RPD - 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	3.13%	2.64%	2.75%	4.25%	6.56%	6.66%	6.15	7.02	5.76	7.49
Weekly	7.12%	7.06%	7.85%	9.98%	14.45%	14.65%	5.69	7.59	4.92	8.77
Monthly	13.01%	12.43%	14.72%	20.65%	30.07%	30.50%	4.86	8.87	3.60	11.99
Quarterly	22.91%	21.08%	26.34%	35.00%	52.08%	52.83%	3.90	11.06	2.32	18.62
Annual	—	—	—	—	104.17%	105.66%	2.32	18.62	0.82	52.77
Option Time Horizon	—	—	—	—	40.07%	40.64%	4.40	9.81	2.95	14.64

Calculation Notes: Computed at 2026-02-22T13:43 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $6.57 | Strike (K): $7.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.9000 (Bid $0.5000 / Ask $1.3000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 104.17% (CRR binomial tree, American, n=20 steps) | BS IV: 105.21% (European Black-Scholes) | Yahoo IV (Annual): 105.66% → 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 -0.34. Further, an Excess Kurtosis of 10.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.41%	17	0.64%	0.64%
-9.41% to -7.05%	29	1.09%	1.73%
-7.05% to -4.70%	90	3.38%	5.11%
-4.70% to -2.35%	307	11.52%	16.63%
-2.35% to -0.00%	858	32.21%	48.84%
-0.00% to 2.35%	899	33.75%	82.58%
2.35% to 4.70%	335	12.58%	95.16%
4.70% to 7.05%	87	3.27%	98.42%
7.05% to 9.40%	27	1.01%	99.44%
Greater than 9.40%	15	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.14%	3.13%	77.78%	68.27%
±2σ	-6.27%	6.27%	95.16%	95.45%
±3σ	-9.41%	9.40%	98.80%	99.73%

Descriptive Statistics

Mean	-0.001%
Standard Error	0.061%
Median	0.060%
Mode	0.000%
Standard Deviation	3.135%
Sample Variance	9.827%
Kurtosis	10.19
Skewness	-0.34
Range	60.196%
Minimum	-28.970%
Maximum	31.226%
Count	2664

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.152%	1347	50.56%	1.088%
Negative	-2.230%	1301	48.84%	-1.089%
Zero	0.000%	16	0.60%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.36%
20	1 Month	8.03%
60	1 Quarter	5.03%
250	1 Year	4.32%
750	3 Years	4.00%
1,250	5 Years	4.25%
2,500	10 Years	4.21%
5,000	20 Years	4.36%
12,500	50 Years	4.36%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.94. Further, an Excess Kurtosis of 34.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.62%	0	0.00%	0.00%
-3.62% to -1.65%	0	0.00%	0.00%
-1.65% to 0.33%	0	0.00%	0.00%
0.33% to 2.31%	404	15.16%	15.16%
2.31% to 4.29%	1282	48.11%	63.26%
4.29% to 6.26%	606	22.74%	86.00%
6.26% to 8.24%	209	7.84%	93.85%
8.24% to 10.22%	81	3.04%	96.89%
10.22% to 12.20%	42	1.58%	98.46%
Greater than 12.20%	41	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.65%	6.92%	87.09%	68.27%
±2σ	-0.99%	9.56%	96.10%	95.45%
±3σ	-3.62%	12.20%	98.46%	99.73%

Descriptive Statistics

Mean	4.287%
Standard Error	0.051%
Median	3.637%
Mode	2.857%
Standard Deviation	2.637%
Sample Variance	6.953%
Kurtosis	34.14
Skewness	3.94
Range	43.668%
Minimum	0.834%
Maximum	44.502%
Count	2665

