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%	4.29%	2.88%	3.14%	78.07	82.70	75.85	85.12
Weekly	7.29%	6.89%	7.58%	10.21%	6.34%	6.91%	75.41	85.61	70.78	91.22
Monthly	14.31%	10.51%	13.22%	21.50%	13.20%	14.38%	70.41	91.69	61.70	104.63
Quarterly	22.51%	22.71%	24.00%	34.02%	22.87%	24.91%	63.92	101.00	50.86	126.95
Annual	—	—	—	—	45.74%	49.83%	50.86	126.95	32.19	200.57
Option Time Horizon	—	—	—	—	17.26%	18.81%	67.61	95.49	56.89	113.48

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $80.35 | Strike (K): $82.50 (first OTM call ≥ spot) | Observed Mid-Price: $4.8250 (Bid $4.4500 / Ask $5.2000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 45.74% (CRR binomial tree, American, n=20 steps) | BS IV: 46.18% (European Black-Scholes) | Yahoo IV (Annual): 49.83% → 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 -0.05. Further, an Excess Kurtosis of 10.91 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	0.53%	0.53%
-9.86% to -7.36%	32	1.42%	1.96%
-7.36% to -4.87%	73	3.24%	5.20%
-4.87% to -2.38%	262	11.64%	16.84%
-2.38% to 0.11%	738	32.80%	49.64%
0.11% to 2.60%	768	34.13%	83.78%
2.60% to 5.09%	269	11.96%	95.73%
5.09% to 7.58%	61	2.71%	98.44%
7.58% to 10.08%	16	0.71%	99.16%
Greater than 10.08%	19	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.21%	3.43%	79.11%	68.27%
±2σ	-6.53%	6.75%	95.42%	95.45%
±3σ	-9.86%	10.08%	98.62%	99.73%

Descriptive Statistics

Mean	0.110%
Standard Error	0.070%
Median	0.124%
Mode	-0.872%
Standard Deviation	3.322%
Sample Variance	11.038%
Kurtosis	10.91
Skewness	-0.05
Range	60.161%
Minimum	-33.698%
Maximum	26.463%
Count	2250

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.286%	1182	52.53%	1.201%
Negative	-2.304%	1065	47.33%	-1.091%
Zero	0.000%	3	0.13%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.03%
20	1 Month	4.65%
60	1 Quarter	4.39%
250	1 Year	3.69%
750	3 Years	3.57%
1,250	5 Years	4.29%
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 10.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.02%	0	0.00%	0.00%
-3.02% to -1.19%	0	0.00%	0.00%
-1.19% to 0.63%	0	0.00%	0.00%
0.63% to 2.46%	416	18.48%	18.48%
2.46% to 4.29%	990	43.98%	62.46%
4.29% to 6.12%	511	22.70%	85.16%
6.12% to 7.94%	168	7.46%	92.63%
7.94% to 9.77%	95	4.22%	96.85%
9.77% to 11.60%	33	1.47%	98.31%
Greater than 11.60%	38	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.85%	6.72%	82.59%	68.27%
±2σ	-0.58%	9.16%	95.96%	95.45%
±3σ	-3.02%	11.60%	98.31%	99.73%

Descriptive Statistics

Mean	4.288%
Standard Error	0.051%
Median	3.672%
Mode	2.776%
Standard Deviation	2.436%
Sample Variance	5.934%
Kurtosis	10.17
Skewness	2.46
Range	23.750%
Minimum	0.985%
Maximum	24.735%
Count	2251

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.288%	2251	100.00%	4.288%
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 0.40. Further, an Excess Kurtosis of 2.80 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.35%	11	0.49%	0.49%
-8.35% to -6.25%	26	1.16%	1.64%
-6.25% to -4.16%	72	3.20%	4.84%
-4.16% to -2.06%	322	14.30%	19.15%
-2.06% to 0.03%	737	32.74%	51.89%
0.03% to 2.12%	670	29.76%	81.65%
2.12% to 4.22%	277	12.31%	93.96%
4.22% to 6.31%	91	4.04%	98.00%
6.31% to 8.40%	27	1.20%	99.20%
Greater than 8.40%	18	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.76%	2.82%	75.34%	68.27%
±2σ	-5.55%	5.61%	94.36%	95.45%
±3σ	-8.35%	8.40%	98.71%	99.73%

