FISV - 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	2.15%	1.83%	1.90%	2.33%	3.78%	3.84%	55.02	59.34	52.98	61.62
Weekly	4.38%	4.69%	4.67%	5.36%	8.31%	8.45%	52.58	62.09	48.39	67.48
Monthly	8.31%	9.55%	8.97%	12.21%	17.31%	17.58%	48.06	67.94	40.42	80.77
Quarterly	12.54%	16.31%	14.45%	21.01%	29.97%	30.46%	42.34	77.11	31.38	104.06
Annual	—	—	—	—	59.95%	60.91%	31.38	104.06	17.23	189.52
Option Time Horizon	—	—	—	—	22.63%	22.99%	45.57	71.65	36.34	89.84

Calculation Notes: Computed at 2026-03-23T16:33 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $57.14 | Strike (K): $60.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.1500 (Bid $3.7000 / Ask $4.6000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 59.95% (CRR binomial tree, American, n=20 steps) | BS IV: 60.68% (European Black-Scholes) | Yahoo IV (Annual): 60.91% → 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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.78. Further, an Excess Kurtosis of 25.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.36%	60	0.61%	0.61%
-6.36% to -4.75%	108	1.10%	1.71%
-4.75% to -3.14%	311	3.17%	4.88%
-3.14% to -1.53%	1036	10.55%	15.43%
-1.53% to 0.08%	3588	36.55%	51.98%
0.08% to 1.69%	3252	33.12%	85.10%
1.69% to 3.30%	984	10.02%	95.12%
3.30% to 4.90%	277	2.82%	97.94%
4.90% to 6.51%	119	1.21%	99.15%
Greater than 6.51%	83	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.07%	2.22%	79.07%	68.27%
±2σ	-4.21%	4.37%	94.77%	95.45%
±3σ	-6.36%	6.51%	98.54%	99.73%

Descriptive Statistics

Mean	0.078%
Standard Error	0.022%
Median	0.000%
Mode	0.000%
Standard Deviation	2.145%
Sample Variance	4.599%
Kurtosis	25.16
Skewness	-0.78
Range	62.099%
Minimum	-44.044%
Maximum	18.055%
Count	9818

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.506%	4881	49.72%	0.749%
Negative	-1.514%	4349	44.30%	-0.671%
Zero	0.000%	588	5.99%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.05%
20	1 Month	3.58%
60	1 Quarter	3.39%
250	1 Year	3.34%
750	3 Years	2.23%
1,250	5 Years	2.33%
2,500	10 Years	2.19%
5,000	20 Years	2.12%
12,500	50 Years	2.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.83. Further, an Excess Kurtosis of 15.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.87%	0	0.00%	0.00%
-2.87% to -1.50%	0	0.00%	0.00%
-1.50% to -0.12%	0	0.00%	0.00%
-0.12% to 1.25%	1809	18.42%	18.42%
1.25% to 2.62%	4472	45.54%	63.97%
2.62% to 3.98%	2023	20.60%	84.57%
3.98% to 5.36%	815	8.30%	92.87%
5.36% to 6.73%	377	3.84%	96.71%
6.73% to 8.10%	148	1.51%	98.22%
Greater than 8.10%	175	1.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.79%	4.44%	85.02%	68.27%
±2σ	-1.04%	6.27%	95.59%	95.45%
±3σ	-2.87%	8.10%	98.22%	99.73%

Descriptive Statistics

Mean	2.615%
Standard Error	0.018%
Median	2.174%
Mode	2.299%
Standard Deviation	1.827%
Sample Variance	3.339%
Kurtosis	15.35
Skewness	2.83
Range	25.536%
Minimum	0.270%
Maximum	25.806%
Count	9819

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.615%	9819	100.00%	2.615%
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 0.24. Further, an Excess Kurtosis of 6.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.71%	73	0.74%	0.74%
-5.71% to -4.29%	113	1.15%	1.89%
-4.29% to -2.87%	319	3.25%	5.14%
-2.87% to -1.45%	1033	10.52%	15.66%
-1.45% to -0.02%	3218	32.77%	48.44%
-0.02% to 1.40%	3488	35.52%	83.96%
1.40% to 2.82%	1056	10.75%	94.71%
2.82% to 4.25%	311	3.17%	97.88%
4.25% to 5.67%	128	1.30%	99.19%
Greater than 5.67%	80	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.92%	1.88%	77.64%	68.27%
±2σ	-3.82%	3.77%	94.52%	95.45%
±3σ	-5.71%	5.67%	98.44%	99.73%

