PANW - 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	2.46%	1.76%	2.04%	3.25%	2.54%	2.68%	144.97	152.52	141.34	156.45
Weekly	5.47%	4.60%	5.33%	7.72%	5.59%	5.90%	140.62	157.25	132.97	166.29
Monthly	10.26%	8.23%	10.13%	16.64%	11.63%	12.29%	132.37	167.05	117.83	187.66
Quarterly	17.74%	14.19%	15.52%	29.56%	20.15%	21.29%	121.56	181.90	99.38	222.50
Annual	—	—	—	—	40.30%	42.57%	99.38	222.50	66.41	332.93
Option Time Horizon	—	—	—	—	15.50%	16.37%	127.35	173.63	109.06	202.75

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $148.70 | Strike (K): $150.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.9500 (Bid $8.7000 / Ask $9.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 40.30% (CRR binomial tree, American, n=20 steps) | BS IV: 40.24% (European Black-Scholes) | Yahoo IV (Annual): 42.57% → 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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.57. Further, an Excess Kurtosis of 13.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.27%	23	0.67%	0.67%
-7.27% to -5.42%	33	0.97%	1.64%
-5.42% to -3.58%	112	3.28%	4.92%
-3.58% to -1.73%	374	10.95%	15.87%
-1.73% to 0.11%	1144	33.50%	49.37%
0.11% to 1.96%	1180	34.55%	83.92%
1.96% to 3.80%	390	11.42%	95.34%
3.80% to 5.65%	109	3.19%	98.54%
5.65% to 7.49%	28	0.82%	99.36%
Greater than 7.49%	22	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.35%	2.57%	79.03%	68.27%
±2σ	-4.81%	5.03%	95.40%	95.45%
±3σ	-7.27%	7.49%	98.68%	99.73%

Descriptive Statistics

Mean	0.113%
Standard Error	0.042%
Median	0.142%
Mode	0.000%
Standard Deviation	2.460%
Sample Variance	6.054%
Kurtosis	13.16
Skewness	-0.57
Range	47.042%
Minimum	-28.441%
Maximum	18.601%
Count	3415

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.687%	1816	53.18%	0.897%
Negative	-1.681%	1593	46.65%	-0.784%
Zero	0.000%	6	0.18%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.84%
20	1 Month	4.74%
60	1 Quarter	3.20%
250	1 Year	3.07%
750	3 Years	3.06%
1,250	5 Years	3.25%
2,500	10 Years	3.04%
5,000	20 Years	3.24%
12,500	50 Years	3.24%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.39. Further, an Excess Kurtosis of 29.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.22%	0	0.00%	0.00%
-2.22% to -0.90%	0	0.00%	0.00%
-0.90% to 0.42%	0	0.00%	0.00%
0.42% to 1.74%	565	16.54%	16.54%
1.74% to 3.06%	1608	47.07%	63.61%
3.06% to 4.38%	733	21.46%	85.07%
4.38% to 5.70%	281	8.23%	93.30%
5.70% to 7.02%	111	3.25%	96.55%
7.02% to 8.34%	54	1.58%	98.13%
Greater than 8.34%	64	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.30%	4.82%	84.37%	68.27%
±2σ	-0.46%	6.58%	95.76%	95.45%
±3σ	-2.22%	8.34%	98.13%	99.73%

Descriptive Statistics

Mean	3.056%
Standard Error	0.030%
Median	2.612%
Mode	2.074%
Standard Deviation	1.760%
Sample Variance	3.098%
Kurtosis	29.07
Skewness	3.39
Range	31.442%
Minimum	0.633%
Maximum	32.075%
Count	3416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.056%	3416	100.00%	3.056%
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 1.23. Further, an Excess Kurtosis of 19.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.08%	14	0.41%	0.41%
-6.08% to -4.56%	30	0.88%	1.29%
-4.56% to -3.03%	121	3.54%	4.83%
-3.03% to -1.50%	467	13.67%	18.50%
-1.50% to 0.02%	1144	33.49%	51.99%
0.02% to 1.55%	1055	30.88%	82.87%
1.55% to 3.08%	395	11.56%	94.44%
3.08% to 4.61%	115	3.37%	97.80%
4.61% to 6.13%	45	1.32%	99.12%
Greater than 6.13%	30	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.01%	2.06%	76.49%	68.27%
±2σ	-4.05%	4.10%	95.17%	95.45%
±3σ	-6.08%	6.13%	98.71%	99.73%