Descriptive Statistics

Mean	0.029%
Standard Error	0.059%
Median	-0.050%
Mode	0.000%
Standard Deviation	2.792%
Sample Variance	7.794%
Kurtosis	2.80
Skewness	0.40
Range	29.780%
Minimum	-12.439%
Maximum	17.341%
Count	2251

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.126%	1095	48.65%	1.034%
Negative	-1.974%	1146	50.91%	-1.005%
Zero	0.000%	10	0.44%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.12. Further, an Excess Kurtosis of 1.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.33%	3	0.64%	0.64%
-21.33% to -15.87%	5	1.07%	1.71%
-15.87% to -10.40%	20	4.28%	6.00%
-10.40% to -4.93%	62	13.28%	19.27%
-4.93% to 0.54%	138	29.55%	48.82%
0.54% to 6.00%	148	31.69%	80.51%
6.00% to 11.47%	67	14.35%	94.86%
11.47% to 16.93%	13	2.78%	97.64%
16.93% to 22.40%	8	1.71%	99.36%
Greater than 22.40%	3	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.75%	7.82%	75.16%	68.27%
±2σ	-14.04%	15.11%	94.43%	95.45%
±3σ	-21.33%	22.40%	98.72%	99.73%

Descriptive Statistics

Mean	0.535%
Standard Error	0.337%
Median	0.693%
Mode	-5.040%
Standard Deviation	7.289%
Sample Variance	53.131%
Kurtosis	1.69
Skewness	-0.12
Range	54.922%
Minimum	-28.346%
Maximum	26.576%
Count	467

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.454%	254	54.39%	2.966%
Negative	-5.331%	213	45.61%	-2.431%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.26%
12	1 Quarter	10.21%
52	1 Year	8.53%
156	3 Years	8.54%
260	5 Years	10.21%
520	10 Years	10.48%
1,040	20 Years	10.48%
2,600	50 Years	10.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.42. Further, an Excess Kurtosis of 9.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.51%	0	0.00%	0.00%
-9.51% to -4.34%	0	0.00%	0.00%
-4.34% to 0.82%	0	0.00%	0.00%
0.82% to 5.99%	80	17.09%	17.09%
5.99% to 11.15%	220	47.01%	64.10%
11.15% to 16.32%	100	21.37%	85.47%
16.32% to 21.48%	27	5.77%	91.24%
21.48% to 26.65%	24	5.13%	96.37%
26.65% to 31.81%	8	1.71%	98.08%
Greater than 31.81%	9	1.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.26%	18.04%	82.69%	68.27%
±2σ	-2.62%	24.92%	95.94%	95.45%
±3σ	-9.51%	31.81%	98.08%	99.73%

Descriptive Statistics

Mean	11.151%
Standard Error	0.318%
Median	9.468%
Mode	5.106%
Standard Deviation	6.887%
Sample Variance	47.427%
Kurtosis	9.54
Skewness	2.42
Range	59.876%
Minimum	3.202%
Maximum	63.078%
Count	468

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.151%	468	100.00%	11.151%
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 1.12. Further, an Excess Kurtosis of 4.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.63%	0	0.00%	0.00%
-22.63% to -16.94%	5	1.07%	1.07%
-16.94% to -11.26%	14	2.99%	4.06%
-11.26% to -5.58%	63	13.46%	17.52%
-5.58% to 0.11%	183	39.10%	56.62%
0.11% to 5.79%	123	26.28%	82.91%
5.79% to 11.48%	52	11.11%	94.02%
11.48% to 17.16%	16	3.42%	97.44%
17.16% to 22.85%	4	0.85%	98.29%
Greater than 22.85%	8	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.47%	7.69%	77.14%	68.27%
±2σ	-15.05%	15.27%	95.09%	95.45%
±3σ	-22.63%	22.85%	98.29%	99.73%

