	132.855%
Minimum	-42.715%
Maximum	90.140%
Count	139

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.004%	78	56.12%	12.348%
Negative	-14.336%	61	43.88%	-6.291%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.21%
12	3 Years	18.73%
20	5 Years	19.53%
40	10 Years	22.23%
80	20 Years	28.27%
200	50 Years	38.42%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.71. Further, an Excess Kurtosis of 3.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.97%	0	0.00%	0.00%
-46.97% to -23.50%	0	0.00%	0.00%
-23.50% to -0.02%	0	0.00%	0.00%
-0.02% to 23.45%	33	23.57%	23.57%
23.45% to 46.92%	57	40.71%	64.29%
46.92% to 70.40%	26	18.57%	82.86%
70.40% to 93.87%	13	9.29%	92.14%
93.87% to 117.34%	6	4.29%	96.43%
117.34% to 140.82%	2	1.43%	97.86%
Greater than 140.82%	3	2.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.63%	78.22%	79.29%	68.27%
±2σ	-15.67%	109.52%	95.00%	95.45%
±3σ	-46.97%	140.82%	97.86%	99.73%

Descriptive Statistics

Mean	46.925%
Standard Error	2.645%
Median	38.962%
Mode	13.567%
Standard Deviation	31.298%
Sample Variance	979.582%
Kurtosis	3.55
Skewness	1.71
Range	167.466%
Minimum	2.778%
Maximum	170.244%
Count	140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.925%	140	100.00%	46.925%
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 0.68. Further, an Excess Kurtosis of 0.89 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.37%	0	0.00%	0.00%
-67.37% to -50.67%	0	0.00%	0.00%
-50.67% to -33.96%	8	5.71%	5.71%
-33.96% to -17.26%	22	15.71%	21.43%
-17.26% to -0.56%	47	33.57%	55.00%
-0.56% to 16.14%	41	29.29%	84.29%
16.14% to 32.84%	11	7.86%	92.14%
32.84% to 49.54%	6	4.29%	96.43%
49.54% to 66.25%	4	2.86%	99.29%
Greater than 66.25%	1	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.83%	21.71%	73.57%	68.27%
±2σ	-45.10%	43.98%	94.29%	95.45%
±3σ	-67.37%	66.25%	99.29%	99.73%

Descriptive Statistics

Mean	-0.561%
Standard Error	1.882%
Median	-3.011%
Mode	-47.659%
Standard Deviation	22.269%
Sample Variance	495.922%
Kurtosis	0.89
Skewness	0.68
Range	121.414%
Minimum	-47.659%
Maximum	73.755%
Count	140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.908%	61	43.57%	8.238%
Negative	-15.594%	79	56.43%	-8.800%
Zero	0.000%	0	0.00%	0.000%

VRTX Deep Analytical Report