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%	2.45%	2.65%	159.81	167.82	155.95	171.98
Weekly	5.48%	4.60%	5.34%	7.72%	5.38%	5.84%	155.19	172.83	147.05	182.39
Monthly	10.24%	8.24%	10.12%	16.74%	11.21%	12.15%	146.41	183.19	130.89	204.92
Quarterly	17.57%	14.10%	15.29%	29.77%	19.41%	21.04%	134.88	198.85	111.08	241.45
Annual	—	—	—	—	38.82%	42.08%	111.08	241.45	75.34	355.98
Option Time Horizon	—	—	—	—	14.65%	15.88%	141.45	189.61	122.17	219.54

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $163.77 | Strike (K): $165.00 (first OTM call ≥ spot) | Observed Mid-Price: $9.3750 (Bid $8.7500 / Ask $10.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 38.82% (CRR binomial tree, American, n=20 steps) | BS IV: 38.73% (European Black-Scholes) | Yahoo IV (Annual): 42.08% → 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 13.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.25%	23	0.67%	0.67%
-7.25% to -5.41%	34	0.99%	1.66%
-5.41% to -3.57%	112	3.26%	4.92%
-3.57% to -1.73%	377	10.97%	15.89%
-1.73% to 0.12%	1153	33.56%	49.45%
0.12% to 1.96%	1184	34.46%	83.91%
1.96% to 3.80%	393	11.44%	95.34%
3.80% to 5.64%	110	3.20%	98.54%
5.64% to 7.49%	28	0.81%	99.36%
Greater than 7.49%	22	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.34%	2.57%	78.99%	68.27%
±2σ	-4.80%	5.03%	95.43%	95.45%
±3σ	-7.25%	7.49%	98.69%	99.73%

Descriptive Statistics

Mean	0.116%
Standard Error	0.042%
Median	0.142%
Mode	0.000%
Standard Deviation	2.457%
Sample Variance	6.039%
Kurtosis	13.15
Skewness	-0.57
Range	47.042%
Minimum	-28.441%
Maximum	18.601%
Count	3436

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.686%	1830	53.26%	0.898%
Negative	-1.680%	1600	46.57%	-0.782%
Zero	0.000%	6	0.17%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.90%
20	1 Month	3.42%
60	1 Quarter	3.59%
250	1 Year	3.08%
750	3 Years	3.09%
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 3.38. 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 -2.21%	0	0.00%	0.00%
-2.21% to -0.90%	0	0.00%	0.00%
-0.90% to 0.42%	0	0.00%	0.00%
0.42% to 1.74%	570	16.58%	16.58%
1.74% to 3.06%	1612	46.90%	63.49%
3.06% to 4.38%	741	21.56%	85.05%
4.38% to 5.69%	280	8.15%	93.19%
5.69% to 7.01%	116	3.38%	96.57%
7.01% to 8.33%	53	1.54%	98.11%
Greater than 8.33%	65	1.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.30%	4.81%	84.14%	68.27%
±2σ	-0.46%	6.57%	95.75%	95.45%
±3σ	-2.21%	8.33%	98.11%	99.73%

Descriptive Statistics

Mean	3.058%
Standard Error	0.030%
Median	2.616%
Mode	2.074%
Standard Deviation	1.757%
Sample Variance	3.088%
Kurtosis	29.07
Skewness	3.38
Range	31.442%
Minimum	0.633%
Maximum	32.075%
Count	3437

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.058%	3437	100.00%	3.058%
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 19.50 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	0.87%	1.28%
-4.56% to -3.03%	122	3.55%	4.83%
-3.03% to -1.50%	470	13.67%	18.50%
-1.50% to 0.02%	1153	33.55%	52.05%
0.02% to 1.55%	1061	30.87%	82.92%
1.55% to 3.07%	396	11.52%	94.44%
3.07% to 4.60%	116	3.38%	97.82%
4.60% to 6.13%	45	1.31%	99.13%
Greater than 6.13%	30	0.87%	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%	4.09%	95.17%	95.45%
±3σ	-6.08%	6.13%	98.72%	99.73%