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.287%	2665	100.00%	4.287%
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 4.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.16%	14	0.53%	0.53%
-8.16% to -6.10%	18	0.68%	1.20%
-6.10% to -4.04%	106	3.98%	5.18%
-4.04% to -1.97%	363	13.62%	18.80%
-1.97% to 0.10%	890	33.40%	52.20%
0.10% to 2.16%	796	29.87%	82.06%
2.16% to 4.22%	319	11.97%	94.03%
4.22% to 6.29%	103	3.86%	97.90%
6.29% to 8.35%	37	1.39%	99.29%
Greater than 8.35%	19	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.66%	2.85%	74.52%	68.27%
±2σ	-5.41%	5.60%	95.38%	95.45%
±3σ	-8.16%	8.35%	98.76%	99.73%

Descriptive Statistics

Mean	0.095%
Standard Error	0.053%
Median	0.000%
Mode	0.000%
Standard Deviation	2.753%
Sample Variance	7.578%
Kurtosis	4.63
Skewness	0.19
Range	40.380%
Minimum	-23.547%
Maximum	16.833%
Count	2665

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.114%	1316	49.38%	1.044%
Negative	-1.905%	1327	49.79%	-0.949%
Zero	0.000%	22	0.83%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.63. Further, an Excess Kurtosis of 3.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.32%	5	0.90%	0.90%
-21.32% to -15.98%	4	0.72%	1.63%
-15.98% to -10.64%	19	3.44%	5.06%
-10.64% to -5.30%	82	14.83%	19.89%
-5.30% to 0.04%	159	28.75%	48.64%
0.04% to 5.38%	184	33.27%	81.92%
5.38% to 10.72%	68	12.30%	94.21%
10.72% to 16.06%	25	4.52%	98.73%
16.06% to 21.40%	5	0.90%	99.64%
Greater than 21.40%	2	0.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.08%	7.16%	74.86%	68.27%
±2σ	-14.20%	14.28%	96.20%	95.45%
±3σ	-21.32%	21.40%	98.73%	99.73%

Descriptive Statistics

Mean	0.038%
Standard Error	0.303%
Median	0.270%
Mode	-2.338%
Standard Deviation	7.121%
Sample Variance	50.716%
Kurtosis	3.87
Skewness	-0.63
Range	69.729%
Minimum	-40.800%
Maximum	28.929%
Count	553

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.094%	284	51.36%	2.616%
Negative	-5.319%	268	48.46%	-2.578%
Zero	0.000%	1	0.18%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	19.06%
12	1 Quarter	11.62%
52	1 Year	10.11%
156	3 Years	9.44%
260	5 Years	9.98%
520	10 Years	9.74%
1,040	20 Years	10.11%
2,600	50 Years	10.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.47. Further, an Excess Kurtosis of 20.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.34%	0	0.00%	0.00%
-10.34% to -5.05%	0	0.00%	0.00%
-5.05% to 0.24%	0	0.00%	0.00%
0.24% to 5.54%	76	13.72%	13.72%
5.54% to 10.83%	286	51.62%	65.34%
10.83% to 16.12%	116	20.94%	86.28%
16.12% to 21.42%	46	8.30%	94.58%
21.42% to 26.71%	15	2.71%	97.29%
26.71% to 32.01%	5	0.90%	98.19%
Greater than 32.01%	10	1.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.77%	17.89%	88.81%	68.27%
±2σ	-3.29%	24.95%	96.75%	95.45%
±3σ	-10.34%	32.00%	98.19%	99.73%

Descriptive Statistics

Mean	10.831%
Standard Error	0.300%
Median	8.965%
Mode	7.467%
Standard Deviation	7.058%
Sample Variance	49.811%
Kurtosis	20.18
Skewness	3.47
Range	69.700%
Minimum	3.088%
Maximum	72.788%
Count	554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.831%	554	100.00%	10.831%
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 2.44. Further, an Excess Kurtosis of 15.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.95%	0	0.00%	0.00%
-22.95% to -17.06%	4	0.72%	0.72%
-17.06% to -11.17%	11	1.99%	2.71%
-11.17% to -5.28%	79	14.26%	16.97%
-5.28% to 0.61%	215	38.81%	55.78%
0.61% to 6.50%	157	28.34%	84.12%
6.50% to 12.39%	62	11.19%	95.31%
12.39% to 18.28%	16	2.89%	98.19%
18.28% to 24.17%	2	0.36%	98.56%
Greater than 24.17%	8	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.25%	8.46%	79.42%	68.27%
±2σ	-15.10%	16.32%	96.93%	95.45%
±3σ	-22.95%	24.17%	98.56%	99.73%