Descriptive Statistics

Mean	-0.022%
Standard Error	0.019%
Median	0.000%
Mode	0.000%
Standard Deviation	1.897%
Sample Variance	3.599%
Kurtosis	6.42
Skewness	0.24
Range	32.329%
Minimum	-12.941%
Maximum	19.388%
Count	9819

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.424%	4384	44.65%	0.636%
Negative	-1.346%	4798	48.86%	-0.658%
Zero	0.000%	637	6.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.37. Further, an Excess Kurtosis of 12.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.79%	11	0.53%	0.53%
-12.79% to -9.50%	19	0.92%	1.46%
-9.50% to -6.21%	67	3.25%	4.71%
-6.21% to -2.93%	238	11.55%	16.26%
-2.93% to 0.36%	715	34.71%	50.97%
0.36% to 3.64%	693	33.64%	84.61%
3.64% to 6.93%	207	10.05%	94.66%
6.93% to 10.22%	73	3.54%	98.20%
10.22% to 13.50%	20	0.97%	99.17%
Greater than 13.50%	17	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.02%	4.74%	78.35%	68.27%
±2σ	-8.41%	9.12%	95.15%	95.45%
±3σ	-12.79%	13.50%	98.64%	99.73%

Descriptive Statistics

Mean	0.358%
Standard Error	0.097%
Median	0.268%
Mode	0.000%
Standard Deviation	4.382%
Sample Variance	19.201%
Kurtosis	12.01
Skewness	-0.37
Range	76.223%
Minimum	-48.522%
Maximum	27.701%
Count	2060

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.161%	1084	52.62%	1.663%
Negative	-2.961%	908	44.08%	-1.305%
Zero	0.000%	68	3.30%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.87%
12	1 Quarter	7.21%
52	1 Year	7.58%
156	3 Years	5.10%
260	5 Years	5.36%
520	10 Years	5.00%
1,040	20 Years	4.85%
2,600	50 Years	5.89%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.69. Further, an Excess Kurtosis of 83.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.98%	0	0.00%	0.00%
-7.98% to -4.46%	0	0.00%	0.00%
-4.46% to -0.94%	0	0.00%	0.00%
-0.94% to 2.57%	267	12.95%	12.95%
2.57% to 6.09%	1056	51.24%	64.19%
6.09% to 9.61%	438	21.25%	85.44%
9.61% to 13.12%	180	8.73%	94.18%
13.12% to 16.64%	58	2.81%	96.99%
16.64% to 20.16%	31	1.50%	98.50%
Greater than 20.16%	31	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.40%	10.78%	88.94%	68.27%
±2σ	-3.29%	15.47%	96.65%	95.45%
±3σ	-7.98%	20.16%	98.50%	99.73%

Descriptive Statistics

Mean	6.091%
Standard Error	0.103%
Median	4.878%
Mode	10.000%
Standard Deviation	4.689%
Sample Variance	21.987%
Kurtosis	83.02
Skewness	5.69
Range	98.597%
Minimum	1.000%
Maximum	99.597%
Count	2061

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.091%	2061	100.00%	6.091%
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 4.63. Further, an Excess Kurtosis of 86.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.13%	9	0.44%	0.44%
-14.13% to -10.63%	18	0.87%	1.31%
-10.63% to -7.13%	54	2.62%	3.93%
-7.13% to -3.63%	208	10.09%	14.02%
-3.63% to -0.13%	787	38.19%	52.21%
-0.13% to 3.37%	695	33.72%	85.93%
3.37% to 6.87%	202	9.80%	95.73%
6.87% to 10.37%	58	2.81%	98.54%
10.37% to 13.87%	17	0.82%	99.37%
Greater than 13.87%	13	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.80%	4.53%	81.61%	68.27%
±2σ	-9.47%	9.20%	96.17%	95.45%
±3σ	-14.13%	13.87%	98.93%	99.73%

