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%	2.30%	2.88%	3.28%	59.72	63.27	58.03	65.11
Weekly	4.38%	4.69%	4.67%	5.30%	6.34%	7.21%	57.69	65.49	54.15	69.78
Monthly	8.31%	9.56%	8.98%	12.15%	13.20%	15.02%	53.87	70.14	47.21	80.04
Quarterly	12.51%	16.32%	14.42%	20.85%	22.86%	26.01%	48.91	77.26	38.91	97.10
Annual	—	—	—	—	45.72%	52.03%	38.91	97.10	24.64	153.38
Option Time Horizon	—	—	—	—	14.94%	17.01%	52.94	71.38	45.59	82.88

Calculation Notes: Computed at 2026-02-22T14:18 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $61.47 | Strike (K): $65.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.3500 (Bid $1.9000 / Ask $2.8000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 45.72% (CRR binomial tree, American, n=20 steps) | BS IV: 45.77% (European Black-Scholes) | Yahoo IV (Annual): 52.03% → 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 -0.79. Further, an Excess Kurtosis of 25.22 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%	107	1.09%	1.70%
-4.75% to -3.14%	311	3.17%	4.88%
-3.14% to -1.53%	1031	10.52%	15.40%
-1.53% to 0.08%	3586	36.60%	52.01%
0.08% to 1.69%	3242	33.09%	85.10%
1.69% to 3.30%	982	10.02%	95.12%
3.30% to 4.91%	276	2.82%	97.94%
4.91% 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%	79.09%	68.27%
±2σ	-4.21%	4.37%	94.77%	95.45%
±3σ	-6.36%	6.51%	98.54%	99.73%

Descriptive Statistics

Mean	0.079%
Standard Error	0.022%
Median	0.000%
Mode	0.000%
Standard Deviation	2.145%
Sample Variance	4.599%
Kurtosis	25.22
Skewness	-0.79
Range	62.099%
Minimum	-44.044%
Maximum	18.055%
Count	9797

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.506%	4870	49.71%	0.749%
Negative	-1.513%	4339	44.29%	-0.670%
Zero	0.000%	588	6.00%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.91%
20	1 Month	3.83%
60	1 Quarter	3.06%
250	1 Year	3.25%
750	3 Years	2.21%
1,250	5 Years	2.30%
2,500	10 Years	2.17%
5,000	20 Years	2.12%
12,500	50 Years	2.69%

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 15.38 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 -0.13%	0	0.00%	0.00%
-0.13% to 1.24%	1807	18.44%	18.44%
1.24% to 2.61%	4467	45.59%	64.03%
2.61% to 3.98%	2015	20.57%	84.60%
3.98% to 5.36%	812	8.29%	92.89%
5.36% to 6.73%	374	3.82%	96.70%
6.73% to 8.10%	148	1.51%	98.21%
Greater than 8.10%	175	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.78%	4.44%	85.12%	68.27%
±2σ	-1.04%	6.27%	95.59%	95.45%
±3σ	-2.87%	8.10%	98.21%	99.73%

Descriptive Statistics

Mean	2.613%
Standard Error	0.018%
Median	2.172%
Mode	2.299%
Standard Deviation	1.828%
Sample Variance	3.341%
Kurtosis	15.38
Skewness	2.83
Range	25.536%
Minimum	0.270%
Maximum	25.806%
Count	9798

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.613%	9798	100.00%	2.613%
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 6.44 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	0.75%	0.75%
-5.71% to -4.29%	113	1.15%	1.90%
-4.29% to -2.87%	317	3.24%	5.13%
-2.87% to -1.45%	1031	10.52%	15.66%
-1.45% to -0.02%	3210	32.76%	48.42%
-0.02% to 1.40%	3484	35.56%	83.98%
1.40% to 2.82%	1053	10.75%	94.72%
2.82% to 4.25%	309	3.15%	97.88%
4.25% to 5.67%	128	1.31%	99.18%
Greater than 5.67%	80	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.92%	1.88%	77.67%	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	6.44
Skewness	0.24
Range	32.329%
Minimum	-12.941%
Maximum	19.388%
Count	9798

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.423%	4375	44.65%	0.635%
Negative	-1.346%	4786	48.85%	-0.657%
Zero	0.000%	637	6.50%	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 12.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.78%	11	0.54%	0.54%
-12.78% to -9.50%	19	0.92%	1.46%
-9.50% to -6.21%	67	3.26%	4.72%
-6.21% to -2.92%	238	11.58%	16.29%
-2.92% to 0.36%	712	34.63%	50.92%
0.36% to 3.65%	693	33.71%	84.63%
3.65% to 6.93%	206	10.02%	94.65%
6.93% to 10.22%	73	3.55%	98.20%
10.22% to 13.51%	20	0.97%	99.17%
Greater than 13.51%	17	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.02%	4.74%	78.55%	68.27%
±2σ	-8.40%	9.13%	95.09%	95.45%
±3σ	-12.78%	13.51%	98.64%	99.73%

