PINS - 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	3.89%	2.65%	2.91%	4.37%	3.10%	3.16%	17.23	18.33	16.70	18.91
Weekly	8.47%	8.19%	8.52%	10.52%	6.83%	6.95%	16.60	19.03	15.50	20.37
Monthly	15.02%	15.01%	14.54%	21.73%	14.22%	14.46%	15.41	20.49	13.37	23.62
Quarterly	27.45%	31.62%	25.02%	36.17%	24.63%	25.05%	13.89	22.73	10.86	29.08
Annual	—	—	—	—	49.26%	50.10%	10.86	29.08	6.64	47.59
Option Time Horizon	—	—	—	—	16.10%	16.38%	15.13	20.87	12.88	24.52

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $17.77 | Strike (K): $18.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.0700 (Bid $0.9600 / Ask $1.1800) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 49.26% (CRR binomial tree, American, n=20 steps) | BS IV: 49.35% (European Black-Scholes) | Yahoo IV (Annual): 50.10% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.56. Further, an Excess Kurtosis of 10.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.60%	18	1.05%	1.05%
-11.60% to -8.69%	12	0.70%	1.75%
-8.69% to -5.77%	39	2.27%	4.01%
-5.77% to -2.86%	197	11.46%	15.47%
-2.86% to 0.06%	607	35.31%	50.79%
0.06% to 2.97%	601	34.96%	85.75%
2.97% to 5.89%	170	9.89%	95.64%
5.89% to 8.80%	39	2.27%	97.91%
8.80% to 11.72%	17	0.99%	98.89%
Greater than 11.72%	19	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.83%	3.94%	81.09%	68.27%
±2σ	-7.72%	7.83%	95.17%	95.45%
±3σ	-11.60%	11.72%	97.85%	99.73%

Descriptive Statistics

Mean	0.057%
Standard Error	0.094%
Median	0.000%
Mode	0.000%
Standard Deviation	3.887%
Sample Variance	15.108%
Kurtosis	10.50
Skewness	0.56
Range	59.764%
Minimum	-23.639%
Maximum	36.125%
Count	1719

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.614%	855	49.74%	1.300%
Negative	-2.497%	856	49.80%	-1.243%
Zero	0.000%	8	0.47%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	11.73%
20	1 Month	6.56%
60	1 Quarter	4.03%
250	1 Year	4.08%
750	3 Years	3.62%
1,250	5 Years	4.37%
2,500	10 Years	4.77%
5,000	20 Years	4.77%
12,500	50 Years	4.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.41. Further, an Excess Kurtosis of 26.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.55%	0	0.00%	0.00%
-3.55% to -1.56%	0	0.00%	0.00%
-1.56% to 0.43%	0	0.00%	0.00%
0.43% to 2.42%	309	17.97%	17.97%
2.42% to 4.42%	747	43.43%	61.40%
4.42% to 6.41%	401	23.31%	84.71%
6.41% to 8.40%	157	9.13%	93.84%
8.40% to 10.39%	59	3.43%	97.27%
10.39% to 12.38%	24	1.40%	98.66%
Greater than 12.38%	23	1.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.76%	7.07%	84.19%	68.27%
±2σ	-0.89%	9.73%	95.99%	95.45%
±3σ	-3.55%	12.38%	98.66%	99.73%

Descriptive Statistics

Mean	4.416%
Standard Error	0.064%
Median	3.816%
Mode	2.039%
Standard Deviation	2.655%
Sample Variance	7.051%
Kurtosis	26.99
Skewness	3.41
Range	39.506%
Minimum	0.795%
Maximum	40.301%
Count	1720

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.416%	1720	100.00%	4.416%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.63. Further, an Excess Kurtosis of 7.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.68%	12	0.70%	0.70%
-8.68% to -6.50%	18	1.05%	1.74%
-6.50% to -4.32%	50	2.91%	4.65%
-4.32% to -2.14%	227	13.20%	17.85%
-2.14% to 0.04%	555	32.27%	50.12%
0.04% to 2.22%	552	32.09%	82.21%
2.22% to 4.40%	194	11.28%	93.49%
4.40% to 6.58%	85	4.94%	98.43%
6.58% to 8.76%	18	1.05%	99.48%
Greater than 8.76%	9	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.86%	2.95%	75.52%	68.27%
±2σ	-5.77%	5.86%	95.23%	95.45%
±3σ	-8.68%	8.76%	98.78%	99.73%