Descriptive Statistics

Mean	0.021%
Standard Error	0.035%
Median	-0.054%
Mode	0.000%
Standard Deviation	2.035%
Sample Variance	4.141%
Kurtosis	19.50
Skewness	1.23
Range	45.344%
Minimum	-13.498%
Maximum	31.846%
Count	3437

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.517%	1664	48.41%	0.734%
Negative	-1.390%	1764	51.32%	-0.713%
Zero	0.000%	9	0.26%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.30. Further, an Excess Kurtosis of 2.58 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.87%	7	0.98%	0.98%
-15.87% to -11.76%	10	1.40%	2.38%
-11.76% to -7.65%	24	3.37%	5.75%
-7.65% to -3.54%	87	12.20%	17.95%
-3.54% to 0.57%	218	30.58%	48.53%
0.57% to 4.68%	237	33.24%	81.77%
4.68% to 8.78%	94	13.18%	94.95%
8.78% to 12.89%	24	3.37%	98.32%
12.89% to 17.00%	8	1.12%	99.44%
Greater than 17.00%	4	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.91%	6.04%	74.47%	68.27%
±2σ	-10.39%	11.52%	94.95%	95.45%
±3σ	-15.87%	17.00%	98.46%	99.73%

Descriptive Statistics

Mean	0.567%
Standard Error	0.205%
Median	0.684%
Mode	-5.352%
Standard Deviation	5.478%
Sample Variance	30.010%
Kurtosis	2.58
Skewness	-0.30
Range	48.773%
Minimum	-25.528%
Maximum	23.245%
Count	713

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.116%	399	55.96%	2.303%
Negative	-3.943%	314	44.04%	-1.736%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.56%
12	1 Quarter	8.62%
52	1 Year	7.40%
156	3 Years	7.43%
260	5 Years	7.72%
520	10 Years	7.25%
1,040	20 Years	7.64%
2,600	50 Years	7.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.42. Further, an Excess Kurtosis of 9.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.93%	0	0.00%	0.00%
-5.93% to -2.48%	0	0.00%	0.00%
-2.48% to 0.97%	0	0.00%	0.00%
0.97% to 4.42%	116	16.25%	16.25%
4.42% to 7.87%	340	47.62%	63.87%
7.87% to 11.31%	143	20.03%	83.89%
11.31% to 14.76%	60	8.40%	92.30%
14.76% to 18.21%	30	4.20%	96.50%
18.21% to 21.66%	9	1.26%	97.76%
Greater than 21.66%	16	2.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.27%	12.46%	83.05%	68.27%
±2σ	-1.33%	17.06%	95.94%	95.45%
±3σ	-5.93%	21.66%	97.76%	99.73%

Descriptive Statistics

Mean	7.865%
Standard Error	0.172%
Median	6.570%
Mode	4.713%
Standard Deviation	4.597%
Sample Variance	21.133%
Kurtosis	9.44
Skewness	2.42
Range	40.070%
Minimum	1.915%
Maximum	41.985%
Count	714

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.865%	714	100.00%	7.865%
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 1.19. Further, an Excess Kurtosis of 5.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.15%	1	0.14%	0.14%
-16.15% to -12.14%	4	0.56%	0.70%
-12.14% to -8.14%	21	2.94%	3.64%
-8.14% to -4.13%	111	15.55%	19.19%
-4.13% to -0.12%	247	34.59%	53.78%
-0.12% to 3.89%	206	28.85%	82.63%
3.89% to 7.90%	84	11.76%	94.40%
7.90% to 11.91%	24	3.36%	97.76%
11.91% to 15.92%	5	0.70%	98.46%
Greater than 15.92%	11	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.46%	5.23%	76.33%	68.27%
±2σ	-10.81%	10.57%	95.66%	95.45%
±3σ	-16.15%	15.92%	98.32%	99.73%