Descriptive Statistics

Mean	-0.134%
Standard Error	0.103%
Median	-0.334%
Mode	0.000%
Standard Deviation	4.667%
Sample Variance	21.777%
Kurtosis	86.39
Skewness	4.63
Range	112.296%
Minimum	-17.746%
Maximum	94.550%
Count	2061

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.224%	893	43.33%	1.397%
Negative	-2.866%	1101	53.42%	-1.531%
Zero	0.000%	67	3.25%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.24. Further, an Excess Kurtosis of 4.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.45%	4	0.84%	0.84%
-23.45% to -17.22%	2	0.42%	1.27%
-17.22% to -10.98%	20	4.22%	5.49%
-10.98% to -4.75%	66	13.92%	19.41%
-4.75% to 1.49%	137	28.90%	48.31%
1.49% to 7.72%	161	33.97%	82.28%
7.72% to 13.95%	60	12.66%	94.94%
13.95% to 20.19%	15	3.16%	98.10%
20.19% to 26.42%	5	1.05%	99.16%
Greater than 26.42%	4	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.83%	9.80%	74.68%	68.27%
±2σ	-15.14%	18.11%	95.78%	95.45%
±3σ	-23.45%	26.42%	98.31%	99.73%

Descriptive Statistics

Mean	1.485%
Standard Error	0.382%
Median	1.636%
Mode	0.000%
Standard Deviation	8.312%
Sample Variance	69.086%
Kurtosis	4.30
Skewness	-0.24
Range	84.742%
Minimum	-48.274%
Maximum	36.468%
Count	474

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.232%	290	61.18%	3.813%
Negative	-6.269%	176	37.13%	-2.328%
Zero	0.000%	8	1.69%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	12.00%
12	1 Year	17.57%
36	3 Years	12.36%
60	5 Years	12.21%
120	10 Years	11.14%
240	20 Years	10.51%
600	50 Years	12.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.73. Further, an Excess Kurtosis of 23.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.97%	0	0.00%	0.00%
-14.97% to -7.81%	0	0.00%	0.00%
-7.81% to -0.65%	0	0.00%	0.00%
-0.65% to 6.51%	67	14.11%	14.11%
6.51% to 13.68%	235	49.47%	63.58%
13.68% to 20.84%	107	22.53%	86.11%
20.84% to 28.00%	43	9.05%	95.16%
28.00% to 35.16%	10	2.11%	97.26%
35.16% to 42.33%	5	1.05%	98.32%
Greater than 42.33%	8	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.13%	23.23%	88.21%	68.27%
±2σ	-5.42%	32.78%	96.63%	95.45%
±3σ	-14.97%	42.33%	98.32%	99.73%

Descriptive Statistics

Mean	13.677%
Standard Error	0.438%
Median	11.350%
Mode	6.965%
Standard Deviation	9.550%
Sample Variance	91.209%
Kurtosis	23.74
Skewness	3.73
Range	98.175%
Minimum	3.080%
Maximum	101.255%
Count	475

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.677%	475	100.00%	13.677%
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 2.84. Further, an Excess Kurtosis of 25.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.58%	1	0.21%	0.21%
-27.58% to -20.85%	2	0.42%	0.63%
-20.85% to -14.12%	10	2.11%	2.74%
-14.12% to -7.39%	65	13.68%	16.42%
-7.39% to -0.66%	190	40.00%	56.42%
-0.66% to 6.07%	130	27.37%	83.79%
6.07% to 12.80%	53	11.16%	94.95%
12.80% to 19.53%	17	3.58%	98.53%
19.53% to 26.26%	3	0.63%	99.16%
Greater than 26.26%	4	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.63%	8.31%	78.32%	68.27%
±2σ	-18.61%	17.29%	96.84%	95.45%
±3σ	-27.58%	26.26%	98.95%	99.73%

