PYPL - 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	2.42%	1.56%	1.91%	3.33%	2.33%	2.49%	40.69	42.63	39.75	43.64
Weekly	5.07%	4.46%	5.15%	8.06%	5.13%	5.48%	39.57	43.84	37.59	46.15
Monthly	9.83%	10.11%	10.63%	17.40%	10.68%	11.41%	37.43	46.34	33.64	51.57
Quarterly	18.66%	17.29%	22.06%	28.94%	18.50%	19.76%	34.62	50.11	28.77	60.29
Annual	—	—	—	—	36.99%	39.53%	28.77	60.29	19.87	87.28
Option Time Horizon	—	—	—	—	14.23%	15.20%	36.13	48.02	31.33	55.36

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $41.65 | Strike (K): $42.50 (first OTM call ≥ spot) | Observed Mid-Price: $2.0850 (Bid $2.0000 / Ask $2.1700) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.67% | Binomial IV (Annual): 36.99% (CRR binomial tree, American, n=20 steps) | BS IV: 37.32% (European Black-Scholes) | Yahoo IV (Annual): 39.53% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2025-11-19	$0.1400

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.23%	17	0.64%	0.64%
-7.23% to -5.41%	29	1.08%	1.72%
-5.41% to -3.60%	89	3.33%	5.05%
-3.60% to -1.78%	310	11.60%	16.65%
-1.78% to 0.03%	852	31.87%	48.52%
0.03% to 1.85%	940	35.17%	83.69%
1.85% to 3.66%	310	11.60%	95.29%
3.66% to 5.48%	83	3.11%	98.39%
5.48% to 7.29%	24	0.90%	99.29%
Greater than 7.29%	19	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.39%	2.45%	77.59%	68.27%
±2σ	-4.81%	4.87%	95.32%	95.45%
±3σ	-7.23%	7.29%	98.65%	99.73%

Descriptive Statistics

Mean	0.034%
Standard Error	0.047%
Median	0.094%
Mode	0.000%
Standard Deviation	2.420%
Sample Variance	5.855%
Kurtosis	9.87
Skewness	-0.57
Range	38.700%
Minimum	-24.590%
Maximum	14.110%
Count	2673

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.639%	1389	51.96%	0.852%
Negative	-1.712%	1276	47.74%	-0.817%
Zero	0.000%	8	0.30%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.96%
20	1 Month	4.25%
60	1 Quarter	2.95%
250	1 Year	3.09%
750	3 Years	2.94%
1,250	5 Years	3.33%
2,500	10 Years	3.00%
5,000	20 Years	3.04%
12,500	50 Years	3.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.04. Further, an Excess Kurtosis of 7.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.87%	0	0.00%	0.00%
-1.87% to -0.70%	0	0.00%	0.00%
-0.70% to 0.48%	0	0.00%	0.00%
0.48% to 1.65%	558	20.87%	20.87%
1.65% to 2.82%	1076	40.24%	61.11%
2.82% to 4.00%	576	21.54%	82.65%
4.00% to 5.17%	269	10.06%	92.71%
5.17% to 6.34%	106	3.96%	96.67%
6.34% to 7.51%	49	1.83%	98.50%
Greater than 7.51%	40	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.26%	4.39%	79.47%	68.27%
±2σ	-0.31%	5.95%	95.89%	95.45%
±3σ	-1.87%	7.52%	98.50%	99.73%

Descriptive Statistics

Mean	2.823%
Standard Error	0.030%
Median	2.444%
Mode	2.039%
Standard Deviation	1.564%
Sample Variance	2.446%
Kurtosis	7.42
Skewness	2.04
Range	15.512%
Minimum	0.655%
Maximum	16.167%
Count	2674