Descriptive Statistics

Mean	0.043%
Standard Error	0.070%
Median	0.040%
Mode	0.000%
Standard Deviation	2.906%
Sample Variance	8.443%
Kurtosis	7.20
Skewness	-0.63
Range	41.910%
Minimum	-28.288%
Maximum	13.622%
Count	1720

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.085%	875	50.87%	1.061%
Negative	-2.094%	836	48.60%	-1.018%
Zero	0.000%	9	0.52%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.53. Further, an Excess Kurtosis of 4.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.14%	2	0.56%	0.56%
-25.14% to -18.79%	7	1.96%	2.52%
-18.79% to -12.44%	10	2.80%	5.32%
-12.44% to -6.09%	39	10.92%	16.25%
-6.09% to 0.26%	129	36.13%	52.38%
0.26% to 6.61%	113	31.65%	84.03%
6.61% to 12.96%	36	10.08%	94.12%
12.96% to 19.31%	13	3.64%	97.76%
19.31% to 25.66%	6	1.68%	99.44%
Greater than 25.66%	2	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.21%	8.73%	77.87%	68.27%
±2σ	-16.68%	17.19%	93.84%	95.45%
±3σ	-25.14%	25.66%	98.88%	99.73%

Descriptive Statistics

Mean	0.258%
Standard Error	0.448%
Median	0.000%
Mode	0.000%
Standard Deviation	8.467%
Sample Variance	71.686%
Kurtosis	4.43
Skewness	0.53
Range	76.853%
Minimum	-28.192%
Maximum	48.661%
Count	357

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.228%	176	49.30%	3.070%
Negative	-5.640%	178	49.86%	-2.812%
Zero	0.000%	3	0.84%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	21.01%
12	1 Quarter	10.61%
52	1 Year	10.09%
156	3 Years	8.89%
260	5 Years	10.52%
520	10 Years	11.49%
1,040	20 Years	11.49%
2,600	50 Years	11.49%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.30%	0	0.00%	0.00%
-12.30% to -6.15%	0	0.00%	0.00%
-6.15% to -0.01%	0	0.00%	0.00%
-0.01% to 6.14%	65	18.16%	18.16%
6.14% to 12.28%	168	46.93%	65.08%
12.28% to 18.43%	60	16.76%	81.84%
18.43% to 24.57%	42	11.73%	93.58%
24.57% to 30.72%	8	2.23%	95.81%
30.72% to 36.86%	8	2.23%	98.04%
Greater than 36.86%	7	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.09%	20.48%	81.28%	68.27%
±2σ	-4.10%	28.67%	95.53%	95.45%
±3σ	-12.30%	36.86%	98.04%	99.73%

Descriptive Statistics

Mean	12.283%
Standard Error	0.433%
Median	9.848%
Mode	3.299%
Standard Deviation	8.193%
Sample Variance	67.124%
Kurtosis	5.71
Skewness	2.07
Range	54.303%
Minimum	2.053%
Maximum	56.356%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.283%	358	100.00%	12.283%
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 0.98. Further, an Excess Kurtosis of 4.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.99%	2	0.56%	0.56%
-24.99% to -18.60%	0	0.00%	0.56%
-18.60% to -12.21%	15	4.19%	4.75%
-12.21% to -5.82%	45	12.57%	17.32%
-5.82% to 0.57%	135	37.71%	55.03%
0.57% to 6.96%	106	29.61%	84.64%
6.96% to 13.36%	34	9.50%	94.13%
13.36% to 19.75%	9	2.51%	96.65%
19.75% to 26.14%	6	1.68%	98.32%
Greater than 26.14%	6	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.95%	9.10%	79.33%	68.27%
±2σ	-16.47%	17.62%	94.41%	95.45%
±3σ	-24.99%	26.14%	97.77%	99.73%