Descriptive Statistics

Mean	0.024%
Standard Error	0.035%
Median	-0.054%
Mode	0.000%
Standard Deviation	2.036%
Sample Variance	4.147%
Kurtosis	19.56
Skewness	1.23
Range	45.344%
Minimum	-13.498%
Maximum	31.846%
Count	3416

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.517%	1658	48.54%	0.736%
Negative	-1.391%	1749	51.20%	-0.712%
Zero	0.000%	9	0.26%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.29. Further, an Excess Kurtosis of 2.59 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.86%	7	0.99%	0.99%
-15.86% to -11.76%	9	1.27%	2.26%
-11.76% to -7.65%	25	3.53%	5.78%
-7.65% to -3.55%	87	12.27%	18.05%
-3.55% to 0.55%	216	30.47%	48.52%
0.55% to 4.66%	236	33.29%	81.81%
4.66% to 8.76%	94	13.26%	95.06%
8.76% to 12.86%	23	3.24%	98.31%
12.86% to 16.97%	8	1.13%	99.44%
Greater than 16.97%	4	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.92%	6.03%	74.19%	68.27%
±2σ	-10.39%	11.50%	94.78%	95.45%
±3σ	-15.86%	16.97%	98.45%	99.73%

Descriptive Statistics

Mean	0.554%
Standard Error	0.205%
Median	0.680%
Mode	-5.352%
Standard Deviation	5.471%
Sample Variance	29.928%
Kurtosis	2.59
Skewness	-0.29
Range	48.773%
Minimum	-25.528%
Maximum	23.245%
Count	709

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.108%	396	55.85%	2.294%
Negative	-3.941%	313	44.15%	-1.740%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.72%
12	1 Quarter	7.17%
52	1 Year	7.21%
156	3 Years	7.30%
260	5 Years	7.72%
520	10 Years	7.23%
1,040	20 Years	7.63%
2,600	50 Years	7.63%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.43. Further, an Excess Kurtosis of 9.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.94%	0	0.00%	0.00%
-5.94% to -2.49%	0	0.00%	0.00%
-2.49% to 0.96%	0	0.00%	0.00%
0.96% to 4.41%	116	16.34%	16.34%
4.41% to 7.86%	337	47.46%	63.80%
7.86% to 11.30%	143	20.14%	83.94%
11.30% to 14.75%	60	8.45%	92.39%
14.75% to 18.20%	29	4.08%	96.48%
18.20% to 21.65%	9	1.27%	97.75%
Greater than 21.65%	16	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.26%	12.45%	82.96%	68.27%
±2σ	-1.34%	17.05%	95.92%	95.45%
±3σ	-5.94%	21.65%	97.75%	99.73%

Descriptive Statistics

Mean	7.856%
Standard Error	0.173%
Median	6.570%
Mode	4.713%
Standard Deviation	4.598%
Sample Variance	21.145%
Kurtosis	9.50
Skewness	2.43
Range	40.070%
Minimum	1.915%
Maximum	41.985%
Count	710

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.856%	710	100.00%	7.856%
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 1.18. Further, an Excess Kurtosis of 5.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.10%	1	0.14%	0.14%
-16.10% to -12.10%	4	0.56%	0.70%
-12.10% to -8.10%	21	2.96%	3.66%
-8.10% to -4.11%	111	15.63%	19.30%
-4.11% to -0.11%	248	34.93%	54.23%
-0.11% to 3.89%	201	28.31%	82.54%
3.89% to 7.89%	84	11.83%	94.37%
7.89% to 11.89%	25	3.52%	97.89%
11.89% to 15.89%	4	0.56%	98.45%
Greater than 15.89%	11	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.44%	5.23%	76.20%	68.27%
±2σ	-10.77%	10.56%	95.49%	95.45%
±3σ	-16.10%	15.89%	98.31%	99.73%