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.823%	2674	100.00%	2.823%
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 2.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.66%	12	0.45%	0.45%
-5.66% to -4.23%	25	0.93%	1.38%
-4.23% to -2.80%	108	4.04%	5.42%
-2.80% to -1.37%	357	13.35%	18.77%
-1.37% to 0.06%	878	32.83%	51.61%
0.06% to 1.48%	799	29.88%	81.49%
1.48% to 2.91%	322	12.04%	93.53%
2.91% to 4.34%	106	3.96%	97.49%
4.34% to 5.77%	48	1.80%	99.29%
Greater than 5.77%	19	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.85%	1.96%	74.20%	68.27%
±2σ	-3.76%	3.87%	94.39%	95.45%
±3σ	-5.66%	5.77%	98.84%	99.73%

Descriptive Statistics

Mean	0.055%
Standard Error	0.037%
Median	-0.018%
Mode	-0.785%
Standard Deviation	1.906%
Sample Variance	3.634%
Kurtosis	2.35
Skewness	0.14
Range	21.721%
Minimum	-11.384%
Maximum	10.337%
Count	2674

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.484%	1321	49.40%	0.733%
Negative	-1.344%	1349	50.45%	-0.678%
Zero	0.000%	4	0.15%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.65. Further, an Excess Kurtosis of 3.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.05%	6	1.08%	1.08%
-15.05% to -11.25%	9	1.62%	2.70%
-11.25% to -7.45%	23	4.14%	6.85%
-7.45% to -3.65%	48	8.65%	15.50%
-3.65% to 0.15%	180	32.43%	47.93%
0.15% to 3.96%	186	33.51%	81.44%
3.96% to 7.76%	78	14.05%	95.50%
7.76% to 11.56%	19	3.42%	98.92%
11.56% to 15.36%	2	0.36%	99.28%
Greater than 15.36%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.91%	5.22%	77.30%	68.27%
±2σ	-9.98%	10.29%	94.59%	95.45%
±3σ	-15.05%	15.36%	98.20%	99.73%

Descriptive Statistics

Mean	0.155%
Standard Error	0.215%
Median	0.321%
Mode	-1.619%
Standard Deviation	5.067%
Sample Variance	25.670%
Kurtosis	3.76
Skewness	-0.65
Range	47.742%
Minimum	-29.388%
Maximum	18.354%
Count	555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.401%	305	54.95%	1.869%
Negative	-3.820%	249	44.87%	-1.714%
Zero	0.000%	1	0.18%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.80%
12	1 Quarter	7.57%
52	1 Year	7.45%
156	3 Years	7.10%
260	5 Years	8.06%
520	10 Years	7.09%
1,040	20 Years	7.18%
2,600	50 Years	7.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.55. Further, an Excess Kurtosis of 12.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.98%	0	0.00%	0.00%
-5.98% to -2.64%	0	0.00%	0.00%
-2.64% to 0.71%	0	0.00%	0.00%
0.71% to 4.06%	106	19.06%	19.06%
4.06% to 7.41%	249	44.78%	63.85%
7.41% to 10.75%	112	20.14%	83.99%
10.75% to 14.10%	51	9.17%	93.17%
14.10% to 17.45%	17	3.06%	96.22%
17.45% to 20.80%	10	1.80%	98.02%
Greater than 20.80%	11	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.94%	11.87%	83.09%	68.27%
±2σ	-1.52%	16.33%	95.32%	95.45%
±3σ	-5.98%	20.79%	98.02%	99.73%

Descriptive Statistics

Mean	7.406%
Standard Error	0.189%
Median	6.316%
Mode	3.361%
Standard Deviation	4.463%
Sample Variance	19.921%
Kurtosis	12.54
Skewness	2.55
Range	44.269%
Minimum	1.955%
Maximum	46.224%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.406%	556	100.00%	7.406%
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 1.63. Further, an Excess Kurtosis of 9.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.29%	0	0.00%	0.00%
-15.29% to -11.42%	5	0.90%	0.90%
-11.42% to -7.56%	15	2.70%	3.60%
-7.56% to -3.69%	78	14.03%	17.63%
-3.69% to 0.17%	221	39.75%	57.37%
0.17% to 4.04%	148	26.62%	83.99%
4.04% to 7.90%	51	9.17%	93.17%
7.90% to 11.76%	23	4.14%	97.30%
11.76% to 15.63%	11	1.98%	99.28%
Greater than 15.63%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.98%	5.32%	77.34%	68.27%
±2σ	-10.13%	10.47%	94.42%	95.45%
±3σ	-15.29%	15.63%	99.28%	99.73%

