OKTA - 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	3.32%	2.44%	2.79%	4.31%	4.78%	4.78%	70.83	77.92	67.52	81.74
Weekly	7.27%	6.88%	7.54%	10.29%	10.51%	10.52%	66.88	82.53	60.20	91.67
Monthly	14.33%	10.53%	13.21%	21.61%	21.89%	21.90%	59.69	92.47	47.95	115.09
Quarterly	22.64%	22.92%	24.11%	33.73%	37.91%	37.94%	50.85	108.53	34.81	158.56
Annual	—	—	—	—	75.81%	75.88%	34.81	158.56	16.31	338.41
Option Time Horizon	—	—	—	—	24.78%	24.80%	57.98	95.18	45.26	121.95

Calculation Notes: Computed at 2026-02-22T14:20 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $74.29 | Strike (K): $100.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.2500 (Bid $0.0000 / Ask $2.5000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 75.81% (CRR binomial tree, American, n=20 steps) | BS IV: 76.15% (European Black-Scholes) | Yahoo IV (Annual): 75.88% → 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 -0.06. Further, an Excess Kurtosis of 11.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.86%	12	0.54%	0.54%
-9.86% to -7.37%	32	1.44%	1.97%
-7.37% to -4.87%	72	3.23%	5.20%
-4.87% to -2.38%	259	11.62%	16.82%
-2.38% to 0.11%	731	32.79%	49.62%
0.11% to 2.60%	763	34.23%	83.85%
2.60% to 5.09%	265	11.89%	95.74%
5.09% to 7.58%	61	2.74%	98.47%
7.58% to 10.07%	16	0.72%	99.19%
Greater than 10.07%	18	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.21%	3.43%	78.96%	68.27%
±2σ	-6.54%	6.75%	95.38%	95.45%
±3σ	-9.86%	10.07%	98.65%	99.73%

Descriptive Statistics

Mean	0.107%
Standard Error	0.070%
Median	0.123%
Mode	-0.872%
Standard Deviation	3.321%
Sample Variance	11.028%
Kurtosis	11.00
Skewness	-0.06
Range	60.161%
Minimum	-33.698%
Maximum	26.463%
Count	2229

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.280%	1171	52.53%	1.198%
Negative	-2.305%	1055	47.33%	-1.091%
Zero	0.000%	3	0.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.17%
20	1 Month	4.83%
60	1 Quarter	3.88%
250	1 Year	3.73%
750	3 Years	3.56%
1,250	5 Years	4.31%
2,500	10 Years	4.44%
5,000	20 Years	4.44%
12,500	50 Years	4.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.46. Further, an Excess Kurtosis of 10.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.04%	0	0.00%	0.00%
-3.04% to -1.21%	0	0.00%	0.00%
-1.21% to 0.62%	0	0.00%	0.00%
0.62% to 2.45%	407	18.25%	18.25%
2.45% to 4.28%	987	44.26%	62.51%
4.28% to 6.12%	504	22.60%	85.11%
6.12% to 7.95%	167	7.49%	92.60%
7.95% to 9.78%	95	4.26%	96.86%
9.78% to 11.61%	32	1.43%	98.30%
Greater than 11.61%	38	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.84%	6.73%	82.56%	68.27%
±2σ	-0.60%	9.17%	95.96%	95.45%
±3σ	-3.04%	11.61%	98.30%	99.73%

Descriptive Statistics

Mean	4.284%
Standard Error	0.052%
Median	3.657%
Mode	2.776%
Standard Deviation	2.442%
Sample Variance	5.964%
Kurtosis	10.16
Skewness	2.46
Range	23.750%
Minimum	0.985%
Maximum	24.735%
Count	2230