Descriptive Statistics

Mean	-0.119%
Standard Error	0.200%
Median	-0.568%
Mode	-4.566%
Standard Deviation	5.345%
Sample Variance	28.569%
Kurtosis	5.04
Skewness	1.19
Range	52.825%
Minimum	-19.053%
Maximum	33.772%
Count	714

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.170%	318	44.54%	1.857%
Negative	-3.573%	395	55.32%	-1.977%
Zero	0.000%	1	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.00. 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 -28.46%	0	0.00%	0.00%
-28.46% to -20.78%	2	1.22%	1.22%
-20.78% to -13.10%	9	5.49%	6.71%
-13.10% to -5.42%	27	16.46%	23.17%
-5.42% to 2.27%	47	28.66%	51.83%
2.27% to 9.95%	40	24.39%	76.22%
9.95% to 17.63%	27	16.46%	92.68%
17.63% to 25.32%	11	6.71%	99.39%
25.32% to 33.00%	1	0.61%	100.00%
Greater than 33.00%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.98%	12.51%	64.63%	68.27%
±2σ	-18.22%	22.76%	96.95%	95.45%
±3σ	-28.46%	33.00%	100.00%	99.73%

Descriptive Statistics

Mean	2.268%
Standard Error	0.800%
Median	1.978%
Mode	-10.117%
Standard Deviation	10.244%
Sample Variance	104.942%
Kurtosis	-0.20
Skewness	0.00
Range	58.701%
Minimum	-25.820%
Maximum	32.881%
Count	164

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.306%	94	57.32%	5.334%
Negative	-7.183%	70	42.68%	-3.066%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	17.53%
12	1 Year	15.03%
36	3 Years	16.43%
60	5 Years	16.74%
120	10 Years	16.01%
240	20 Years	16.60%
600	50 Years	16.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 1.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.46%	0	0.00%	0.00%
-6.46% to -0.28%	0	0.00%	0.00%
-0.28% to 5.89%	0	0.00%	0.00%
5.89% to 12.07%	38	23.03%	23.03%
12.07% to 18.25%	54	32.73%	55.76%
18.25% to 24.43%	40	24.24%	80.00%
24.43% to 30.60%	21	12.73%	92.73%
30.60% to 36.78%	6	3.64%	96.36%
36.78% to 42.96%	4	2.42%	98.79%
Greater than 42.96%	2	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.01%	26.48%	73.33%	68.27%
±2σ	1.78%	34.72%	93.94%	95.45%
±3σ	-6.46%	42.96%	98.79%	99.73%

Descriptive Statistics

Mean	18.248%
Standard Error	0.641%
Median	16.679%
Mode	6.349%
Standard Deviation	8.236%
Sample Variance	67.839%
Kurtosis	1.91
Skewness	1.20
Range	46.006%
Minimum	6.349%
Maximum	52.355%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.248%	165	100.00%	18.248%
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 0.56. 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 -31.42%	0	0.00%	0.00%
-31.42% to -23.82%	1	0.61%	0.61%
-23.82% to -16.23%	7	4.24%	4.85%
-16.23% to -8.64%	32	19.39%	24.24%
-8.64% to -1.04%	45	27.27%	51.52%
-1.04% to 6.55%	47	28.48%	80.00%
6.55% to 14.14%	21	12.73%	92.73%
14.14% to 21.74%	7	4.24%	96.97%
21.74% to 29.33%	4	2.42%	99.39%
Greater than 29.33%	1	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.17%	9.08%	67.88%	68.27%
±2σ	-21.29%	19.21%	96.36%	95.45%
±3σ	-31.42%	29.33%	99.39%	99.73%