Descriptive Statistics

Mean	-0.106%
Standard Error	0.200%
Median	-0.558%
Mode	-4.566%
Standard Deviation	5.332%
Sample Variance	28.428%
Kurtosis	5.08
Skewness	1.18
Range	52.825%
Minimum	-19.053%
Maximum	33.772%
Count	710

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.165%	317	44.65%	1.860%
Negative	-3.560%	392	55.21%	-1.966%
Zero	0.000%	1	0.14%	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 -0.20 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.55%	0	0.00%	0.00%
-28.55% to -20.86%	2	1.23%	1.23%
-20.86% to -13.17%	8	4.91%	6.13%
-13.17% to -5.47%	28	17.18%	23.31%
-5.47% to 2.22%	47	28.83%	52.15%
2.22% to 9.91%	40	24.54%	76.69%
9.91% to 17.60%	26	15.95%	92.64%
17.60% to 25.30%	11	6.75%	99.39%
25.30% to 32.99%	1	0.61%	100.00%
Greater than 32.99%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.04%	12.47%	65.03%	68.27%
±2σ	-18.30%	22.73%	96.93%	95.45%
±3σ	-28.55%	32.99%	100.00%	99.73%

Descriptive Statistics

Mean	2.218%
Standard Error	0.803%
Median	1.809%
Mode	-10.117%
Standard Deviation	10.257%
Sample Variance	105.207%
Kurtosis	-0.20
Skewness	0.01
Range	58.701%
Minimum	-25.820%
Maximum	32.881%
Count	163

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.295%	93	57.05%	5.303%
Negative	-7.185%	70	42.95%	-3.086%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.18%
12	1 Year	14.41%
36	3 Years	16.10%
60	5 Years	16.64%
120	10 Years	15.95%
240	20 Years	16.57%
600	50 Years	16.57%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.21. Further, an Excess Kurtosis of 1.96 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.49%	0	0.00%	0.00%
-6.49% to -0.31%	0	0.00%	0.00%
-0.31% to 5.86%	0	0.00%	0.00%
5.86% to 12.04%	38	23.17%	23.17%
12.04% to 18.21%	53	32.32%	55.49%
18.21% to 24.39%	40	24.39%	79.88%
24.39% to 30.56%	20	12.20%	92.07%
30.56% to 36.73%	7	4.27%	96.34%
36.73% to 42.91%	4	2.44%	98.78%
Greater than 42.91%	2	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.98%	26.44%	74.39%	68.27%
±2σ	1.74%	34.68%	93.90%	95.45%
±3σ	-6.49%	42.91%	98.78%	99.73%

Descriptive Statistics

Mean	18.210%
Standard Error	0.643%
Median	16.504%
Mode	6.349%
Standard Deviation	8.233%
Sample Variance	67.785%
Kurtosis	1.96
Skewness	1.21
Range	46.006%
Minimum	6.349%
Maximum	52.355%
Count	164

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.210%	164	100.00%	18.210%
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 0.55. Further, an Excess Kurtosis of 0.51 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.39%	0	0.00%	0.00%
-31.39% to -23.79%	1	0.61%	0.61%
-23.79% to -16.19%	7	4.27%	4.88%
-16.19% to -8.59%	31	18.90%	23.78%
-8.59% to -0.99%	46	28.05%	51.83%
-0.99% to 6.61%	46	28.05%	79.88%
6.61% to 14.21%	21	12.80%	92.68%
14.21% to 21.81%	7	4.27%	96.95%
21.81% to 29.41%	4	2.44%	99.39%
Greater than 29.41%	1	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.12%	9.14%	67.68%	68.27%
±2σ	-21.25%	19.28%	95.73%	95.45%
±3σ	-31.39%	29.41%	99.39%	99.73%