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.284%	2230	100.00%	4.284%
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 0.41. Further, an Excess Kurtosis of 2.81 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.34%	10	0.45%	0.45%
-8.34% to -6.24%	26	1.17%	1.61%
-6.24% to -4.15%	72	3.23%	4.84%
-4.15% to -2.06%	319	14.30%	19.15%
-2.06% to 0.04%	730	32.74%	51.88%
0.04% to 2.13%	665	29.82%	81.70%
2.13% to 4.22%	273	12.24%	93.95%
4.22% to 6.32%	90	4.04%	97.98%
6.32% to 8.41%	27	1.21%	99.19%
Greater than 8.41%	18	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.75%	2.83%	75.34%	68.27%
±2σ	-5.54%	5.62%	94.39%	95.45%
±3σ	-8.34%	8.41%	98.74%	99.73%

Descriptive Statistics

Mean	0.037%
Standard Error	0.059%
Median	-0.045%
Mode	0.000%
Standard Deviation	2.791%
Sample Variance	7.792%
Kurtosis	2.81
Skewness	0.41
Range	29.780%
Minimum	-12.439%
Maximum	17.341%
Count	2230

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.131%	1086	48.70%	1.038%
Negative	-1.968%	1134	50.85%	-1.001%
Zero	0.000%	10	0.45%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.09. Further, an Excess Kurtosis of 1.67 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.30%	3	0.65%	0.65%
-21.30% to -15.85%	4	0.86%	1.51%
-15.85% to -10.39%	21	4.54%	6.05%
-10.39% to -4.94%	62	13.39%	19.44%
-4.94% to 0.52%	137	29.59%	49.03%
0.52% to 5.97%	147	31.75%	80.78%
5.97% to 11.43%	65	14.04%	94.82%
11.43% to 16.88%	13	2.81%	97.62%
16.88% to 22.34%	8	1.73%	99.35%
Greater than 22.34%	3	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.76%	7.79%	74.95%	68.27%
±2σ	-14.03%	15.07%	93.95%	95.45%
±3σ	-21.30%	22.34%	98.70%	99.73%

Descriptive Statistics

Mean	0.518%
Standard Error	0.338%
Median	0.689%
Mode	-5.040%
Standard Deviation	7.274%
Sample Variance	52.905%
Kurtosis	1.67
Skewness	-0.09
Range	54.922%
Minimum	-28.346%
Maximum	26.576%
Count	463

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.444%	251	54.21%	2.951%
Negative	-5.315%	212	45.79%	-2.434%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.78%
12	1 Quarter	8.87%
52	1 Year	8.67%
156	3 Years	8.55%
260	5 Years	10.29%
520	10 Years	10.47%
1,040	20 Years	10.47%
2,600	50 Years	10.47%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.43. Further, an Excess Kurtosis of 9.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.49%	0	0.00%	0.00%
-9.49% to -4.33%	0	0.00%	0.00%
-4.33% to 0.82%	0	0.00%	0.00%
0.82% to 5.98%	80	17.24%	17.24%
5.98% to 11.14%	217	46.77%	64.01%
11.14% to 16.30%	99	21.34%	85.34%
16.30% to 21.45%	28	6.03%	91.38%
21.45% to 26.61%	24	5.17%	96.55%
26.61% to 31.77%	7	1.51%	98.06%
Greater than 31.77%	9	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.26%	18.02%	82.54%	68.27%
±2σ	-2.61%	24.89%	96.12%	95.45%
±3σ	-9.49%	31.77%	98.06%	99.73%

Descriptive Statistics

Mean	11.139%
Standard Error	0.319%
Median	9.468%
Mode	5.106%
Standard Deviation	6.876%
Sample Variance	47.278%
Kurtosis	9.68
Skewness	2.43
Range	59.876%
Minimum	3.202%
Maximum	63.078%
Count	464

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.139%	464	100.00%	11.139%
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 1.09. Further, an Excess Kurtosis of 4.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.48%	0	0.00%	0.00%
-22.48% to -16.83%	5	1.08%	1.08%
-16.83% to -11.17%	14	3.02%	4.09%
-11.17% to -5.52%	64	13.79%	17.89%
-5.52% to 0.13%	179	38.58%	56.47%
0.13% to 5.78%	122	26.29%	82.76%
5.78% to 11.44%	52	11.21%	93.97%
11.44% to 17.09%	16	3.45%	97.41%
17.09% to 22.74%	5	1.08%	98.49%
Greater than 22.74%	7	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.41%	7.67%	76.72%	68.27%
±2σ	-14.94%	15.21%	94.83%	95.45%
±3σ	-22.48%	22.74%	98.49%	99.73%

