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%	2.36%	2.24%	2.49%	444.69	465.02	434.86	475.54
Weekly	7.63%	7.63%	7.49%	5.35%	4.92%	5.47%	432.91	477.68	412.12	501.77
Monthly	14.98%	17.44%	14.97%	11.30%	10.24%	11.39%	410.47	503.79	370.51	558.13
Quarterly	24.43%	31.28%	22.27%	19.62%	17.74%	19.73%	380.82	543.02	318.91	648.44
Annual	—	—	—	—	35.48%	39.46%	318.91	648.44	223.65	924.63
Option Time Horizon	—	—	—	—	13.39%	14.89%	397.74	519.92	347.89	594.43

Calculation Notes: Computed at 2026-03-23T16:33 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $454.74 | Strike (K): $470.00 (first OTM call ≥ spot) | Observed Mid-Price: $19.0500 (Bid $17.1000 / Ask $21.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 35.48% (CRR binomial tree, American, n=20 steps) | BS IV: 35.91% (European Black-Scholes) | Yahoo IV (Annual): 39.46% → 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	0.89%	1.38%
-7.69% to -5.09%	277	3.18%	4.55%
-5.09% to -2.49%	954	10.95%	15.50%
-2.49% to 0.11%	3301	37.87%	53.37%
0.11% to 2.71%	2775	31.84%	85.21%
2.71% to 5.31%	847	9.72%	94.93%
5.31% to 7.91%	275	3.16%	98.08%
7.91% to 10.51%	87	1.00%	99.08%
Greater than 10.51%	80	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.35%	3.58%	79.78%	68.27%
±2σ	-6.82%	7.05%	95.35%	95.45%
±3σ	-10.29%	10.51%	98.60%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.037%
Median	0.000%
Mode	0.000%
Standard Deviation	3.467%
Sample Variance	12.017%
Kurtosis	26.79
Skewness	1.54
Range	98.666%
Minimum	-36.759%
Maximum	61.907%
Count	8716

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.467%	4219	48.41%	1.194%
Negative	-2.261%	4172	47.87%	-1.082%
Zero	0.000%	325	3.73%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.16%
20	1 Month	3.02%
60	1 Quarter	2.82%
250	1 Year	2.65%
750	3 Years	2.30%
1,250	5 Years	2.36%
2,500	10 Years	2.68%
5,000	20 Years	3.34%
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 2.13. Further, an Excess Kurtosis of 7.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.46%	0	0.00%	0.00%
-4.46% to -2.25%	0	0.00%	0.00%
-2.25% to -0.03%	0	0.00%	0.00%
-0.03% to 2.19%	1793	20.57%	20.57%
2.19% to 4.40%	3640	41.76%	62.33%
4.40% to 6.62%	1786	20.49%	82.82%
6.62% to 8.84%	830	9.52%	92.34%
8.84% to 11.05%	346	3.97%	96.31%
11.05% to 13.27%	163	1.87%	98.18%
Greater than 13.27%	159	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.45%	7.36%	82.37%	68.27%
±2σ	-1.51%	10.31%	95.47%	95.45%
±3σ	-4.47%	13.27%	98.18%	99.73%

Descriptive Statistics

Mean	4.403%
Standard Error	0.032%
Median	3.560%
Mode	5.128%
Standard Deviation	2.956%
Sample Variance	8.738%
Kurtosis	7.64
Skewness	2.13
Range	32.459%
Minimum	0.605%
Maximum	33.064%
Count	8717

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.403%	8717	100.00%	4.403%
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 0.16. 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 -6.82%	113	1.30%	1.96%
-6.82% to -4.53%	335	3.84%	5.80%
-4.53% to -2.24%	973	11.16%	16.97%
-2.24% to 0.05%	3096	35.52%	52.48%
0.05% to 2.34%	2654	30.45%	82.93%
2.34% to 4.64%	959	11.00%	93.93%
4.64% to 6.93%	343	3.93%	97.87%
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	-3.00%	3.11%	76.37%	68.27%
±2σ	-6.06%	6.16%	94.03%	95.45%
±3σ	-9.12%	9.22%	98.53%	99.73%

Descriptive Statistics

Mean	0.052%
Standard Error	0.033%
Median	0.000%
Mode	0.000%
Standard Deviation	3.056%
Sample Variance	9.338%
Kurtosis	3.54
Skewness	0.16
Range	40.043%
Minimum	-19.355%
Maximum	20.688%
Count	8717

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.279%	4206	48.25%	1.100%
Negative	-2.178%	4193	48.10%	-1.048%
Zero	0.000%	318	3.65%	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 5.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.36%	9	0.50%	0.50%
-22.36% to -16.64%	20	1.11%	1.60%
-16.64% to -10.91%	55	3.04%	4.65%
-10.91% to -5.19%	210	11.62%	16.26%
-5.19% to 0.54%	673	37.22%	53.48%
0.54% to 6.26%	569	31.47%	84.96%
6.26% to 11.99%	162	8.96%	93.92%
11.99% to 17.71%	60	3.32%	97.23%
17.71% to 23.44%	28	1.55%	98.78%
Greater than 23.44%	22	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.09%	8.17%	80.09%	68.27%
±2σ	-14.73%	15.80%	94.25%	95.45%
±3σ	-22.36%	23.44%	98.29%	99.73%

