BSX - 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	2.38%	1.96%	2.00%	2.07%	2.21%	2.40%	72.95	76.25	71.35	77.96
Weekly	5.30%	5.17%	5.36%	4.77%	4.88%	5.28%	71.03	78.31	67.65	82.22
Monthly	9.98%	10.88%	10.04%	10.01%	10.15%	10.99%	67.38	82.55	60.88	91.36
Quarterly	18.36%	20.80%	19.27%	16.81%	17.58%	19.04%	62.56	88.91	52.47	106.00
Annual	—	—	—	—	35.16%	38.09%	52.47	106.00	36.92	150.66
Option Time Horizon	—	—	—	—	13.52%	14.65%	65.15	85.38	56.91	97.74

Calculation Notes: Computed at 2026-02-22T14:18 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $74.58 | Strike (K): $75.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.0000 (Bid $3.8000 / Ask $4.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 35.16% (CRR binomial tree, American, n=20 steps) | BS IV: 35.01% (European Black-Scholes) | Yahoo IV (Annual): 38.09% → 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 -0.21. Further, an Excess Kurtosis of 11.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.07%	53	0.62%	0.62%
-7.07% to -5.29%	89	1.05%	1.67%
-5.29% to -3.50%	231	2.72%	4.39%
-3.50% to -1.72%	948	11.16%	15.55%
-1.72% to 0.06%	3093	36.40%	51.95%
0.06% to 1.85%	2742	32.27%	84.22%
1.85% to 3.63%	910	10.71%	94.93%
3.63% to 5.41%	266	3.13%	98.06%
5.41% to 7.20%	92	1.08%	99.14%
Greater than 7.20%	73	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.32%	2.44%	79.83%	68.27%
±2σ	-4.69%	4.82%	95.09%	95.45%
±3σ	-7.07%	7.20%	98.52%	99.73%

Descriptive Statistics

Mean	0.062%
Standard Error	0.026%
Median	0.000%
Mode	0.000%
Standard Deviation	2.378%
Sample Variance	5.653%
Kurtosis	11.78
Skewness	-0.21
Range	52.828%
Minimum	-26.699%
Maximum	26.129%
Count	8497

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.692%	4151	48.85%	0.827%
Negative	-1.596%	4069	47.89%	-0.764%
Zero	0.000%	277	3.26%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.12%
20	1 Month	3.47%
60	1 Quarter	2.64%
250	1 Year	2.39%
750	3 Years	1.95%
1,250	5 Years	2.07%
2,500	10 Years	2.18%
5,000	20 Years	2.65%
12,500	50 Years	3.00%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 19.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.02%	0	0.00%	0.00%
-3.02% to -1.55%	0	0.00%	0.00%
-1.55% to -0.08%	0	0.00%	0.00%
-0.08% to 1.39%	1382	16.26%	16.26%
1.39% to 2.86%	4010	47.19%	63.45%
2.86% to 4.33%	1868	21.98%	85.43%
4.33% to 5.79%	694	8.17%	93.60%
5.79% to 7.26%	262	3.08%	96.68%
7.26% to 8.73%	118	1.39%	98.07%
Greater than 8.73%	164	1.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.90%	4.82%	85.58%	68.27%
±2σ	-1.06%	6.77%	95.85%	95.45%
±3σ	-3.02%	8.73%	98.07%	99.73%

Descriptive Statistics

Mean	2.858%
Standard Error	0.021%
Median	2.364%
Mode	1.754%
Standard Deviation	1.958%
Sample Variance	3.834%
Kurtosis	19.53
Skewness	3.09
Range	32.460%
Minimum	0.334%
Maximum	32.794%
Count	8498

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.858%	8498	100.00%	2.858%
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 0.13. Further, an Excess Kurtosis of 5.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.99%	64	0.75%	0.75%
-5.99% to -4.49%	101	1.19%	1.94%
-4.49% to -2.99%	280	3.29%	5.24%
-2.99% to -1.49%	998	11.74%	16.98%
-1.49% to 0.02%	2933	34.51%	51.49%
0.02% to 1.52%	2705	31.83%	83.33%
1.52% to 3.02%	982	11.56%	94.88%
3.02% to 4.52%	265	3.12%	98.00%
4.52% to 6.03%	104	1.22%	99.22%
Greater than 6.03%	66	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.99%	2.02%	77.70%	68.27%
±2σ	-3.99%	4.02%	94.80%	95.45%
±3σ	-5.99%	6.03%	98.47%	99.73%