Descriptive Statistics

Mean	0.362%
Standard Error	0.097%
Median	0.272%
Mode	0.000%
Standard Deviation	4.382%
Sample Variance	19.205%
Kurtosis	12.03
Skewness	-0.38
Range	76.223%
Minimum	-48.522%
Maximum	27.701%
Count	2056

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.159%	1084	52.72%	1.666%
Negative	-2.964%	904	43.97%	-1.303%
Zero	0.000%	68	3.31%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.00%
12	1 Quarter	6.27%
52	1 Year	7.40%
156	3 Years	5.08%
260	5 Years	5.30%
520	10 Years	4.96%
1,040	20 Years	4.83%
2,600	50 Years	5.88%

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 83.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.99%	0	0.00%	0.00%
-7.99% to -4.47%	0	0.00%	0.00%
-4.47% to -0.95%	0	0.00%	0.00%
-0.95% to 2.57%	264	12.83%	12.83%
2.57% to 6.08%	1056	51.34%	64.17%
6.08% to 9.60%	438	21.29%	85.46%
9.60% to 13.12%	179	8.70%	94.17%
13.12% to 16.64%	58	2.82%	96.99%
16.64% to 20.16%	31	1.51%	98.49%
Greater than 20.16%	31	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.39%	10.78%	88.92%	68.27%
±2σ	-3.30%	15.47%	96.65%	95.45%
±3σ	-7.99%	20.16%	98.49%	99.73%

Descriptive Statistics

Mean	6.085%
Standard Error	0.103%
Median	4.850%
Mode	10.000%
Standard Deviation	4.691%
Sample Variance	22.009%
Kurtosis	83.05
Skewness	5.69
Range	98.597%
Minimum	1.000%
Maximum	99.597%
Count	2057

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.085%	2057	100.00%	6.085%
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 4.64. Further, an Excess Kurtosis of 86.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.14%	9	0.44%	0.44%
-14.14% to -10.64%	18	0.88%	1.31%
-10.64% to -7.14%	54	2.63%	3.94%
-7.14% to -3.64%	207	10.06%	14.00%
-3.64% to -0.14%	786	38.21%	52.21%
-0.14% to 3.36%	695	33.79%	86.00%
3.36% to 6.86%	200	9.72%	95.72%
6.86% to 10.36%	58	2.82%	98.54%
10.36% to 13.86%	17	0.83%	99.37%
Greater than 13.86%	13	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.80%	4.53%	81.67%	68.27%
±2σ	-9.47%	9.20%	96.16%	95.45%
±3σ	-14.14%	13.86%	98.93%	99.73%

Descriptive Statistics

Mean	-0.137%
Standard Error	0.103%
Median	-0.335%
Mode	0.000%
Standard Deviation	4.667%
Sample Variance	21.777%
Kurtosis	86.57
Skewness	4.64
Range	112.296%
Minimum	-17.746%
Maximum	94.550%
Count	2057

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.222%	890	43.27%	1.394%
Negative	-2.863%	1100	53.48%	-1.531%
Zero	0.000%	67	3.26%	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 4.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.43%	4	0.85%	0.85%
-23.43% to -17.20%	2	0.42%	1.27%
-17.20% to -10.96%	20	4.23%	5.50%
-10.96% to -4.73%	66	13.95%	19.45%
-4.73% to 1.50%	137	28.96%	48.41%
1.50% to 7.74%	160	33.83%	82.24%
7.74% to 13.97%	61	12.90%	95.14%
13.97% to 20.20%	14	2.96%	98.10%
20.20% to 26.43%	5	1.06%	99.15%
Greater than 26.43%	4	0.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.81%	9.81%	75.05%	68.27%
±2σ	-15.12%	18.12%	95.98%	95.45%
±3σ	-23.43%	26.43%	98.31%	99.73%

Descriptive Statistics

Mean	1.502%
Standard Error	0.382%
Median	1.641%
Mode	0.000%
Standard Deviation	8.311%
Sample Variance	69.065%
Kurtosis	4.32
Skewness	-0.24
Range	84.742%
Minimum	-48.274%
Maximum	36.468%
Count	473

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.232%	290	61.31%	3.821%
Negative	-6.267%	175	37.00%	-2.319%
Zero	0.000%	8	1.69%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	12.14%
12	1 Year	17.49%
36	3 Years	12.34%
60	5 Years	12.15%
120	10 Years	11.08%
240	20 Years	10.47%
600	50 Years	12.52%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.72. Further, an Excess Kurtosis of 23.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.01%	0	0.00%	0.00%
-15.01% to -7.84%	0	0.00%	0.00%
-7.84% to -0.67%	0	0.00%	0.00%
-0.67% to 6.50%	67	14.14%	14.14%
6.50% to 13.67%	235	49.58%	63.71%
13.67% to 20.84%	106	22.36%	86.08%
20.84% to 28.01%	43	9.07%	95.15%
28.01% to 35.18%	10	2.11%	97.26%
35.18% to 42.35%	5	1.05%	98.31%
Greater than 42.35%	8	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.11%	23.23%	88.19%	68.27%
±2σ	-5.45%	32.79%	96.62%	95.45%
±3σ	-15.01%	42.35%	98.31%	99.73%

