PDFS - 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	3.29%	3.33%	3.07%	3.76%	2.37%	3.64%	31.67	33.21	30.93	34.01
Weekly	7.40%	7.49%	7.51%	9.02%	5.23%	8.01%	30.78	34.17	29.21	36.00
Monthly	14.93%	15.56%	15.24%	19.42%	10.88%	16.68%	29.09	36.16	26.09	40.31
Quarterly	24.09%	30.74%	28.10%	35.10%	18.84%	28.89%	26.86	39.15	22.25	47.27
Annual	—	—	—	—	37.69%	57.79%	22.25	47.27	15.26	68.91
Option Time Horizon	—	—	—	—	17.86%	27.39%	27.12	38.77	22.69	46.36

Calculation Notes: Computed at 2026-02-22T13:01 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $32.43 | Strike (K): $35.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.4000 (Bid $0.2500 / Ask $2.5500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 37.69% (CRR binomial tree, American, n=20 steps) | BS IV: 37.35% (European Black-Scholes) | Yahoo IV (Annual): 57.79% → 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 0.12. Further, an Excess Kurtosis of 10.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.79%	52	0.84%	0.84%
-9.79% to -7.33%	46	0.75%	1.59%
-7.33% to -4.86%	188	3.05%	4.63%
-4.86% to -2.40%	680	11.02%	15.65%
-2.40% to 0.07%	2167	35.10%	50.75%
0.07% to 2.53%	2080	33.70%	84.45%
2.53% to 4.99%	665	10.77%	95.22%
4.99% to 7.46%	182	2.95%	98.17%
7.46% to 9.92%	62	1.00%	99.17%
Greater than 9.92%	51	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.22%	3.35%	79.17%	68.27%
±2σ	-6.50%	6.64%	95.61%	95.45%
±3σ	-9.79%	9.92%	98.33%	99.73%

Descriptive Statistics

Mean	0.066%
Standard Error	0.042%
Median	0.000%
Mode	0.000%
Standard Deviation	3.285%
Sample Variance	10.792%
Kurtosis	10.26
Skewness	0.12
Range	58.147%
Minimum	-28.692%
Maximum	29.455%
Count	6173

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.267%	3065	49.65%	1.126%
Negative	-2.214%	2955	47.87%	-1.060%
Zero	0.000%	153	2.48%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.14%
20	1 Month	5.82%
60	1 Quarter	4.67%
250	1 Year	4.48%
750	3 Years	3.80%
1,250	5 Years	3.76%
2,500	10 Years	3.74%
5,000	20 Years	4.33%
12,500	50 Years	4.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.07. Further, an Excess Kurtosis of 15.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.51%	0	0.00%	0.00%
-5.51% to -3.01%	0	0.00%	0.00%
-3.01% to -0.51%	0	0.00%	0.00%
-0.51% to 1.99%	807	13.07%	13.07%
1.99% to 4.50%	3213	52.04%	65.11%
4.50% to 7.00%	1302	21.09%	86.20%
7.00% to 9.50%	440	7.13%	93.33%
9.50% to 12.00%	203	3.29%	96.61%
12.00% to 14.50%	85	1.38%	97.99%
Greater than 14.50%	124	2.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.16%	7.83%	87.79%	68.27%
±2σ	-2.17%	11.16%	95.97%	95.45%
±3σ	-5.51%	14.50%	97.99%	99.73%

Descriptive Statistics

Mean	4.495%
Standard Error	0.042%
Median	3.579%
Mode	4.167%
Standard Deviation	3.335%
Sample Variance	11.123%
Kurtosis	15.27
Skewness	3.07
Range	39.629%
Minimum	0.077%
Maximum	39.706%
Count	6174