Descriptive Statistics

Mean	0.016%
Standard Error	0.022%
Median	0.000%
Mode	0.000%
Standard Deviation	2.003%
Sample Variance	4.013%
Kurtosis	5.70
Skewness	0.13
Range	36.061%
Minimum	-17.083%
Maximum	18.978%
Count	8498

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.462%	4122	48.51%	0.709%
Negative	-1.443%	4080	48.01%	-0.693%
Zero	0.000%	296	3.48%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.18. Further, an Excess Kurtosis of 4.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.60%	17	0.97%	0.97%
-15.60% to -11.63%	17	0.97%	1.93%
-11.63% to -7.65%	50	2.84%	4.77%
-7.65% to -3.67%	211	11.98%	16.75%
-3.67% to 0.30%	588	33.39%	50.14%
0.30% to 4.28%	590	33.50%	83.65%
4.28% to 8.26%	194	11.02%	94.66%
8.26% to 12.23%	59	3.35%	98.01%
12.23% to 16.21%	20	1.14%	99.15%
Greater than 16.21%	15	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.00%	5.60%	77.06%	68.27%
±2σ	-10.30%	10.91%	94.72%	95.45%
±3σ	-15.60%	16.21%	98.18%	99.73%

Descriptive Statistics

Mean	0.302%
Standard Error	0.126%
Median	0.292%
Mode	0.000%
Standard Deviation	5.302%
Sample Variance	28.111%
Kurtosis	4.39
Skewness	-0.18
Range	63.176%
Minimum	-35.765%
Maximum	27.411%
Count	1761

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.823%	927	52.64%	2.012%
Negative	-3.706%	813	46.17%	-1.711%
Zero	0.000%	21	1.19%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.05%
12	1 Quarter	6.64%
52	1 Year	5.71%
156	3 Years	4.46%
260	5 Years	4.77%
520	10 Years	5.05%
1,040	20 Years	6.06%
2,600	50 Years	7.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.38. Further, an Excess Kurtosis of 21.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.13%	0	0.00%	0.00%
-8.13% to -4.25%	0	0.00%	0.00%
-4.25% to -0.38%	0	0.00%	0.00%
-0.38% to 3.50%	255	14.47%	14.47%
3.50% to 7.37%	869	49.32%	63.79%
7.37% to 11.25%	387	21.96%	85.75%
11.25% to 15.12%	142	8.06%	93.81%
15.12% to 19.00%	56	3.18%	96.99%
19.00% to 22.87%	21	1.19%	98.18%
Greater than 22.87%	32	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.21%	12.54%	87.34%	68.27%
±2σ	-2.96%	17.70%	95.86%	95.45%
±3σ	-8.13%	22.87%	98.18%	99.73%

Descriptive Statistics

Mean	7.371%
Standard Error	0.123%
Median	6.106%
Mode	9.091%
Standard Deviation	5.166%
Sample Variance	26.688%
Kurtosis	21.72
Skewness	3.38
Range	67.702%
Minimum	1.068%
Maximum	68.770%
Count	1762

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.371%	1762	100.00%	7.371%
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 10.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.04%	7	0.40%	0.40%
-16.04% to -12.02%	15	0.85%	1.25%
-12.02% to -8.00%	50	2.84%	4.09%
-8.00% to -3.98%	220	12.49%	16.57%
-3.98% to 0.04%	663	37.63%	54.20%
0.04% to 4.05%	538	30.53%	84.73%
4.05% to 8.07%	169	9.59%	94.32%
8.07% to 12.09%	60	3.41%	97.73%
12.09% to 16.11%	22	1.25%	98.98%
Greater than 16.11%	18	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.32%	5.39%	79.34%	68.27%
±2σ	-10.68%	10.75%	94.84%	95.45%
±3σ	-16.04%	16.11%	98.58%	99.73%