Descriptive Statistics

Mean	0.131%
Standard Error	0.350%
Median	-0.734%
Mode	-1.971%
Standard Deviation	7.537%
Sample Variance	56.806%
Kurtosis	4.14
Skewness	1.09
Range	62.000%
Minimum	-20.657%
Maximum	41.343%
Count	464

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.109%	208	44.83%	2.739%
Negative	-4.745%	255	54.96%	-2.608%
Zero	0.000%	1	0.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.18. Further, an Excess Kurtosis of 0.13 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.99%	0	0.00%	0.00%
-40.99% to -30.24%	2	1.89%	1.89%
-30.24% to -19.50%	4	3.77%	5.66%
-19.50% to -8.75%	16	15.09%	20.75%
-8.75% to 2.00%	37	34.91%	55.66%
2.00% to 12.75%	27	25.47%	81.13%
12.75% to 23.50%	9	8.49%	89.62%
23.50% to 34.25%	10	9.43%	99.06%
34.25% to 44.99%	1	0.94%	100.00%
Greater than 44.99%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.33%	16.33%	70.75%	68.27%
±2σ	-26.66%	30.66%	94.34%	95.45%
±3σ	-40.99%	44.99%	100.00%	99.73%

Descriptive Statistics

Mean	2.001%
Standard Error	1.392%
Median	0.294%
Mode	-37.779%
Standard Deviation	14.331%
Sample Variance	205.379%
Kurtosis	0.13
Skewness	0.18
Range	72.798%
Minimum	-37.779%
Maximum	35.019%
Count	106

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.212%	56	52.83%	6.452%
Negative	-9.435%	50	47.17%	-4.450%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.10%
12	1 Year	17.72%
36	3 Years	18.98%
60	5 Years	21.61%
120	10 Years	22.26%
240	20 Years	22.26%
600	50 Years	22.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 1.00. Further, an Excess Kurtosis of 1.13 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.15%	0	0.00%	0.00%
-7.15% to 0.75%	0	0.00%	0.00%
0.75% to 8.64%	1	0.93%	0.93%
8.64% to 16.54%	24	22.43%	23.36%
16.54% to 24.43%	36	33.64%	57.01%
24.43% to 32.33%	23	21.50%	78.50%
32.33% to 40.22%	13	12.15%	90.65%
40.22% to 48.12%	7	6.54%	97.20%
48.12% to 56.01%	2	1.87%	99.07%
Greater than 56.01%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.91%	34.96%	65.42%	68.27%
±2σ	3.38%	45.48%	97.20%	95.45%
±3σ	-7.15%	56.01%	99.07%	99.73%

Descriptive Statistics

Mean	24.432%
Standard Error	1.018%
Median	22.939%
Mode	7.417%
Standard Deviation	10.526%
Sample Variance	110.787%
Kurtosis	1.13
Skewness	1.00
Range	55.289%
Minimum	7.417%
Maximum	62.706%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.432%	107	100.00%	24.432%
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 0.31. Further, an Excess Kurtosis of 0.34 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.81%	0	0.00%	0.00%
-39.81% to -29.91%	0	0.00%	0.00%
-29.91% to -20.00%	8	7.48%	7.48%
-20.00% to -10.10%	11	10.28%	17.76%
-10.10% to -0.19%	35	32.71%	50.47%
-0.19% to 9.71%	32	29.91%	80.37%
9.71% to 19.62%	10	9.35%	89.72%
19.62% to 29.52%	10	9.35%	99.07%
29.52% to 39.43%	0	0.00%	99.07%
Greater than 39.43%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.40%	13.01%	70.09%	68.27%
±2σ	-26.61%	26.22%	97.20%	95.45%
±3σ	-39.81%	39.43%	99.07%	99.73%