Descriptive Statistics

Mean	13.673%
Standard Error	0.439%
Median	11.320%
Mode	6.965%
Standard Deviation	9.560%
Sample Variance	91.395%
Kurtosis	23.69
Skewness	3.72
Range	98.175%
Minimum	3.080%
Maximum	101.255%
Count	474

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.673%	474	100.00%	13.673%
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 2.85. Further, an Excess Kurtosis of 25.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.61%	1	0.21%	0.21%
-27.61% to -20.87%	2	0.42%	0.63%
-20.87% to -14.14%	10	2.11%	2.74%
-14.14% to -7.41%	65	13.71%	16.46%
-7.41% to -0.67%	190	40.08%	56.54%
-0.67% to 6.06%	130	27.43%	83.97%
6.06% to 12.79%	52	10.97%	94.94%
12.79% to 19.53%	17	3.59%	98.52%
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	-9.65%	8.31%	78.27%	68.27%
±2σ	-18.63%	17.28%	96.84%	95.45%
±3σ	-27.61%	26.26%	98.95%	99.73%

Descriptive Statistics

Mean	-0.672%
Standard Error	0.412%
Median	-1.612%
Mode	0.000%
Standard Deviation	8.978%
Sample Variance	80.606%
Kurtosis	25.58
Skewness	2.85
Range	121.141%
Minimum	-28.788%
Maximum	92.353%
Count	474

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.255%	175	36.92%	2.679%
Negative	-5.534%	287	60.55%	-3.351%
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 -0.52. Further, an Excess Kurtosis of 2.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.32%	1	0.63%	0.63%
-33.32% to -23.94%	3	1.90%	2.53%
-23.94% to -14.56%	3	1.90%	4.43%
-14.56% to -5.18%	23	14.56%	18.99%
-5.18% to 4.20%	43	27.22%	46.20%
4.20% to 13.57%	59	37.34%	83.54%
13.57% to 22.95%	14	8.86%	92.41%
22.95% to 32.33%	10	6.33%	98.73%
32.33% to 41.71%	2	1.27%	100.00%
Greater than 41.71%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.31%	16.70%	74.68%	68.27%
±2σ	-20.82%	29.21%	94.30%	95.45%
±3σ	-33.32%	41.71%	99.37%	99.73%

Descriptive Statistics

Mean	4.195%
Standard Error	0.995%
Median	5.129%
Mode	8.822%
Standard Deviation	12.505%
Sample Variance	156.382%
Kurtosis	2.35
Skewness	-0.52
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	-8.073%	57	36.08%	-2.912%
Zero	0.000%	1	0.63%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	29.07%
12	3 Years	22.95%
20	5 Years	20.85%
40	10 Years	19.39%
80	20 Years	18.18%
200	50 Years	21.52%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.80. Further, an Excess Kurtosis of 10.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.14%	0	0.00%	0.00%
-24.14% to -11.90%	0	0.00%	0.00%
-11.90% to 0.35%	0	0.00%	0.00%
0.35% to 12.59%	24	15.09%	15.09%
12.59% to 24.83%	77	48.43%	63.52%
24.83% to 37.07%	41	25.79%	89.31%
37.07% to 49.32%	7	4.40%	93.71%
49.32% to 61.56%	3	1.89%	95.60%
61.56% to 73.80%	2	1.26%	96.86%
Greater than 73.80%	5	3.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.51%	41.15%	91.82%	68.27%
±2σ	-7.82%	57.48%	95.60%	95.45%
±3σ	-24.14%	73.80%	96.86%	99.73%

Descriptive Statistics

Mean	24.831%
Standard Error	1.295%
Median	20.563%
Mode	7.386%
Standard Deviation	16.323%
Sample Variance	266.454%
Kurtosis	10.25
Skewness	2.80
Range	110.252%
Minimum	7.386%
Maximum	117.638%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.831%	159	100.00%	24.831%
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 3.29. Further, an Excess Kurtosis of 21.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.72%	0	0.00%	0.00%
-45.72% to -34.91%	0	0.00%	0.00%
-34.91% to -24.09%	2	1.26%	1.26%
-24.09% to -13.28%	21	13.21%	14.47%
-13.28% to -2.47%	70	44.03%	58.49%
-2.47% to 8.34%	47	29.56%	88.05%
8.34% to 19.16%	13	8.18%	96.23%
19.16% to 29.97%	1	0.63%	96.86%
29.97% to 40.78%	3	1.89%	98.74%
Greater than 40.78%	2	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.89%	11.95%	83.02%	68.27%
±2σ	-31.30%	26.36%	96.23%	95.45%
±3σ	-45.72%	40.78%	98.74%	99.73%

Descriptive Statistics

Mean	-2.470%
Standard Error	1.143%
Median	-4.839%
Mode	-4.817%
Standard Deviation	14.417%
Sample Variance	207.850%
Kurtosis	21.44
Skewness	3.29
Range	133.573%
Minimum	-25.986%
Maximum	107.587%
Count	159

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.831%	54	33.96%	3.678%
Negative	-9.492%	103	64.78%	-6.149%
Zero	0.000%	2	1.26%	0.000%

FISV Deep Analytical Report