Descriptive Statistics

Mean	0.171%
Standard Error	0.218%
Median	-0.410%
Mode	-2.724%
Standard Deviation	5.152%
Sample Variance	26.542%
Kurtosis	9.17
Skewness	1.63
Range	57.379%
Minimum	-15.076%
Maximum	42.303%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.164%	248	44.60%	1.857%
Negative	-3.044%	308	55.40%	-1.686%
Zero	0.000%	0	0.00%	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 1.28 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.95%	1	0.79%	0.79%
-28.95% to -21.57%	1	0.79%	1.57%
-21.57% to -14.20%	6	4.72%	6.30%
-14.20% to -6.82%	18	14.17%	20.47%
-6.82% to 0.56%	36	28.35%	48.82%
0.56% to 7.93%	36	28.35%	77.17%
7.93% to 15.31%	24	18.90%	96.06%
15.31% to 22.68%	2	1.57%	97.64%
22.68% to 30.06%	3	2.36%	100.00%
Greater than 30.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.28%	10.39%	71.65%	68.27%
±2σ	-19.11%	20.22%	93.70%	95.45%
±3σ	-28.95%	30.06%	99.21%	99.73%

Descriptive Statistics

Mean	0.555%
Standard Error	0.873%
Median	0.904%
Mode	-34.902%
Standard Deviation	9.834%
Sample Variance	96.704%
Kurtosis	1.28
Skewness	-0.30
Range	63.375%
Minimum	-34.902%
Maximum	28.473%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.291%	70	55.12%	4.019%
Negative	-7.717%	57	44.88%	-3.464%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	17.10%
12	1 Year	14.56%
36	3 Years	15.43%
60	5 Years	17.40%
120	10 Years	15.45%
240	20 Years	15.53%
600	50 Years	15.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.12. Further, an Excess Kurtosis of 16.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.90%	0	0.00%	0.00%
-12.90% to -5.32%	0	0.00%	0.00%
-5.32% to 2.26%	0	0.00%	0.00%
2.26% to 9.85%	18	14.06%	14.06%
9.85% to 17.43%	60	46.88%	60.94%
17.43% to 25.01%	30	23.44%	84.38%
25.01% to 32.59%	12	9.38%	93.75%
32.59% to 40.17%	5	3.91%	97.66%
40.17% to 47.75%	1	0.78%	98.44%
Greater than 47.75%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.32%	27.53%	81.25%	68.27%
±2σ	-2.79%	37.64%	96.09%	95.45%
±3σ	-12.90%	47.75%	98.44%	99.73%

Descriptive Statistics

Mean	17.426%
Standard Error	0.893%
Median	15.136%
Mode	13.779%
Standard Deviation	10.108%
Sample Variance	102.168%
Kurtosis	16.80
Skewness	3.12
Range	81.520%
Minimum	4.935%
Maximum	86.455%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.426%	128	100.00%	17.426%
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 1.38. Further, an Excess Kurtosis of 5.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.34%	0	0.00%	0.00%
-31.34% to -23.36%	1	0.78%	0.78%
-23.36% to -15.39%	2	1.56%	2.34%
-15.39% to -7.42%	23	17.97%	20.31%
-7.42% to 0.56%	45	35.16%	55.47%
0.56% to 8.53%	35	27.34%	82.81%
8.53% to 16.50%	14	10.94%	93.75%
16.50% to 24.48%	4	3.12%	96.88%
24.48% to 32.45%	3	2.34%	99.22%
Greater than 32.45%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.07%	11.19%	77.34%	68.27%
±2σ	-20.70%	21.82%	92.97%	95.45%
±3σ	-31.34%	32.45%	99.22%	99.73%

