FTNT - 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	2.60%	1.85%	2.08%	3.33%	3.06%	3.40%	79.83	84.87	77.43	87.50
Weekly	5.63%	5.51%	5.73%	7.94%	6.73%	7.48%	76.95	88.04	71.94	94.17
Monthly	10.51%	9.32%	10.46%	16.99%	14.01%	15.57%	71.55	94.69	62.20	108.93
Quarterly	18.76%	13.78%	16.51%	28.97%	24.26%	26.97%	64.58	104.91	50.66	133.72
Annual	—	—	—	—	48.53%	53.94%	50.66	133.72	31.18	217.26
Option Time Horizon	—	—	—	—	18.32%	20.36%	68.53	98.86	57.06	118.73

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $82.31 | Strike (K): $85.00 (first OTM call ≥ spot) | Observed Mid-Price: $5.1000 (Bid $4.5500 / Ask $5.6500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 48.53% (CRR binomial tree, American, n=20 steps) | BS IV: 49.07% (European Black-Scholes) | Yahoo IV (Annual): 53.94% → 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 -0.07. Further, an Excess Kurtosis of 14.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.66%	30	0.73%	0.73%
-7.66% to -5.71%	31	0.75%	1.48%
-5.71% to -3.76%	117	2.85%	4.33%
-3.76% to -1.82%	452	11.00%	15.34%
-1.82% to 0.13%	1397	34.01%	49.34%
0.13% to 2.08%	1458	35.49%	84.83%
2.08% to 4.02%	469	11.42%	96.25%
4.02% to 5.97%	95	2.31%	98.56%
5.97% to 7.91%	28	0.68%	99.25%
Greater than 7.91%	31	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.47%	2.72%	80.67%	68.27%
±2σ	-5.06%	5.32%	95.93%	95.45%
±3σ	-7.66%	7.91%	98.52%	99.73%

Descriptive Statistics

Mean	0.129%
Standard Error	0.040%
Median	0.165%
Mode	0.000%
Standard Deviation	2.595%
Sample Variance	6.734%
Kurtosis	14.55
Skewness	-0.07
Range	50.366%
Minimum	-25.066%
Maximum	25.300%
Count	4108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.733%	2190	53.31%	0.924%
Negative	-1.726%	1892	46.06%	-0.795%
Zero	0.000%	26	0.63%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.24%
20	1 Month	3.42%
60	1 Quarter	3.31%
250	1 Year	3.25%
750	3 Years	2.96%
1,250	5 Years	3.33%
2,500	10 Years	3.13%
5,000	20 Years	3.31%
12,500	50 Years	3.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.79. Further, an Excess Kurtosis of 13.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.43%	0	0.00%	0.00%
-2.43% to -1.04%	0	0.00%	0.00%
-1.04% to 0.35%	0	0.00%	0.00%
0.35% to 1.74%	684	16.65%	16.65%
1.74% to 3.13%	1899	46.22%	62.86%
3.13% to 4.52%	908	22.10%	84.96%
4.52% to 5.91%	348	8.47%	93.43%
5.91% to 7.31%	137	3.33%	96.76%
7.31% to 8.70%	55	1.34%	98.10%
Greater than 8.70%	78	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.28%	4.99%	84.79%	68.27%
±2σ	-0.58%	6.84%	96.13%	95.45%
±3σ	-2.43%	8.70%	98.10%	99.73%

Descriptive Statistics

Mean	3.132%
Standard Error	0.029%
Median	2.658%
Mode	2.068%
Standard Deviation	1.855%
Sample Variance	3.442%
Kurtosis	13.51
Skewness	2.79
Range	21.053%
Minimum	0.604%
Maximum	21.657%
Count	4109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.132%	4109	100.00%	3.132%
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 4.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.26%	24	0.58%	0.58%
-6.26% to -4.70%	39	0.95%	1.53%
-4.70% to -3.15%	117	2.85%	4.38%
-3.15% to -1.59%	562	13.68%	18.06%
-1.59% to -0.03%	1407	34.24%	52.30%
-0.03% to 1.53%	1236	30.08%	82.38%
1.53% to 3.09%	482	11.73%	94.11%
3.09% to 4.65%	160	3.89%	98.00%
4.65% to 6.21%	46	1.12%	99.12%
Greater than 6.21%	36	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.11%	2.05%	76.51%	68.27%
±2σ	-4.18%	4.13%	95.28%	95.45%
±3σ	-6.26%	6.21%	98.54%	99.73%