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.495%	6174	100.00%	4.495%
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 0.47. Further, an Excess Kurtosis of 7.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.20%	41	0.66%	0.66%
-9.20% to -6.89%	70	1.13%	1.80%
-6.89% to -4.58%	156	2.53%	4.32%
-4.58% to -2.28%	729	11.81%	16.13%
-2.28% to 0.03%	2223	36.01%	52.14%
0.03% to 2.33%	2000	32.39%	84.53%
2.33% to 4.64%	618	10.01%	94.54%
4.64% to 6.94%	205	3.32%	97.86%
6.94% to 9.25%	73	1.18%	99.04%
Greater than 9.25%	59	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.05%	3.10%	79.04%	68.27%
±2σ	-6.12%	6.17%	95.00%	95.45%
±3σ	-9.20%	9.25%	98.38%	99.73%

Descriptive Statistics

Mean	0.027%
Standard Error	0.039%
Median	0.000%
Mode	0.000%
Standard Deviation	3.074%
Sample Variance	9.452%
Kurtosis	7.54
Skewness	0.47
Range	51.029%
Minimum	-22.727%
Maximum	28.302%
Count	6174

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.212%	2955	47.86%	1.059%
Negative	-2.070%	3077	49.84%	-1.032%
Zero	0.000%	142	2.30%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 3.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.87%	12	0.94%	0.94%
-21.87% to -16.32%	18	1.41%	2.34%
-16.32% to -10.77%	31	2.42%	4.76%
-10.77% to -5.22%	151	11.79%	16.55%
-5.22% to 0.33%	452	35.28%	51.83%
0.33% to 5.88%	403	31.46%	83.29%
5.88% to 11.44%	132	10.30%	93.60%
11.44% to 16.99%	57	4.45%	98.05%
16.99% to 22.54%	12	0.94%	98.99%
Greater than 22.54%	13	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.07%	7.73%	77.21%	68.27%
±2σ	-14.47%	15.14%	94.46%	95.45%
±3σ	-21.87%	22.54%	98.05%	99.73%

Descriptive Statistics

Mean	0.334%
Standard Error	0.207%
Median	0.112%
Mode	0.000%
Standard Deviation	7.401%
Sample Variance	54.770%
Kurtosis	3.41
Skewness	0.21
Range	73.999%
Minimum	-32.053%
Maximum	41.946%
Count	1281

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.505%	646	50.43%	2.776%
Negative	-4.997%	626	48.87%	-2.442%
Zero	0.000%	9	0.70%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.26%
12	1 Quarter	10.92%
52	1 Year	10.32%
156	3 Years	9.07%
260	5 Years	9.02%
520	10 Years	8.90%
1,040	20 Years	9.99%
2,600	50 Years	10.52%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.27. Further, an Excess Kurtosis of 7.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.23%	0	0.00%	0.00%
-11.23% to -5.61%	0	0.00%	0.00%
-5.61% to 0.00%	0	0.00%	0.00%
0.00% to 5.61%	228	17.78%	17.78%
5.61% to 11.23%	599	46.72%	64.51%
11.23% to 16.84%	260	20.28%	84.79%
16.84% to 22.46%	98	7.64%	92.43%
22.46% to 28.07%	44	3.43%	95.87%
28.07% to 33.68%	26	2.03%	97.89%
Greater than 33.68%	27	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.74%	18.71%	84.17%	68.27%
±2σ	-3.74%	26.20%	94.85%	95.45%
±3σ	-11.23%	33.68%	97.89%	99.73%

Descriptive Statistics

Mean	11.228%
Standard Error	0.209%
Median	9.055%
Mode	6.250%
Standard Deviation	7.485%
Sample Variance	56.021%
Kurtosis	7.35
Skewness	2.27
Range	59.369%
Minimum	2.086%
Maximum	61.455%
Count	1282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.228%	1282	100.00%	11.228%
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 0.84. Further, an Excess Kurtosis of 4.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.37%	4	0.31%	0.31%
-22.37% to -16.74%	14	1.09%	1.40%
-16.74% to -11.10%	48	3.74%	5.15%
-11.10% to -5.47%	154	12.01%	17.16%
-5.47% to 0.16%	447	34.87%	52.03%
0.16% to 5.80%	418	32.61%	84.63%
5.80% to 11.43%	135	10.53%	95.16%
11.43% to 17.06%	27	2.11%	97.27%
17.06% to 22.70%	17	1.33%	98.60%
Greater than 22.70%	18	1.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.35%	7.67%	78.08%	68.27%
±2σ	-14.86%	15.19%	94.70%	95.45%
±3σ	-22.37%	22.70%	98.28%	99.73%