Descriptive Statistics

Mean	0.558%
Standard Error	0.940%
Median	-0.679%
Mode	-24.618%
Standard Deviation	10.631%
Sample Variance	113.012%
Kurtosis	5.00
Skewness	1.38
Range	78.973%
Minimum	-24.618%
Maximum	54.355%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.936%	58	45.31%	4.049%
Negative	-6.385%	70	54.69%	-3.492%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.04. Further, an Excess Kurtosis of 1.86 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.04%	0	0.00%	0.00%
-54.04% to -40.04%	1	2.33%	2.33%
-40.04% to -26.04%	2	4.65%	6.98%
-26.04% to -12.04%	5	11.63%	18.60%
-12.04% to 1.96%	14	32.56%	51.16%
1.96% to 15.95%	12	27.91%	79.07%
15.95% to 29.95%	8	18.60%	97.67%
29.95% to 43.95%	0	0.00%	97.67%
43.95% to 57.95%	0	0.00%	97.67%
Greater than 57.95%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.71%	20.62%	74.42%	68.27%
±2σ	-35.38%	39.28%	95.35%	95.45%
±3σ	-54.04%	57.95%	97.67%	99.73%

Descriptive Statistics

Mean	1.955%
Standard Error	2.846%
Median	0.742%
Mode	-48.860%
Standard Deviation	18.665%
Sample Variance	348.365%
Kurtosis	1.86
Skewness	0.04
Range	108.267%
Minimum	-48.860%
Maximum	59.407%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.615%	23	53.49%	7.817%
Negative	-12.603%	20	46.51%	-5.862%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	24.43%
12	3 Years	27.37%
20	5 Years	28.94%
40	10 Years	27.64%
80	20 Years	27.48%
200	50 Years	27.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.77. Further, an Excess Kurtosis of 10.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.86%	0	0.00%	0.00%
-18.86% to -5.90%	0	0.00%	0.00%
-5.90% to 7.07%	0	0.00%	0.00%
7.07% to 20.04%	6	13.64%	13.64%
20.04% to 33.00%	23	52.27%	65.91%
33.00% to 45.97%	9	20.45%	86.36%
45.97% to 58.94%	3	6.82%	93.18%
58.94% to 71.90%	2	4.55%	97.73%
71.90% to 84.87%	0	0.00%	97.73%
Greater than 84.87%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.71%	50.29%	84.09%	68.27%
±2σ	-1.57%	67.58%	97.73%	95.45%
±3σ	-18.86%	84.87%	97.73%	99.73%

Descriptive Statistics

Mean	33.004%
Standard Error	2.606%
Median	28.172%
Mode	11.666%
Standard Deviation	17.289%
Sample Variance	298.925%
Kurtosis	10.87
Skewness	2.77
Range	102.898%
Minimum	11.666%
Maximum	114.564%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.004%	44	100.00%	33.004%
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 2.10. Further, an Excess Kurtosis of 7.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.58%	0	0.00%	0.00%
-64.58% to -48.04%	0	0.00%	0.00%
-48.04% to -31.49%	1	2.27%	2.27%
-31.49% to -14.95%	7	15.91%	18.18%
-14.95% to 1.60%	18	40.91%	59.09%
1.60% to 18.15%	11	25.00%	84.09%
18.15% to 34.69%	4	9.09%	93.18%
34.69% to 51.24%	2	4.55%	97.73%
51.24% to 67.78%	0	0.00%	97.73%
Greater than 67.78%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.46%	23.66%	81.82%	68.27%
±2σ	-42.52%	45.72%	95.45%	95.45%
±3σ	-64.58%	67.78%	97.73%	99.73%

Descriptive Statistics

Mean	1.600%
Standard Error	3.326%
Median	-1.821%
Mode	-38.874%
Standard Deviation	22.061%
Sample Variance	486.689%
Kurtosis	7.25
Skewness	2.10
Range	135.360%
Minimum	-38.874%
Maximum	96.486%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.357%	20	45.45%	7.890%
Negative	-11.530%	24	54.55%	-6.289%
Zero	0.000%	0	0.00%	0.000%

PYPL Deep Analytical Report