Descriptive Statistics

Mean	0.539%
Standard Error	0.180%
Median	0.116%
Mode	0.000%
Standard Deviation	7.633%
Sample Variance	58.270%
Kurtosis	5.93
Skewness	0.76
Range	90.266%
Minimum	-37.972%
Maximum	52.294%
Count	1808

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.631%	917	50.72%	2.856%
Negative	-4.894%	856	47.34%	-2.317%
Zero	0.000%	35	1.94%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.51%
12	1 Quarter	6.75%
52	1 Year	5.95%
156	3 Years	5.23%
260	5 Years	5.35%
520	10 Years	6.04%
1,040	20 Years	7.71%
2,600	50 Years	9.98%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.31%	0	0.00%	0.00%
-12.31% to -6.59%	0	0.00%	0.00%
-6.59% to -0.87%	0	0.00%	0.00%
-0.87% to 4.85%	316	17.47%	17.47%
4.85% to 10.57%	840	46.43%	63.90%
10.57% to 16.30%	387	21.39%	85.30%
16.30% to 22.02%	130	7.19%	92.48%
22.02% to 27.74%	67	3.70%	96.19%
27.74% to 33.46%	38	2.10%	98.29%
Greater than 33.46%	31	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.95%	18.20%	85.46%	68.27%
±2σ	-4.68%	25.83%	95.14%	95.45%
±3σ	-12.31%	33.46%	98.29%	99.73%

Descriptive Statistics

Mean	10.574%
Standard Error	0.179%
Median	8.455%
Mode	10.000%
Standard Deviation	7.628%
Sample Variance	58.185%
Kurtosis	11.74
Skewness	2.61
Range	81.103%
Minimum	1.619%
Maximum	82.722%
Count	1809

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.574%	1809	100.00%	10.574%
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 8.66 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 -16.76%	18	1.00%	1.49%
-16.76% to -11.15%	67	3.70%	5.20%
-11.15% to -5.54%	191	10.56%	15.75%
-5.54% to 0.08%	652	36.04%	51.80%
0.08% to 5.69%	598	33.06%	84.85%
5.69% to 11.31%	179	9.89%	94.75%
11.31% to 16.92%	56	3.10%	97.84%
16.92% to 22.53%	24	1.33%	99.17%
Greater than 22.53%	15	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.41%	7.56%	79.82%	68.27%
±2σ	-14.89%	15.05%	94.42%	95.45%
±3σ	-22.38%	22.53%	98.67%	99.73%

Descriptive Statistics

Mean	0.079%
Standard Error	0.176%
Median	0.000%
Mode	0.000%
Standard Deviation	7.485%
Sample Variance	56.024%
Kurtosis	8.66
Skewness	1.07
Range	96.331%
Minimum	-33.930%
Maximum	62.401%
Count	1809

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.304%	877	48.48%	2.571%
Negative	-4.988%	904	49.97%	-2.493%
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 -20.29%	18	4.33%	5.29%
-20.29% to -9.05%	51	12.26%	17.55%
-9.05% to 2.18%	144	34.62%	52.16%
2.18% to 13.42%	125	30.05%	82.21%
13.42% to 24.65%	46	11.06%	93.27%
24.65% to 35.89%	17	4.09%	97.36%
35.89% to 47.12%	7	1.68%	99.04%
Greater than 47.12%	4	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.80%	17.16%	74.28%	68.27%
±2σ	-27.78%	32.14%	95.91%	95.45%
±3σ	-42.76%	47.12%	98.80%	99.73%

Descriptive Statistics

Mean	2.184%
Standard Error	0.734%
Median	1.360%
Mode	6.667%
Standard Deviation	14.980%
Sample Variance	224.406%
Kurtosis	3.21
Skewness	0.78
Range	128.232%
Minimum	-51.098%
Maximum	77.134%
Count	416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.966%	227	54.57%	6.529%
Negative	-9.615%	188	45.19%	-4.345%
Zero	0.000%	1	0.24%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.73%
12	1 Year	11.80%
36	3 Years	11.16%
60	5 Years	11.30%
120	10 Years	12.76%
240	20 Years	16.23%
600	50 Years	21.35%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.48. Further, an Excess Kurtosis of 9.59 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 -14.74%	0	0.00%	0.00%
-14.74% to -1.65%	0	0.00%	0.00%
-1.65% to 11.43%	67	16.07%	16.07%
11.43% to 24.51%	200	47.96%	64.03%
24.51% to 37.59%	92	22.06%	86.09%
37.59% to 50.67%	23	5.52%	91.61%
50.67% to 63.75%	19	4.56%	96.16%
63.75% to 76.83%	7	1.68%	97.84%
Greater than 76.83%	9	2.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.07%	41.95%	86.09%	68.27%
±2σ	-10.38%	59.39%	95.68%	95.45%
±3σ	-27.82%	76.84%	97.84%	99.73%