Descriptive Statistics

Mean	0.609%
Standard Error	0.334%
Median	-0.136%
Mode	-5.976%
Standard Deviation	7.854%
Sample Variance	61.690%
Kurtosis	15.83
Skewness	2.44
Range	91.633%
Minimum	-21.932%
Maximum	69.701%
Count	554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.963%	272	49.10%	2.928%
Negative	-4.587%	280	50.54%	-2.318%
Zero	0.000%	2	0.36%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.16. Further, an Excess Kurtosis of 0.94 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.14%	1	0.79%	0.79%
-39.14% to -29.38%	1	0.79%	1.57%
-29.38% to -19.62%	5	3.94%	5.51%
-19.62% to -9.86%	17	13.39%	18.90%
-9.86% to -0.10%	42	33.07%	51.97%
-0.10% to 9.66%	33	25.98%	77.95%
9.66% to 19.42%	19	14.96%	92.91%
19.42% to 29.18%	8	6.30%	99.21%
29.18% to 38.94%	1	0.79%	100.00%
Greater than 38.94%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.11%	12.91%	72.44%	68.27%
±2σ	-26.13%	25.93%	95.28%	95.45%
±3σ	-39.14%	38.94%	99.21%	99.73%

Descriptive Statistics

Mean	-0.100%
Standard Error	1.155%
Median	-1.322%
Mode	-44.883%
Standard Deviation	13.013%
Sample Variance	169.339%
Kurtosis	0.94
Skewness	-0.16
Range	82.064%
Minimum	-44.883%
Maximum	37.181%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.495%	60	47.24%	4.958%
Negative	-9.588%	67	52.76%	-5.058%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.04%
12	1 Year	20.63%
36	3 Years	19.11%
60	5 Years	20.65%
120	10 Years	20.55%
240	20 Years	21.06%
600	50 Years	21.06%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.93. Further, an Excess Kurtosis of 5.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.82%	0	0.00%	0.00%
-12.82% to -3.50%	0	0.00%	0.00%
-3.50% to 5.82%	0	0.00%	0.00%
5.82% to 15.14%	26	20.31%	20.31%
15.14% to 24.46%	58	45.31%	65.62%
24.46% to 33.78%	21	16.41%	82.03%
33.78% to 43.11%	15	11.72%	93.75%
43.11% to 52.43%	2	1.56%	95.31%
52.43% to 61.75%	4	3.12%	98.44%
Greater than 61.75%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.04%	36.89%	77.34%	68.27%
±2σ	-0.39%	49.32%	95.31%	95.45%
±3σ	-12.82%	61.75%	98.44%	99.73%

Descriptive Statistics

Mean	24.464%
Standard Error	1.098%
Median	21.569%
Mode	14.283%
Standard Deviation	12.428%
Sample Variance	154.449%
Kurtosis	5.61
Skewness	1.93
Range	78.232%
Minimum	7.896%
Maximum	86.128%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.464%	128	100.00%	24.464%
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 1.57. Further, an Excess Kurtosis of 5.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.03%	0	0.00%	0.00%
-42.03% to -30.99%	0	0.00%	0.00%
-30.99% to -19.96%	4	3.12%	3.12%
-19.96% to -8.92%	25	19.53%	22.66%
-8.92% to 2.12%	41	32.03%	54.69%
2.12% to 13.15%	36	28.12%	82.81%
13.15% to 24.19%	14	10.94%	93.75%
24.19% to 35.23%	6	4.69%	98.44%
35.23% to 46.27%	0	0.00%	98.44%
Greater than 46.27%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.60%	16.83%	75.78%	68.27%
±2σ	-27.31%	31.55%	96.88%	95.45%
±3σ	-42.03%	46.27%	98.44%	99.73%