Descriptive Statistics

Mean	-0.029%
Standard Error	0.032%
Median	-0.136%
Mode	0.000%
Standard Deviation	2.078%
Sample Variance	4.318%
Kurtosis	4.66
Skewness	0.31
Range	27.370%
Minimum	-12.188%
Maximum	15.182%
Count	4109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.559%	1931	46.99%	0.733%
Negative	-1.447%	2164	52.66%	-0.762%
Zero	0.000%	14	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.05. Further, an Excess Kurtosis of 4.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.26%	8	0.94%	0.94%
-16.26% to -12.04%	8	0.94%	1.88%
-12.04% to -7.82%	36	4.23%	6.10%
-7.82% to -3.60%	85	9.98%	16.08%
-3.60% to 0.62%	280	32.86%	48.94%
0.62% to 4.84%	301	35.33%	84.27%
4.84% to 9.06%	94	11.03%	95.31%
9.06% to 13.28%	20	2.35%	97.65%
13.28% to 17.50%	15	1.76%	99.41%
Greater than 17.50%	5	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.01%	6.24%	78.64%	68.27%
±2σ	-10.64%	11.87%	94.25%	95.45%
±3σ	-16.26%	17.50%	98.47%	99.73%

Descriptive Statistics

Mean	0.617%
Standard Error	0.193%
Median	0.710%
Mode	-2.432%
Standard Deviation	5.626%
Sample Variance	31.647%
Kurtosis	4.25
Skewness	-0.05
Range	58.645%
Minimum	-25.759%
Maximum	32.886%
Count	852

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.889%	498	58.45%	2.273%
Negative	-4.010%	352	41.31%	-1.657%
Zero	0.000%	2	0.23%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.33%
12	1 Quarter	7.86%
52	1 Year	7.46%
156	3 Years	7.05%
260	5 Years	7.94%
520	10 Years	7.51%
1,040	20 Years	7.88%
2,600	50 Years	7.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.54. Further, an Excess Kurtosis of 8.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.25%	0	0.00%	0.00%
-8.25% to -4.12%	0	0.00%	0.00%
-4.12% to 0.01%	0	0.00%	0.00%
0.01% to 4.14%	123	14.42%	14.42%
4.14% to 8.27%	449	52.64%	67.06%
8.27% to 12.40%	153	17.94%	84.99%
12.40% to 16.53%	66	7.74%	92.73%
16.53% to 20.66%	26	3.05%	95.78%
20.66% to 24.80%	15	1.76%	97.54%
Greater than 24.80%	21	2.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.77%	13.78%	86.64%	68.27%
±2σ	-2.74%	19.29%	95.43%	95.45%
±3σ	-8.25%	24.80%	97.54%	99.73%

Descriptive Statistics

Mean	8.274%
Standard Error	0.189%
Median	6.729%
Mode	3.428%
Standard Deviation	5.507%
Sample Variance	30.325%
Kurtosis	8.59
Skewness	2.54
Range	40.152%
Minimum	1.605%
Maximum	41.757%
Count	853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.274%	853	100.00%	8.274%
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 1.20. Further, an Excess Kurtosis of 5.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.38%	3	0.35%	0.35%
-17.38% to -13.09%	4	0.47%	0.82%
-13.09% to -8.79%	29	3.40%	4.22%
-8.79% to -4.50%	103	12.08%	16.30%
-4.50% to -0.20%	335	39.27%	55.57%
-0.20% to 4.09%	252	29.54%	85.11%
4.09% to 8.39%	71	8.32%	93.43%
8.39% to 12.68%	35	4.10%	97.54%
12.68% to 16.98%	6	0.70%	98.24%
Greater than 16.98%	15	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.93%	5.52%	79.02%	68.27%
±2σ	-11.65%	11.25%	94.14%	95.45%
±3σ	-17.38%	16.98%	97.89%	99.73%