Descriptive Statistics

Mean	24.509%
Standard Error	0.854%
Median	19.565%
Mode	16.667%
Standard Deviation	17.442%
Sample Variance	304.224%
Kurtosis	9.59
Skewness	2.48
Range	146.254%
Minimum	2.778%
Maximum	149.032%
Count	417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.509%	417	100.00%	24.509%
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 -44.84%	0	0.00%	0.00%
-44.84% to -33.62%	3	0.72%	0.72%
-33.62% to -22.39%	14	3.36%	4.08%
-22.39% to -11.16%	58	13.91%	17.99%
-11.16% to 0.07%	155	37.17%	55.16%
0.07% to 11.30%	122	29.26%	84.41%
11.30% to 22.52%	36	8.63%	93.05%
22.52% to 33.75%	21	5.04%	98.08%
33.75% to 44.98%	4	0.96%	99.04%
Greater than 44.98%	4	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.90%	15.04%	75.06%	68.27%
±2σ	-29.87%	30.01%	95.92%	95.45%
±3σ	-44.84%	44.98%	99.04%	99.73%

Descriptive Statistics

Mean	0.068%
Standard Error	0.733%
Median	-1.364%
Mode	-3.125%
Standard Deviation	14.971%
Sample Variance	224.126%
Kurtosis	7.19
Skewness	1.33
Range	150.012%
Minimum	-43.804%
Maximum	106.208%
Count	417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.885%	187	44.84%	5.330%
Negative	-9.623%	228	54.68%	-5.261%
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 -67.28%	0	0.00%	0.00%
-67.28% to -48.95%	0	0.00%	0.00%
-48.95% to -30.63%	6	4.32%	4.32%
-30.63% to -12.30%	23	16.55%	20.86%
-12.30% to 6.02%	47	33.81%	54.68%
6.02% to 24.35%	36	25.90%	80.58%
24.35% to 42.67%	17	12.23%	92.81%
42.67% to 61.00%	4	2.88%	95.68%
61.00% to 79.32%	4	2.88%	98.56%
Greater than 79.32%	2	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.41%	30.46%	74.10%	68.27%
±2σ	-42.85%	54.89%	94.96%	95.45%
±3σ	-67.28%	79.32%	98.56%	99.73%

Descriptive Statistics

Mean	6.022%
Standard Error	2.072%
Median	3.558%
Mode	-42.715%
Standard Deviation	24.434%
Sample Variance	597.013%
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	22.271%	77	55.40%	12.337%
Negative	-14.159%	62	44.60%	-6.315%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.68%
12	3 Years	18.88%
20	5 Years	19.62%
40	10 Years	22.28%
80	20 Years	28.29%
200	50 Years	38.43%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.91%	0	0.00%	0.00%
-46.91% to -23.45%	0	0.00%	0.00%
-23.45% to 0.02%	0	0.00%	0.00%
0.02% to 23.48%	33	23.57%	23.57%
23.48% to 46.94%	57	40.71%	64.29%
46.94% to 70.40%	26	18.57%	82.86%
70.40% to 93.86%	13	9.29%	92.14%
93.86% to 117.32%	6	4.29%	96.43%
117.32% to 140.79%	2	1.43%	97.86%
Greater than 140.79%	3	2.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.66%	78.22%	79.29%	68.27%
±2σ	-15.62%	109.50%	95.00%	95.45%
±3σ	-46.91%	140.79%	97.86%	99.73%

Descriptive Statistics

Mean	46.940%
Standard Error	2.644%
Median	38.962%
Mode	13.567%
Standard Deviation	31.282%
Sample Variance	978.552%
Kurtosis	3.56
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	46.940%	140	100.00%	46.940%
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 0.67. 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 -67.34%	0	0.00%	0.00%
-67.34% to -50.64%	0	0.00%	0.00%
-50.64% to -33.93%	8	5.71%	5.71%
-33.93% to -17.23%	22	15.71%	21.43%
-17.23% to -0.53%	46	32.86%	54.29%
-0.53% to 16.18%	42	30.00%	84.29%
16.18% to 32.88%	11	7.86%	92.14%
32.88% to 49.58%	6	4.29%	96.43%
49.58% to 66.29%	4	2.86%	99.29%
Greater than 66.29%	1	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.80%	21.75%	73.57%	68.27%
±2σ	-45.07%	44.02%	94.29%	95.45%
±3σ	-67.34%	66.29%	99.29%	99.73%

Descriptive Statistics

Mean	-0.526%
Standard Error	1.882%
Median	-3.011%
Mode	-47.659%
Standard Deviation	22.271%
Sample Variance	495.983%
Kurtosis	0.89
Skewness	0.67
Range	121.414%
Minimum	-47.659%
Maximum	73.755%
Count	140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.648%	62	44.29%	8.258%
Negative	-15.766%	78	55.71%	-8.784%
Zero	0.000%	0	0.00%	0.000%

VRTX Deep Analytical Report