Descriptive Statistics

Mean	0.574%
Standard Error	0.450%
Median	0.056%
Mode	6.865%
Standard Deviation	8.521%
Sample Variance	72.607%
Kurtosis	4.56
Skewness	0.98
Range	78.742%
Minimum	-33.038%
Maximum	45.704%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.380%	180	50.28%	3.208%
Negative	-5.358%	176	49.16%	-2.634%
Zero	0.000%	2	0.56%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 1.45 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.67%	0	0.00%	0.00%
-44.67% to -33.41%	0	0.00%	0.00%
-33.41% to -22.14%	4	4.88%	4.88%
-22.14% to -10.88%	13	15.85%	20.73%
-10.88% to 0.39%	28	34.15%	54.88%
0.39% to 11.65%	20	24.39%	79.27%
11.65% to 22.92%	13	15.85%	95.12%
22.92% to 34.18%	2	2.44%	97.56%
34.18% to 45.45%	1	1.22%	98.78%
Greater than 45.45%	1	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.63%	15.41%	70.73%	68.27%
±2σ	-29.65%	30.43%	96.34%	95.45%
±3σ	-44.67%	45.45%	98.78%	99.73%

Descriptive Statistics

Mean	0.388%
Standard Error	1.659%
Median	-1.732%
Mode	-27.502%
Standard Deviation	15.020%
Sample Variance	225.587%
Kurtosis	1.45
Skewness	0.78
Range	82.170%
Minimum	-27.502%
Maximum	54.668%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.924%	38	46.34%	5.989%
Negative	-10.438%	44	53.66%	-5.601%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	23.67%
12	1 Year	21.95%
36	3 Years	19.33%
60	5 Years	21.73%
120	10 Years	24.18%
240	20 Years	24.18%
600	50 Years	24.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.89. Further, an Excess Kurtosis of 5.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.84%	0	0.00%	0.00%
-16.84% to -5.58%	0	0.00%	0.00%
-5.58% to 5.68%	0	0.00%	0.00%
5.68% to 16.94%	18	21.69%	21.69%
16.94% to 28.20%	35	42.17%	63.86%
28.20% to 39.46%	15	18.07%	81.93%
39.46% to 50.72%	8	9.64%	91.57%
50.72% to 61.98%	5	6.02%	97.59%
61.98% to 73.24%	1	1.20%	98.80%
Greater than 73.24%	1	1.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.19%	43.22%	80.72%	68.27%
±2σ	-1.82%	58.23%	95.18%	95.45%
±3σ	-16.84%	73.24%	98.80%	99.73%

Descriptive Statistics

Mean	28.203%
Standard Error	1.648%
Median	24.676%
Mode	35.670%
Standard Deviation	15.013%
Sample Variance	225.381%
Kurtosis	5.55
Skewness	1.89
Range	89.918%
Minimum	9.884%
Maximum	99.802%
Count	83

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.203%	83	100.00%	28.203%
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 0.19. Further, an Excess Kurtosis of 0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.12%	0	0.00%	0.00%
-42.12% to -31.21%	1	1.20%	1.20%
-31.21% to -20.31%	3	3.61%	4.82%
-20.31% to -9.40%	14	16.87%	21.69%
-9.40% to 1.50%	24	28.92%	50.60%
1.50% to 12.41%	25	30.12%	80.72%
12.41% to 23.32%	8	9.64%	90.36%
23.32% to 34.22%	6	7.23%	97.59%
34.22% to 45.13%	2	2.41%	100.00%
Greater than 45.13%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.04%	16.05%	67.47%	68.27%
±2σ	-27.58%	30.59%	93.98%	95.45%
±3σ	-42.12%	45.13%	100.00%	99.73%

Descriptive Statistics

Mean	1.504%
Standard Error	1.596%
Median	1.092%
Mode	-34.296%
Standard Deviation	14.542%
Sample Variance	211.473%
Kurtosis	0.03
Skewness	0.19
Range	71.072%
Minimum	-34.296%
Maximum	36.776%
Count	83