Descriptive Statistics

Mean	-0.203%
Standard Error	0.196%
Median	-0.675%
Mode	0.000%
Standard Deviation	5.726%
Sample Variance	32.784%
Kurtosis	5.94
Skewness	1.20
Range	59.305%
Minimum	-24.747%
Maximum	34.558%
Count	853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.431%	356	41.73%	1.849%
Negative	-3.543%	494	57.91%	-2.052%
Zero	0.000%	3	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 0.97 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.00%	0	0.00%	0.00%
-29.00% to -21.11%	5	2.55%	2.55%
-21.11% to -13.23%	8	4.08%	6.63%
-13.23% to -5.34%	28	14.29%	20.92%
-5.34% to 2.54%	56	28.57%	49.49%
2.54% to 10.43%	62	31.63%	81.12%
10.43% to 18.32%	25	12.76%	93.88%
18.32% to 26.20%	7	3.57%	97.45%
26.20% to 34.09%	4	2.04%	99.49%
Greater than 34.09%	1	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.97%	13.06%	74.49%	68.27%
±2σ	-18.48%	23.57%	93.37%	95.45%
±3σ	-29.00%	34.09%	99.49%	99.73%

Descriptive Statistics

Mean	2.545%
Standard Error	0.751%
Median	2.736%
Mode	-25.540%
Standard Deviation	10.514%
Sample Variance	110.537%
Kurtosis	0.97
Skewness	0.08
Range	62.802%
Minimum	-25.540%
Maximum	37.262%
Count	196

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.633%	123	62.76%	5.418%
Negative	-7.714%	73	37.24%	-2.873%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	14.62%
12	1 Year	14.76%
36	3 Years	15.44%
60	5 Years	16.99%
120	10 Years	16.39%
240	20 Years	17.11%
600	50 Years	17.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.35. Further, an Excess Kurtosis of 2.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.04%	0	0.00%	0.00%
-9.04% to -2.05%	0	0.00%	0.00%
-2.05% to 4.94%	0	0.00%	0.00%
4.94% to 11.93%	45	22.84%	22.84%
11.93% to 18.92%	75	38.07%	60.91%
18.92% to 25.91%	36	18.27%	79.19%
25.91% to 32.91%	25	12.69%	91.88%
32.91% to 39.90%	7	3.55%	95.43%
39.90% to 46.89%	6	3.05%	98.48%
Greater than 46.89%	3	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.60%	28.24%	74.11%	68.27%
±2σ	0.28%	37.57%	94.92%	95.45%
±3σ	-9.04%	46.89%	98.48%	99.73%

Descriptive Statistics

Mean	18.923%
Standard Error	0.664%
Median	16.847%
Mode	14.540%
Standard Deviation	9.322%
Sample Variance	86.902%
Kurtosis	2.07
Skewness	1.35
Range	50.990%
Minimum	6.389%
Maximum	57.379%
Count	197

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.923%	197	100.00%	18.923%
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 0.74. 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 -32.52%	0	0.00%	0.00%
-32.52% to -24.68%	1	0.51%	0.51%
-24.68% to -16.83%	6	3.05%	3.55%
-16.83% to -8.99%	36	18.27%	21.83%
-8.99% to -1.14%	71	36.04%	57.87%
-1.14% to 6.71%	44	22.34%	80.20%
6.71% to 14.55%	24	12.18%	92.39%
14.55% to 22.40%	7	3.55%	95.94%
22.40% to 30.25%	6	3.05%	98.98%
Greater than 30.25%	2	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.60%	9.32%	77.16%	68.27%
±2σ	-22.06%	19.79%	92.89%	95.45%
±3σ	-32.52%	30.25%	98.98%	99.73%