Descriptive Statistics

Mean	2.118%
Standard Error	1.301%
Median	0.881%
Mode	-27.208%
Standard Deviation	14.716%
Sample Variance	216.574%
Kurtosis	5.74
Skewness	1.57
Range	105.899%
Minimum	-27.208%
Maximum	78.691%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.306%	66	51.56%	6.345%
Negative	-8.870%	61	47.66%	-4.227%
Zero	0.000%	1	0.78%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.02. Further, an Excess Kurtosis of -0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.91%	0	0.00%	0.00%
-68.91% to -51.73%	0	0.00%	0.00%
-51.73% to -34.55%	4	9.30%	9.30%
-34.55% to -17.37%	6	13.95%	23.26%
-17.37% to -0.19%	13	30.23%	53.49%
-0.19% to 16.99%	8	18.60%	72.09%
16.99% to 34.17%	8	18.60%	90.70%
34.17% to 51.35%	4	9.30%	100.00%
51.35% to 68.53%	0	0.00%	100.00%
Greater than 68.53%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.09%	22.72%	65.12%	68.27%
±2σ	-46.00%	45.62%	100.00%	95.45%
±3σ	-68.91%	68.53%	100.00%	99.73%

Descriptive Statistics

Mean	-0.188%
Standard Error	3.493%
Median	-1.523%
Mode	-44.883%
Standard Deviation	22.906%
Sample Variance	524.669%
Kurtosis	-0.77
Skewness	0.02
Range	85.074%
Minimum	-44.883%
Maximum	40.191%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.926%	20	46.51%	9.268%
Negative	-17.678%	23	53.49%	-9.456%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	32.87%
12	3 Years	30.38%
20	5 Years	35.00%
40	10 Years	35.09%
80	20 Years	35.88%
200	50 Years	35.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.96. 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 -17.19%	0	0.00%	0.00%
-17.19% to -1.38%	0	0.00%	0.00%
-1.38% to 14.43%	0	0.00%	0.00%
14.43% to 30.25%	12	27.27%	27.27%
30.25% to 46.06%	15	34.09%	61.36%
46.06% to 61.87%	8	18.18%	79.55%
61.87% to 77.68%	4	9.09%	88.64%
77.68% to 93.49%	4	9.09%	97.73%
93.49% to 109.30%	1	2.27%	100.00%
Greater than 109.30%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.97%	67.14%	68.18%	68.27%
±2σ	3.89%	88.22%	95.45%	95.45%
±3σ	-17.19%	109.30%	100.00%	99.73%

Descriptive Statistics

Mean	46.056%
Standard Error	3.178%
Median	39.442%
Mode	18.392%
Standard Deviation	21.081%
Sample Variance	444.406%
Kurtosis	0.17
Skewness	0.96
Range	84.480%
Minimum	18.392%
Maximum	102.872%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.056%	44	100.00%	46.056%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.84. Further, an Excess Kurtosis of 0.26 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.79%	0	0.00%	0.00%
-72.79% to -53.03%	0	0.00%	0.00%
-53.03% to -33.28%	0	0.00%	0.00%
-33.28% to -13.53%	12	27.27%	27.27%
-13.53% to 6.22%	13	29.55%	56.82%
6.22% to 25.98%	10	22.73%	79.55%
25.98% to 45.73%	4	9.09%	88.64%
45.73% to 65.48%	4	9.09%	97.73%
65.48% to 85.23%	1	2.27%	100.00%
Greater than 85.23%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.11%	32.56%	68.18%	68.27%
±2σ	-46.45%	58.90%	97.73%	95.45%
±3σ	-72.79%	85.23%	100.00%	99.73%

Descriptive Statistics

Mean	6.223%
Standard Error	3.971%
Median	2.535%
Mode	-28.378%
Standard Deviation	26.337%
Sample Variance	693.662%
Kurtosis	0.26
Skewness	0.84
Range	107.069%
Minimum	-28.378%
Maximum	78.691%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.576%	24	54.55%	13.405%
Negative	-15.800%	20	45.45%	-7.182%
Zero	0.000%	0	0.00%	0.000%

RPD Deep Analytical Report