Descriptive Statistics

Mean	0.163%
Standard Error	0.210%
Median	-0.116%
Mode	0.000%
Standard Deviation	7.511%
Sample Variance	56.408%
Kurtosis	4.51
Skewness	0.84
Range	73.595%
Minimum	-29.602%
Maximum	43.993%
Count	1282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.491%	628	48.99%	2.690%
Negative	-5.006%	647	50.47%	-2.526%
Zero	0.000%	7	0.55%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.44. Further, an Excess Kurtosis of 1.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.45%	0	0.00%	0.00%
-43.45% to -32.26%	4	1.36%	1.36%
-32.26% to -21.06%	9	3.05%	4.41%
-21.06% to -9.86%	49	16.61%	21.02%
-9.86% to 1.33%	92	31.19%	52.20%
1.33% to 12.53%	84	28.47%	80.68%
12.53% to 23.72%	35	11.86%	92.54%
23.72% to 34.92%	15	5.08%	97.63%
34.92% to 46.12%	4	1.36%	98.98%
Greater than 46.12%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.60%	16.26%	71.53%	68.27%
±2σ	-28.52%	31.19%	93.56%	95.45%
±3σ	-43.45%	46.12%	98.98%	99.73%

Descriptive Statistics

Mean	1.332%
Standard Error	0.869%
Median	0.546%
Mode	5.800%
Standard Deviation	14.928%
Sample Variance	222.843%
Kurtosis	1.18
Skewness	0.44
Range	104.747%
Minimum	-42.308%
Maximum	62.439%
Count	295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.077%	154	52.20%	6.305%
Negative	-10.478%	140	47.46%	-4.973%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.66%
12	1 Year	22.89%
36	3 Years	19.44%
60	5 Years	19.42%
120	10 Years	19.51%
240	20 Years	21.24%
600	50 Years	22.34%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.01. Further, an Excess Kurtosis of 5.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.89%	0	0.00%	0.00%
-20.89% to -9.22%	0	0.00%	0.00%
-9.22% to 2.45%	0	0.00%	0.00%
2.45% to 14.13%	56	18.92%	18.92%
14.13% to 25.80%	127	42.91%	61.82%
25.80% to 37.48%	68	22.97%	84.80%
37.48% to 49.15%	23	7.77%	92.57%
49.15% to 60.82%	11	3.72%	96.28%
60.82% to 72.50%	4	1.35%	97.64%
Greater than 72.50%	7	2.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.24%	41.37%	81.76%	68.27%
±2σ	-5.33%	56.93%	94.93%	95.45%
±3σ	-20.89%	72.50%	97.64%	99.73%

Descriptive Statistics

Mean	25.802%
Standard Error	0.905%
Median	21.984%
Mode	22.439%
Standard Deviation	15.565%
Sample Variance	242.279%
Kurtosis	5.41
Skewness	2.01
Range	100.415%
Minimum	6.494%
Maximum	106.909%
Count	296

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.802%	296	100.00%	25.802%
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 0.84. Further, an Excess Kurtosis of 2.16 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.84%	0	0.00%	0.00%
-44.84% to -33.41%	2	0.68%	0.68%
-33.41% to -21.98%	12	4.05%	4.73%
-21.98% to -10.55%	48	16.22%	20.95%
-10.55% to 0.89%	98	33.11%	54.05%
0.89% to 12.32%	80	27.03%	81.08%
12.32% to 23.75%	39	13.18%	94.26%
23.75% to 35.19%	8	2.70%	96.96%
35.19% to 46.62%	5	1.69%	98.65%
Greater than 46.62%	4	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.36%	16.13%	72.64%	68.27%
±2σ	-29.60%	31.38%	95.95%	95.45%
±3σ	-44.84%	46.62%	98.65%	99.73%