Descriptive Statistics

Mean	-1.139%
Standard Error	0.745%
Median	-2.402%
Mode	-1.479%
Standard Deviation	10.462%
Sample Variance	109.460%
Kurtosis	1.13
Skewness	0.74
Range	61.441%
Minimum	-27.927%
Maximum	33.514%
Count	197

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.031%	76	38.58%	3.484%
Negative	-7.527%	121	61.42%	-4.623%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.38. Further, an Excess Kurtosis of 0.22 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.55%	0	0.00%	0.00%
-48.55% to -34.48%	0	0.00%	0.00%
-34.48% to -20.41%	3	4.62%	4.62%
-20.41% to -6.34%	13	20.00%	24.62%
-6.34% to 7.73%	20	30.77%	55.38%
7.73% to 21.80%	13	20.00%	75.38%
21.80% to 35.87%	13	20.00%	95.38%
35.87% to 49.94%	2	3.08%	98.46%
49.94% to 64.01%	0	0.00%	98.46%
Greater than 64.01%	1	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.03%	26.49%	66.15%	68.27%
±2σ	-29.79%	45.25%	98.46%	95.45%
±3σ	-48.55%	64.01%	98.46%	99.73%

Descriptive Statistics

Mean	7.731%
Standard Error	2.327%
Median	5.315%
Mode	-28.027%
Standard Deviation	18.760%
Sample Variance	351.949%
Kurtosis	0.22
Skewness	0.38
Range	94.601%
Minimum	-28.027%
Maximum	66.574%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.785%	41	63.08%	11.849%
Negative	-11.154%	24	36.92%	-4.118%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	19.84%
12	3 Years	27.75%
20	5 Years	28.97%
40	10 Years	29.22%
80	20 Years	30.37%
200	50 Years	30.37%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.11. Further, an Excess Kurtosis of 2.60 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.43%	0	0.00%	0.00%
-6.43% to 3.91%	0	0.00%	0.00%
3.91% to 14.25%	0	0.00%	0.00%
14.25% to 24.58%	15	22.73%	22.73%
24.58% to 34.92%	22	33.33%	56.06%
34.92% to 45.26%	15	22.73%	78.79%
45.26% to 55.59%	11	16.67%	95.45%
55.59% to 65.93%	1	1.52%	96.97%
65.93% to 76.27%	1	1.52%	98.48%
Greater than 76.27%	1	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	21.14%	48.70%	71.21%	68.27%
±2σ	7.35%	62.48%	96.97%	95.45%
±3σ	-6.43%	76.27%	98.48%	99.73%

Descriptive Statistics

Mean	34.919%
Standard Error	1.696%
Median	34.224%
Mode	14.447%
Standard Deviation	13.782%
Sample Variance	189.931%
Kurtosis	2.60
Skewness	1.11
Range	73.498%
Minimum	14.447%
Maximum	87.945%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.919%	66	100.00%	34.919%
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 0.51. Further, an Excess Kurtosis of 0.02 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.32%	0	0.00%	0.00%
-53.32% to -40.94%	0	0.00%	0.00%
-40.94% to -28.55%	1	1.52%	1.52%
-28.55% to -16.17%	17	25.76%	27.27%
-16.17% to -3.79%	19	28.79%	56.06%
-3.79% to 8.60%	16	24.24%	80.30%
8.60% to 20.98%	7	10.61%	90.91%
20.98% to 33.37%	4	6.06%	96.97%
33.37% to 45.75%	2	3.03%	100.00%
Greater than 45.75%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.30%	12.73%	68.18%	68.27%
±2σ	-36.81%	29.24%	93.94%	95.45%
±3σ	-53.32%	45.75%	100.00%	99.73%

Descriptive Statistics

Mean	-3.786%
Standard Error	2.032%
Median	-4.365%
Mode	-39.667%
Standard Deviation	16.512%
Sample Variance	272.649%
Kurtosis	0.02
Skewness	0.51
Range	78.317%
Minimum	-39.667%
Maximum	38.650%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.343%	23	34.85%	4.998%
Negative	-13.483%	43	65.15%	-8.784%
Zero	0.000%	0	0.00%	0.000%

FTNT Deep Analytical Report