Descriptive Statistics

Mean	0.036%
Standard Error	0.128%
Median	-0.296%
Mode	0.000%
Standard Deviation	5.357%
Sample Variance	28.694%
Kurtosis	10.39
Skewness	1.45
Range	74.898%
Minimum	-20.319%
Maximum	54.579%
Count	1762

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.988%	809	45.91%	1.831%
Negative	-3.383%	935	53.06%	-1.795%
Zero	0.000%	18	1.02%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.17. Further, an Excess Kurtosis of 1.99 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.75%	1	0.25%	0.25%
-28.75% to -21.27%	9	2.22%	2.47%
-21.27% to -13.78%	13	3.21%	5.68%
-13.78% to -6.30%	61	15.06%	20.74%
-6.30% to 1.19%	118	29.14%	49.88%
1.19% to 8.67%	124	30.62%	80.49%
8.67% to 16.16%	53	13.09%	93.58%
16.16% to 23.64%	20	4.94%	98.52%
23.64% to 31.13%	5	1.23%	99.75%
Greater than 31.13%	1	0.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.79%	11.17%	71.60%	68.27%
±2σ	-18.77%	21.15%	93.83%	95.45%
±3σ	-28.75%	31.13%	99.51%	99.73%

Descriptive Statistics

Mean	1.188%
Standard Error	0.496%
Median	1.238%
Mode	-1.210%
Standard Deviation	9.980%
Sample Variance	99.601%
Kurtosis	1.99
Skewness	0.17
Range	84.974%
Minimum	-31.672%
Maximum	53.302%
Count	405

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.977%	224	55.31%	4.412%
Negative	-7.254%	180	44.44%	-3.224%
Zero	0.000%	1	0.25%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.29%
12	1 Year	11.83%
36	3 Years	9.76%
60	5 Years	10.01%
120	10 Years	10.83%
240	20 Years	12.70%
600	50 Years	15.20%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.36. Further, an Excess Kurtosis of 8.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.73%	0	0.00%	0.00%
-15.73% to -7.57%	0	0.00%	0.00%
-7.57% to 0.59%	0	0.00%	0.00%
0.59% to 8.75%	71	17.49%	17.49%
8.75% to 16.92%	186	45.81%	63.30%
16.92% to 25.08%	88	21.67%	84.98%
25.08% to 33.24%	34	8.37%	93.35%
33.24% to 41.41%	12	2.96%	96.31%
41.41% to 49.57%	8	1.97%	98.28%
Greater than 49.57%	7	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.03%	27.80%	84.24%	68.27%
±2σ	-4.85%	38.69%	94.58%	95.45%
±3σ	-15.73%	49.57%	98.28%	99.73%

Descriptive Statistics

Mean	16.917%
Standard Error	0.540%
Median	13.906%
Mode	8.889%
Standard Deviation	10.884%
Sample Variance	118.470%
Kurtosis	8.27
Skewness	2.36
Range	83.488%
Minimum	4.209%
Maximum	87.697%
Count	406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.917%	406	100.00%	16.917%
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 0.81. Further, an Excess Kurtosis of 2.05 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.29%	1	0.25%	0.25%
-30.29% to -22.76%	0	0.00%	0.25%
-22.76% to -15.22%	13	3.20%	3.45%
-15.22% to -7.69%	66	16.26%	19.70%
-7.69% to -0.16%	141	34.73%	54.43%
-0.16% to 7.37%	108	26.60%	81.03%
7.37% to 14.90%	51	12.56%	93.60%
14.90% to 22.43%	11	2.71%	96.31%
22.43% to 29.96%	9	2.22%	98.52%
Greater than 29.96%	6	1.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.20%	9.88%	75.12%	68.27%
±2σ	-20.25%	19.92%	94.83%	95.45%
±3σ	-30.29%	29.96%	98.28%	99.73%