Descriptive Statistics

Mean	0.109%
Standard Error	0.350%
Median	-0.762%
Mode	-1.971%
Standard Deviation	7.579%
Sample Variance	57.443%
Kurtosis	4.15
Skewness	1.12
Range	62.000%
Minimum	-20.657%
Maximum	41.343%
Count	468

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.134%	209	44.66%	2.739%
Negative	-4.772%	258	55.13%	-2.631%
Zero	0.000%	1	0.21%	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 0.12 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.87%	0	0.00%	0.00%
-40.87% to -30.14%	2	1.87%	1.87%
-30.14% to -19.40%	4	3.74%	5.61%
-19.40% to -8.67%	17	15.89%	21.50%
-8.67% to 2.07%	36	33.64%	55.14%
2.07% to 12.80%	28	26.17%	81.31%
12.80% to 23.54%	9	8.41%	89.72%
23.54% to 34.28%	10	9.35%	99.07%
34.28% to 45.01%	1	0.93%	100.00%
Greater than 45.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.25%	16.38%	69.16%	68.27%
±2σ	-26.56%	30.70%	94.39%	95.45%
±3σ	-40.87%	45.01%	100.00%	99.73%

Descriptive Statistics

Mean	2.069%
Standard Error	1.384%
Median	0.353%
Mode	-37.779%
Standard Deviation	14.314%
Sample Variance	204.880%
Kurtosis	0.12
Skewness	0.16
Range	72.798%
Minimum	-37.779%
Maximum	35.019%
Count	107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.198%	57	53.27%	6.498%
Negative	-9.478%	50	46.73%	-4.429%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.39%
12	1 Year	16.81%
36	3 Years	18.96%
60	5 Years	21.50%
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 0.99. Further, an Excess Kurtosis of 1.11 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.08%	0	0.00%	0.00%
-7.08% to 0.80%	0	0.00%	0.00%
0.80% to 8.68%	1	0.93%	0.93%
8.68% to 16.57%	25	23.15%	24.07%
16.57% to 24.45%	35	32.41%	56.48%
24.45% to 32.33%	24	22.22%	78.70%
32.33% to 40.22%	13	12.04%	90.74%
40.22% to 48.10%	7	6.48%	97.22%
48.10% to 55.98%	2	1.85%	99.07%
Greater than 55.98%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.94%	34.96%	65.74%	68.27%
±2σ	3.43%	45.47%	97.22%	95.45%
±3σ	-7.08%	55.98%	99.07%	99.73%

Descriptive Statistics

Mean	24.450%
Standard Error	1.011%
Median	23.060%
Mode	7.417%
Standard Deviation	10.511%
Sample Variance	110.476%
Kurtosis	1.11
Skewness	0.99
Range	55.289%
Minimum	7.417%
Maximum	62.706%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.450%	108	100.00%	24.450%
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 0.33. Further, an Excess Kurtosis of 0.32 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.94%	0	0.00%	0.00%
-39.94% to -30.02%	0	0.00%	0.00%
-30.02% to -20.11%	8	7.41%	7.41%
-20.11% to -10.19%	12	11.11%	18.52%
-10.19% to -0.27%	35	32.41%	50.93%
-0.27% to 9.64%	32	29.63%	80.56%
9.64% to 19.56%	10	9.26%	89.81%
19.56% to 29.48%	10	9.26%	99.07%
29.48% to 39.40%	0	0.00%	99.07%
Greater than 39.40%	1	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.50%	12.95%	70.37%	68.27%
±2σ	-26.72%	26.17%	97.22%	95.45%
±3σ	-39.94%	39.40%	99.07%	99.73%