Descriptive Statistics

Mean	-1.044%
Standard Error	0.788%
Median	-1.348%
Mode	4.168%
Standard Deviation	10.125%
Sample Variance	102.515%
Kurtosis	0.51
Skewness	0.56
Range	59.007%
Minimum	-24.200%
Maximum	34.807%
Count	165

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.099%	71	43.03%	3.485%
Negative	-7.949%	94	56.97%	-4.529%
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 0.62. Further, an Excess Kurtosis of 0.17 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.03%	0	0.00%	0.00%
-46.03% to -32.85%	0	0.00%	0.00%
-32.85% to -19.67%	1	1.82%	1.82%
-19.67% to -6.50%	15	27.27%	29.09%
-6.50% to 6.68%	14	25.45%	54.55%
6.68% to 19.86%	13	23.64%	78.18%
19.86% to 33.04%	8	14.55%	92.73%
33.04% to 46.22%	3	5.45%	98.18%
46.22% to 59.40%	1	1.82%	100.00%
Greater than 59.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.89%	24.26%	65.45%	68.27%
±2σ	-28.46%	41.83%	98.18%	95.45%
±3σ	-46.03%	59.40%	100.00%	99.73%

Descriptive Statistics

Mean	6.684%
Standard Error	2.369%
Median	2.987%
Mode	-26.532%
Standard Deviation	17.572%
Sample Variance	308.776%
Kurtosis	0.17
Skewness	0.62
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	-10.483%	20	36.36%	-3.812%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	24.37%
12	3 Years	30.25%
20	5 Years	29.77%
40	10 Years	29.27%
80	20 Years	30.33%
200	50 Years	30.33%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.10. Further, an Excess Kurtosis of 7.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.43%	0	0.00%	0.00%
-7.43% to 3.14%	0	0.00%	0.00%
3.14% to 13.72%	0	0.00%	0.00%
13.72% to 24.29%	12	21.43%	21.43%
24.29% to 34.86%	19	33.93%	55.36%
34.86% to 45.44%	16	28.57%	83.93%
45.44% to 56.01%	6	10.71%	94.64%
56.01% to 66.58%	1	1.79%	96.43%
66.58% to 77.16%	1	1.79%	98.21%
Greater than 77.16%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	20.77%	48.96%	82.14%	68.27%
±2σ	6.67%	63.06%	96.43%	95.45%
±3σ	-7.43%	77.16%	98.21%	99.73%

Descriptive Statistics

Mean	34.864%
Standard Error	1.884%
Median	32.965%
Mode	15.560%
Standard Deviation	14.098%
Sample Variance	198.761%
Kurtosis	7.59
Skewness	2.10
Range	84.575%
Minimum	15.560%
Maximum	100.135%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.864%	56	100.00%	34.864%
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 -0.32 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -49.50%	0	0.00%	0.00%
-49.50% to -38.03%	0	0.00%	0.00%
-38.03% to -26.56%	4	7.14%	7.14%
-26.56% to -15.09%	9	16.07%	23.21%
-15.09% to -3.62%	12	21.43%	44.64%
-3.62% to 7.84%	15	26.79%	71.43%
7.84% to 19.31%	13	23.21%	94.64%
19.31% to 30.78%	2	3.57%	98.21%
30.78% to 42.25%	1	1.79%	100.00%
Greater than 42.25%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.92%	11.67%	66.07%	68.27%
±2σ	-34.21%	26.96%	96.43%	95.45%
±3σ	-49.50%	42.25%	100.00%	99.73%

Descriptive Statistics

Mean	-3.625%
Standard Error	2.043%
Median	-2.902%
Mode	-36.482%
Standard Deviation	15.291%
Sample Variance	233.809%
Kurtosis	-0.32
Skewness	0.13
Range	73.001%
Minimum	-36.482%
Maximum	36.519%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.594%	22	39.29%	4.555%
Negative	-13.472%	34	60.71%	-8.179%
Zero	0.000%	0	0.00%	0.000%

PANW Deep Analytical Report