Descriptive Statistics

Mean	-0.162%
Standard Error	0.498%
Median	-1.082%
Mode	0.000%
Standard Deviation	10.042%
Sample Variance	100.835%
Kurtosis	2.05
Skewness	0.81
Range	77.851%
Minimum	-32.308%
Maximum	45.543%
Count	406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.276%	181	44.58%	3.690%
Negative	-7.044%	222	54.68%	-3.852%
Zero	0.000%	3	0.74%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.45. Further, an Excess Kurtosis of 1.89 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.42%	0	0.00%	0.00%
-51.42% to -37.65%	1	0.74%	0.74%
-37.65% to -23.89%	8	5.93%	6.67%
-23.89% to -10.12%	17	12.59%	19.26%
-10.12% to 3.65%	44	32.59%	51.85%
3.65% to 17.42%	42	31.11%	82.96%
17.42% to 31.19%	15	11.11%	94.07%
31.19% to 44.96%	2	1.48%	95.56%
44.96% to 58.73%	5	3.70%	99.26%
Greater than 58.73%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.71%	22.01%	74.81%	68.27%
±2σ	-33.06%	40.37%	91.85%	95.45%
±3σ	-51.42%	58.73%	99.26%	99.73%

Descriptive Statistics

Mean	3.654%
Standard Error	1.580%
Median	2.797%
Mode	-50.231%
Standard Deviation	18.359%
Sample Variance	337.049%
Kurtosis	1.89
Skewness	0.45
Range	124.846%
Minimum	-50.231%
Maximum	74.615%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.593%	79	58.52%	8.540%
Negative	-11.779%	56	41.48%	-4.886%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	17.54%
12	3 Years	18.06%
20	5 Years	16.81%
40	10 Years	18.17%
80	20 Years	21.87%
200	50 Years	26.68%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.23. Further, an Excess Kurtosis of 6.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.03%	0	0.00%	0.00%
-30.03% to -14.43%	0	0.00%	0.00%
-14.43% to 1.17%	0	0.00%	0.00%
1.17% to 16.78%	23	16.91%	16.91%
16.78% to 32.38%	65	47.79%	64.71%
32.38% to 47.98%	28	20.59%	85.29%
47.98% to 63.59%	10	7.35%	92.65%
63.59% to 79.19%	4	2.94%	95.59%
79.19% to 94.79%	4	2.94%	98.53%
Greater than 94.79%	2	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.57%	53.18%	83.82%	68.27%
±2σ	-9.23%	73.99%	93.38%	95.45%
±3σ	-30.03%	94.79%	98.53%	99.73%

Descriptive Statistics

Mean	32.379%
Standard Error	1.784%
Median	26.524%
Mode	22.727%
Standard Deviation	20.804%
Sample Variance	432.816%
Kurtosis	6.71
Skewness	2.23
Range	130.514%
Minimum	8.632%
Maximum	139.146%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.379%	136	100.00%	32.379%
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 1.59. Further, an Excess Kurtosis of 5.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.17%	0	0.00%	0.00%
-58.17% to -43.72%	0	0.00%	0.00%
-43.72% to -29.27%	6	4.41%	4.41%
-29.27% to -14.82%	18	13.24%	17.65%
-14.82% to -0.36%	53	38.97%	56.62%
-0.36% to 14.09%	39	28.68%	85.29%
14.09% to 28.54%	11	8.09%	93.38%
28.54% to 42.99%	5	3.68%	97.06%
42.99% to 57.44%	2	1.47%	98.53%
Greater than 57.44%	2	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.63%	18.90%	77.21%	68.27%
±2σ	-38.90%	38.17%	94.12%	95.45%
±3σ	-58.17%	57.44%	98.53%	99.73%

Descriptive Statistics

Mean	-0.365%
Standard Error	1.652%
Median	-3.661%
Mode	-43.025%
Standard Deviation	19.269%
Sample Variance	371.283%
Kurtosis	5.42
Skewness	1.59
Range	141.167%
Minimum	-43.025%
Maximum	98.142%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.884%	59	43.38%	6.457%
Negative	-12.050%	77	56.62%	-6.822%
Zero	0.000%	0	0.00%	0.000%

BSX Deep Analytical Report