Descriptive Statistics

Mean	-0.272%
Standard Error	1.272%
Median	-0.422%
Mode	-25.877%
Standard Deviation	13.223%
Sample Variance	174.854%
Kurtosis	0.32
Skewness	0.33
Range	68.454%
Minimum	-25.877%
Maximum	42.577%
Count	108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.279%	52	48.15%	4.949%
Negative	-10.070%	56	51.85%	-5.221%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.12. Further, an Excess Kurtosis of -0.53 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.85%	0	0.00%	0.00%
-61.85% to -44.97%	0	0.00%	0.00%
-44.97% to -28.08%	2	5.56%	5.56%
-28.08% to -11.20%	7	19.44%	25.00%
-11.20% to 5.68%	10	27.78%	52.78%
5.68% to 22.57%	7	19.44%	72.22%
22.57% to 39.45%	7	19.44%	91.67%
39.45% to 56.33%	3	8.33%	100.00%
56.33% to 73.21%	0	0.00%	100.00%
Greater than 73.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.83%	28.19%	69.44%	68.27%
±2σ	-39.34%	50.70%	94.44%	95.45%
±3σ	-61.85%	73.21%	100.00%	99.73%

Descriptive Statistics

Mean	5.682%
Standard Error	3.752%
Median	2.980%
Mode	-42.996%
Standard Deviation	22.510%
Sample Variance	506.692%
Kurtosis	-0.53
Skewness	-0.12
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	-14.992%	16	44.44%	-6.663%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	23.89%
12	3 Years	30.58%
20	5 Years	34.02%
40	10 Years	37.83%
80	20 Years	37.83%
200	50 Years	37.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.90. Further, an Excess Kurtosis of 5.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.07%	0	0.00%	0.00%
-22.07% to -5.04%	0	0.00%	0.00%
-5.04% to 11.99%	0	0.00%	0.00%
11.99% to 29.03%	7	18.92%	18.92%
29.03% to 46.06%	16	43.24%	62.16%
46.06% to 63.09%	9	24.32%	86.49%
63.09% to 80.13%	3	8.11%	94.59%
80.13% to 97.16%	1	2.70%	97.30%
97.16% to 114.20%	0	0.00%	97.30%
Greater than 114.20%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.35%	68.77%	81.08%	68.27%
±2σ	0.64%	91.48%	94.59%	95.45%
±3σ	-22.07%	114.20%	97.30%	99.73%

Descriptive Statistics

Mean	46.061%
Standard Error	3.734%
Median	42.088%
Mode	14.632%
Standard Deviation	22.712%
Sample Variance	515.822%
Kurtosis	5.31
Skewness	1.90
Range	118.729%
Minimum	14.632%
Maximum	133.361%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.061%	37	100.00%	46.061%
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 1.33. Further, an Excess Kurtosis of 2.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.52%	0	0.00%	0.00%
-72.52% to -54.52%	0	0.00%	0.00%
-54.52% to -36.52%	0	0.00%	0.00%
-36.52% to -18.52%	9	24.32%	24.32%
-18.52% to -0.53%	11	29.73%	54.05%
-0.53% to 17.47%	10	27.03%	81.08%
17.47% to 35.47%	5	13.51%	94.59%
35.47% to 53.47%	0	0.00%	94.59%
53.47% to 71.47%	1	2.70%	97.30%
Greater than 71.47%	1	2.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.52%	23.47%	81.08%	68.27%
±2σ	-48.52%	47.47%	94.59%	95.45%
±3σ	-72.52%	71.47%	97.30%	99.73%

Descriptive Statistics

Mean	-0.526%
Standard Error	3.945%
Median	-3.333%
Mode	-32.713%
Standard Deviation	23.998%
Sample Variance	575.925%
Kurtosis	2.26
Skewness	1.33
Range	105.397%
Minimum	-32.713%
Maximum	72.684%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.336%	17	45.95%	8.884%
Negative	-17.409%	20	54.05%	-9.410%
Zero	0.000%	0	0.00%	0.000%

OKTA Deep Analytical Report