Descriptive Statistics

Mean	-0.193%
Standard Error	1.277%
Median	-0.283%
Mode	-25.877%
Standard Deviation	13.207%
Sample Variance	174.436%
Kurtosis	0.34
Skewness	0.31
Range	68.454%
Minimum	-25.877%
Maximum	42.577%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.224%	52	48.60%	4.969%
Negative	-10.042%	55	51.40%	-5.162%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.10. Further, an Excess Kurtosis of -0.59 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -62.46%	0	0.00%	0.00%
-62.46% to -45.48%	0	0.00%	0.00%
-45.48% to -28.50%	2	5.56%	5.56%
-28.50% to -11.52%	8	22.22%	27.78%
-11.52% to 5.47%	9	25.00%	52.78%
5.47% to 22.45%	7	19.44%	72.22%
22.45% to 39.43%	7	19.44%	91.67%
39.43% to 56.42%	3	8.33%	100.00%
56.42% to 73.40%	0	0.00%	100.00%
Greater than 73.40%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.18%	28.11%	69.44%	68.27%
±2σ	-39.82%	50.76%	97.22%	95.45%
±3σ	-62.46%	73.40%	100.00%	99.73%

Descriptive Statistics

Mean	5.468%
Standard Error	3.774%
Median	2.980%
Mode	-42.996%
Standard Deviation	22.644%
Sample Variance	512.755%
Kurtosis	-0.59
Skewness	-0.10
Range	89.050%
Minimum	-42.996%
Maximum	46.054%
Count	36

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.221%	20	55.56%	12.345%
Negative	-15.473%	16	44.44%	-6.877%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	22.43%
12	3 Years	30.10%
20	5 Years	33.73%
40	10 Years	37.67%
80	20 Years	37.67%
200	50 Years	37.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.86. Further, an Excess Kurtosis of 5.12 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 -5.76%	0	0.00%	0.00%
-5.76% to 11.44%	0	0.00%	0.00%
11.44% to 28.63%	6	16.22%	16.22%
28.63% to 45.82%	17	45.95%	62.16%
45.82% to 63.02%	9	24.32%	86.49%
63.02% to 80.21%	3	8.11%	94.59%
80.21% to 97.40%	1	2.70%	97.30%
97.40% to 114.59%	0	0.00%	97.30%
Greater than 114.59%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	22.90%	68.75%	78.38%	68.27%
±2σ	-0.02%	91.67%	94.59%	95.45%
±3σ	-22.95%	114.59%	97.30%	99.73%

Descriptive Statistics

Mean	45.823%
Standard Error	3.769%
Median	42.088%
Mode	14.632%
Standard Deviation	22.924%
Sample Variance	525.491%
Kurtosis	5.12
Skewness	1.86
Range	118.729%
Minimum	14.632%
Maximum	133.361%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	45.823%	37	100.00%	45.823%
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 Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.29. Further, an Excess Kurtosis of 2.11 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.60%	0	0.00%	0.00%
-72.60% to -54.52%	0	0.00%	0.00%
-54.52% to -36.44%	0	0.00%	0.00%
-36.44% to -18.36%	9	24.32%	24.32%
-18.36% to -0.28%	11	29.73%	54.05%
-0.28% to 17.80%	10	27.03%	81.08%
17.80% to 35.88%	5	13.51%	94.59%
35.88% to 53.96%	0	0.00%	94.59%
53.96% to 72.04%	1	2.70%	97.30%
Greater than 72.04%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.38%	23.83%	81.08%	68.27%
±2σ	-48.49%	47.93%	94.59%	95.45%
±3σ	-72.60%	72.04%	97.30%	99.73%

Descriptive Statistics

Mean	-0.278%
Standard Error	3.963%
Median	-3.333%
Mode	-32.713%
Standard Deviation	24.106%
Sample Variance	581.106%
Kurtosis	2.11
Skewness	1.29
Range	105.397%
Minimum	-32.713%
Maximum	72.684%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.878%	17	45.95%	9.133%
Negative	-17.409%	20	54.05%	-9.410%
Zero	0.000%	0	0.00%	0.000%

OKTA Deep Analytical Report