Descriptive Statistics

Mean	0.887%
Standard Error	0.886%
Median	-1.242%
Mode	-38.438%
Standard Deviation	15.244%
Sample Variance	232.370%
Kurtosis	2.16
Skewness	0.84
Range	106.771%
Minimum	-38.438%
Maximum	68.333%
Count	296

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.751%	142	47.97%	6.117%
Negative	-10.053%	154	52.03%	-5.230%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.11. Further, an Excess Kurtosis of 0.23 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.60%	0	0.00%	0.00%
-68.60% to -50.53%	1	1.01%	1.01%
-50.53% to -32.47%	5	5.05%	6.06%
-32.47% to -14.40%	18	18.18%	24.24%
-14.40% to 3.67%	28	28.28%	52.53%
3.67% to 21.73%	25	25.25%	77.78%
21.73% to 39.80%	16	16.16%	93.94%
39.80% to 57.86%	4	4.04%	97.98%
57.86% to 75.93%	2	2.02%	100.00%
Greater than 75.93%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.42%	27.75%	70.71%	68.27%
±2σ	-44.51%	51.84%	92.93%	95.45%
±3σ	-68.60%	75.93%	100.00%	99.73%

Descriptive Statistics

Mean	3.665%
Standard Error	2.421%
Median	3.095%
Mode	-56.081%
Standard Deviation	24.087%
Sample Variance	580.186%
Kurtosis	0.23
Skewness	0.11
Range	130.946%
Minimum	-56.081%
Maximum	74.865%
Count	99

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.387%	56	56.57%	11.532%
Negative	-18.111%	43	43.43%	-7.866%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	41.56%
12	3 Years	36.38%
20	5 Years	35.10%
40	10 Years	34.04%
80	20 Years	36.94%
200	50 Years	38.57%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.22. Further, an Excess Kurtosis of 7.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.91%	0	0.00%	0.00%
-42.91% to -19.86%	0	0.00%	0.00%
-19.86% to 3.20%	0	0.00%	0.00%
3.20% to 26.25%	16	16.00%	16.00%
26.25% to 49.31%	54	54.00%	70.00%
49.31% to 72.37%	12	12.00%	82.00%
72.37% to 95.42%	11	11.00%	93.00%
95.42% to 118.48%	3	3.00%	96.00%
118.48% to 141.53%	2	2.00%	98.00%
Greater than 141.53%	2	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.57%	80.05%	83.00%	68.27%
±2σ	-12.17%	110.79%	95.00%	95.45%
±3σ	-42.91%	141.53%	98.00%	99.73%

Descriptive Statistics

Mean	49.311%
Standard Error	3.074%
Median	41.648%
Mode	10.580%
Standard Deviation	30.741%
Sample Variance	945.020%
Kurtosis	7.02
Skewness	2.22
Range	194.838%
Minimum	10.580%
Maximum	205.418%
Count	100

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.311%	100	100.00%	49.311%
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 1.74. Further, an Excess Kurtosis of 4.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.90%	0	0.00%	0.00%
-81.90% to -60.83%	0	0.00%	0.00%
-60.83% to -39.76%	1	1.00%	1.00%
-39.76% to -18.69%	20	20.00%	21.00%
-18.69% to 2.38%	40	40.00%	61.00%
2.38% to 23.46%	22	22.00%	83.00%
23.46% to 44.53%	10	10.00%	93.00%
44.53% to 65.60%	3	3.00%	96.00%
65.60% to 86.67%	2	2.00%	98.00%
Greater than 86.67%	2	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.71%	30.48%	82.00%	68.27%
±2σ	-53.81%	58.58%	96.00%	95.45%
±3σ	-81.90%	86.67%	98.00%	99.73%

Descriptive Statistics

Mean	2.384%
Standard Error	2.810%
Median	-2.632%
Mode	-43.895%
Standard Deviation	28.096%
Sample Variance	789.371%
Kurtosis	4.70
Skewness	1.74
Range	171.245%
Minimum	-43.895%
Maximum	127.350%
Count	100

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.997%	43	43.00%	11.179%
Negative	-15.430%	57	57.00%	-8.795%
Zero	0.000%	0	0.00%	0.000%

PDFS Deep Analytical Report