Descriptive Statistics

Mean	-0.988%
Standard Error	0.791%
Median	-1.325%
Mode	4.168%
Standard Deviation	10.133%
Sample Variance	102.688%
Kurtosis	0.51
Skewness	0.55
Range	59.007%
Minimum	-24.200%
Maximum	34.807%
Count	164

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.102%	71	43.29%	3.508%
Negative	-7.927%	93	56.71%	-4.495%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.60. Further, an Excess Kurtosis of 0.11 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.70%	0	0.00%	0.00%
-46.70% to -33.39%	0	0.00%	0.00%
-33.39% to -20.09%	1	1.82%	1.82%
-20.09% to -6.78%	15	27.27%	29.09%
-6.78% to 6.52%	14	25.45%	54.55%
6.52% to 19.83%	13	23.64%	78.18%
19.83% to 33.13%	8	14.55%	92.73%
33.13% to 46.44%	3	5.45%	98.18%
46.44% to 59.75%	1	1.82%	100.00%
Greater than 59.75%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.22%	24.26%	65.45%	68.27%
±2σ	-28.96%	42.00%	98.18%	95.45%
±3σ	-46.70%	59.75%	100.00%	99.73%

Descriptive Statistics

Mean	6.523%
Standard Error	2.392%
Median	2.987%
Mode	-26.532%
Standard Deviation	17.741%
Sample Variance	314.740%
Kurtosis	0.11
Skewness	0.60
Range	85.106%
Minimum	-26.532%
Maximum	58.574%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.494%	35	63.64%	10.496%
Negative	-10.927%	20	36.36%	-3.973%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	23.30%
12	3 Years	29.89%
20	5 Years	29.56%
40	10 Years	29.16%
80	20 Years	30.25%
200	50 Years	30.25%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.07. Further, an Excess Kurtosis of 7.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.82%	0	0.00%	0.00%
-7.82% to 2.82%	0	0.00%	0.00%
2.82% to 13.46%	0	0.00%	0.00%
13.46% to 24.11%	13	23.21%	23.21%
24.11% to 34.75%	18	32.14%	55.36%
34.75% to 45.39%	16	28.57%	83.93%
45.39% to 56.03%	6	10.71%	94.64%
56.03% to 66.67%	1	1.79%	96.43%
66.67% to 77.31%	1	1.79%	98.21%
Greater than 77.31%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	20.56%	48.94%	82.14%	68.27%
±2σ	6.37%	63.12%	96.43%	95.45%
±3σ	-7.82%	77.31%	98.21%	99.73%

Descriptive Statistics

Mean	34.747%
Standard Error	1.896%
Median	32.966%
Mode	15.560%
Standard Deviation	14.189%
Sample Variance	201.323%
Kurtosis	7.41
Skewness	2.07
Range	84.575%
Minimum	15.560%
Maximum	100.135%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.747%	56	100.00%	34.747%
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 0.14. Further, an Excess Kurtosis of -0.40 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -49.99%	0	0.00%	0.00%
-49.99% to -38.35%	0	0.00%	0.00%
-38.35% to -26.70%	4	7.14%	7.14%
-26.70% to -15.06%	9	16.07%	23.21%
-15.06% to -3.42%	13	23.21%	46.43%
-3.42% to 8.22%	14	25.00%	71.43%
8.22% to 19.86%	14	25.00%	96.43%
19.86% to 31.50%	1	1.79%	98.21%
31.50% to 43.15%	1	1.79%	100.00%
Greater than 43.15%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.94%	12.10%	66.07%	68.27%
±2σ	-34.47%	27.62%	96.43%	95.45%
±3σ	-49.99%	43.15%	100.00%	99.73%

Descriptive Statistics

Mean	-3.421%
Standard Error	2.074%
Median	-2.902%
Mode	-36.482%
Standard Deviation	15.522%
Sample Variance	240.923%
Kurtosis	-0.40
Skewness	0.14
Range	73.001%
Minimum	-36.482%
Maximum	36.519%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.112%	22	39.29%	4.758%
Negative	-13.472%	34	60.71%	-8.179%
Zero	0.000%	0	0.00%	0.000%

PANW Deep Analytical Report