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.465%	43	51.81%	6.458%
Negative	-10.280%	40	48.19%	-4.954%
Zero	0.000%	0	0.00%	0.000%

Close-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 1.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.15%	0	0.00%	0.00%
-81.15% to -60.57%	0	0.00%	0.00%
-60.57% to -39.99%	0	0.00%	0.00%
-39.99% to -19.40%	6	21.43%	21.43%
-19.40% to 1.18%	12	42.86%	64.29%
1.18% to 21.77%	4	14.29%	78.57%
21.77% to 42.35%	3	10.71%	89.29%
42.35% to 62.93%	1	3.57%	92.86%
62.93% to 83.52%	2	7.14%	100.00%
Greater than 83.52%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.26%	28.63%	78.57%	68.27%
±2σ	-53.71%	56.07%	92.86%	95.45%
±3σ	-81.15%	83.52%	100.00%	99.73%

Descriptive Statistics

Mean	1.182%
Standard Error	5.187%
Median	-5.643%
Mode	-33.781%
Standard Deviation	27.445%
Sample Variance	753.208%
Kurtosis	1.19
Skewness	1.23
Range	105.697%
Minimum	-33.781%
Maximum	71.916%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.790%	10	35.71%	10.639%
Negative	-14.712%	18	64.29%	-9.458%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	39.44%
12	3 Years	35.05%
20	5 Years	36.17%
40	10 Years	42.74%
80	20 Years	42.74%
200	50 Years	42.74%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.20. Further, an Excess Kurtosis of 5.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.32%	0	0.00%	0.00%
-39.32% to -15.61%	0	0.00%	0.00%
-15.61% to 8.11%	0	0.00%	0.00%
8.11% to 31.82%	5	17.24%	17.24%
31.82% to 55.53%	15	51.72%	68.97%
55.53% to 79.25%	5	17.24%	86.21%
79.25% to 102.96%	1	3.45%	89.66%
102.96% to 126.67%	2	6.90%	96.55%
126.67% to 150.39%	0	0.00%	96.55%
Greater than 150.39%	1	3.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.91%	87.15%	86.21%	68.27%
±2σ	-7.70%	118.77%	96.55%	95.45%
±3σ	-39.32%	150.39%	96.55%	99.73%

Descriptive Statistics

Mean	55.532%
Standard Error	5.871%
Median	49.806%
Mode	24.060%
Standard Deviation	31.618%
Sample Variance	999.701%
Kurtosis	5.56
Skewness	2.20
Range	145.742%
Minimum	24.060%
Maximum	169.802%
Count	29

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	55.532%	29	100.00%	55.532%
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 0.05. Further, an Excess Kurtosis of -0.43 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.25%	0	0.00%	0.00%
-71.25% to -52.49%	0	0.00%	0.00%
-52.49% to -33.73%	2	6.90%	6.90%
-33.73% to -14.97%	5	17.24%	24.14%
-14.97% to 3.79%	6	20.69%	44.83%
3.79% to 22.55%	9	31.03%	75.86%
22.55% to 41.31%	4	13.79%	89.66%
41.31% to 60.07%	3	10.34%	100.00%
60.07% to 78.83%	0	0.00%	100.00%
Greater than 78.83%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.23%	28.80%	68.97%	68.27%
±2σ	-46.24%	53.82%	100.00%	95.45%
±3σ	-71.25%	78.84%	100.00%	99.73%

Descriptive Statistics

Mean	3.790%
Standard Error	4.645%
Median	5.544%
Mode	-41.761%
Standard Deviation	25.015%
Sample Variance	625.730%
Kurtosis	-0.43
Skewness	0.05
Range	92.371%
Minimum	-41.761%
Maximum	50.610%
Count	29

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.546%	17	58.62%	12.044%
Negative	-19.946%	12	41.38%	-8.253%
Zero	0.000%	0	0.00%	0.000%

PINS Deep Analytical Report