Descriptive Statistics

Mean	-0.659%
Standard Error	0.412%
Median	-1.599%
Mode	0.000%
Standard Deviation	8.974%
Sample Variance	80.528%
Kurtosis	25.56
Skewness	2.84
Range	121.141%
Minimum	-28.788%
Maximum	92.353%
Count	475

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.244%	176	37.05%	2.684%
Negative	-5.534%	287	60.42%	-3.344%
Zero	0.000%	12	2.53%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.51. Further, an Excess Kurtosis of 2.29 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.47%	1	0.63%	0.63%
-33.47% to -24.07%	3	1.90%	2.53%
-24.07% to -14.66%	2	1.27%	3.80%
-14.66% to -5.25%	25	15.82%	19.62%
-5.25% to 4.15%	42	26.58%	46.20%
4.15% to 13.56%	59	37.34%	83.54%
13.56% to 22.97%	14	8.86%	92.41%
22.97% to 32.37%	10	6.33%	98.73%
32.37% to 41.78%	2	1.27%	100.00%
Greater than 41.78%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.39%	16.70%	74.05%	68.27%
±2σ	-20.93%	29.24%	94.30%	95.45%
±3σ	-33.47%	41.78%	99.37%	99.73%

Descriptive Statistics

Mean	4.154%
Standard Error	0.998%
Median	5.129%
Mode	8.822%
Standard Deviation	12.542%
Sample Variance	157.298%
Kurtosis	2.29
Skewness	-0.51
Range	87.360%
Minimum	-52.001%
Maximum	35.359%
Count	158

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.230%	100	63.29%	7.108%
Negative	-8.188%	57	36.08%	-2.954%
Zero	0.000%	1	0.63%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	29.87%
12	3 Years	23.22%
20	5 Years	21.01%
40	10 Years	19.47%
80	20 Years	18.22%
200	50 Years	21.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.81. Further, an Excess Kurtosis of 10.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.06%	0	0.00%	0.00%
-24.06% to -11.83%	0	0.00%	0.00%
-11.83% to 0.40%	0	0.00%	0.00%
0.40% to 12.63%	23	14.47%	14.47%
12.63% to 24.86%	78	49.06%	63.52%
24.86% to 37.09%	41	25.79%	89.31%
37.09% to 49.31%	7	4.40%	93.71%
49.31% to 61.55%	3	1.89%	95.60%
61.55% to 73.77%	2	1.26%	96.86%
Greater than 73.77%	5	3.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.55%	41.16%	91.82%	68.27%
±2σ	-7.76%	57.47%	95.60%	95.45%
±3σ	-24.06%	73.77%	96.86%	99.73%

Descriptive Statistics

Mean	24.856%
Standard Error	1.293%
Median	20.563%
Mode	7.386%
Standard Deviation	16.306%
Sample Variance	265.872%
Kurtosis	10.29
Skewness	2.81
Range	110.252%
Minimum	7.386%
Maximum	117.638%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.856%	159	100.00%	24.856%
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 3.26. Further, an Excess Kurtosis of 21.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.77%	0	0.00%	0.00%
-45.77% to -34.94%	0	0.00%	0.00%
-34.94% to -24.10%	2	1.26%	1.26%
-24.10% to -13.26%	21	13.21%	14.47%
-13.26% to -2.42%	70	44.03%	58.49%
-2.42% to 8.41%	46	28.93%	87.42%
8.41% to 19.25%	14	8.81%	96.23%
19.25% to 30.09%	1	0.63%	96.86%
30.09% to 40.93%	3	1.89%	98.74%
Greater than 40.93%	2	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.87%	12.03%	83.02%	68.27%
±2σ	-31.32%	26.48%	96.23%	95.45%
±3σ	-45.77%	40.93%	98.74%	99.73%

Descriptive Statistics

Mean	-2.423%
Standard Error	1.146%
Median	-4.839%
Mode	-4.817%
Standard Deviation	14.450%
Sample Variance	208.793%
Kurtosis	21.18
Skewness	3.26
Range	133.573%
Minimum	-25.986%
Maximum	107.587%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.971%	54	33.96%	3.726%
Negative	-9.492%	103	64.78%	-6.149%
Zero	0.000%	2	1.26%	0.000%

FISV Deep Analytical Report