NCNO - 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	3.41%	2.96%	3.13%	4.41%	4.46%	4.40%	14.79	16.16	14.14	16.90
Weekly	6.89%	7.55%	7.13%	10.27%	9.82%	9.70%	14.01	17.05	12.70	18.81
Monthly	10.91%	12.76%	11.88%	21.38%	20.43%	20.18%	12.60	18.97	10.27	23.26
Quarterly	16.85%	18.39%	19.50%	35.38%	35.39%	34.96%	10.85	22.03	7.62	31.38
Annual	—	—	—	—	70.79%	69.92%	7.62	31.38	3.75	63.69
Option Time Horizon	—	—	—	—	26.72%	26.39%	11.84	20.19	9.06	26.38

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $15.46 | Strike (K): $17.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.9250 (Bid $0.8000 / Ask $1.0500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 70.79% (CRR binomial tree, American, n=20 steps) | BS IV: 70.07% (European Black-Scholes) | Yahoo IV (Annual): 69.92% → 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 0.21. Further, an Excess Kurtosis of 6.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.30%	12	0.84%	0.84%
-10.30% to -7.75%	12	0.84%	1.68%
-7.75% to -5.18%	50	3.50%	5.18%
-5.18% to -2.63%	163	11.41%	16.59%
-2.63% to -0.07%	476	33.31%	49.90%
-0.07% to 2.49%	476	33.31%	83.21%
2.49% to 5.05%	175	12.25%	95.45%
5.05% to 7.61%	44	3.08%	98.53%
7.61% to 10.17%	9	0.63%	99.16%
Greater than 10.17%	12	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.48%	3.35%	77.54%	68.27%
±2σ	-6.89%	6.76%	95.31%	95.45%
±3σ	-10.30%	10.17%	98.32%	99.73%

Descriptive Statistics

Mean	-0.066%
Standard Error	0.090%
Median	-0.062%
Mode	0.000%
Standard Deviation	3.413%
Sample Variance	11.648%
Kurtosis	6.37
Skewness	0.21
Range	45.488%
Minimum	-21.018%
Maximum	24.470%
Count	1429

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.359%	696	48.70%	1.149%
Negative	-2.395%	725	50.73%	-1.215%
Zero	0.000%	8	0.56%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.90%
20	1 Month	5.42%
60	1 Quarter	5.08%
250	1 Year	4.07%
750	3 Years	3.67%
1,250	5 Years	4.41%
2,500	10 Years	4.60%
5,000	20 Years	4.60%
12,500	50 Years	4.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.12. Further, an Excess Kurtosis of 17.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.41%	0	0.00%	0.00%
-4.41% to -2.18%	0	0.00%	0.00%
-2.18% to 0.04%	0	0.00%	0.00%
0.04% to 2.26%	242	16.92%	16.92%
2.26% to 4.49%	647	45.24%	62.17%
4.49% to 6.71%	327	22.87%	85.03%
6.71% to 8.93%	128	8.95%	93.99%
8.93% to 11.16%	40	2.80%	96.78%
11.16% to 13.38%	18	1.26%	98.04%
Greater than 13.38%	28	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.52%	7.45%	86.15%	68.27%
±2σ	-1.44%	10.42%	96.29%	95.45%
±3σ	-4.41%	13.38%	98.04%	99.73%

Descriptive Statistics

Mean	4.487%
Standard Error	0.078%
Median	3.718%
Mode	2.158%
Standard Deviation	2.965%
Sample Variance	8.793%
Kurtosis	17.86
Skewness	3.12
Range	34.699%
Minimum	0.906%
Maximum	35.605%
Count	1430

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.487%	1430	100.00%	4.487%
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 -0.09. 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 -9.27%	12	0.84%	0.84%
-9.27% to -6.92%	9	0.63%	1.47%
-6.92% to -4.57%	54	3.78%	5.24%
-4.57% to -2.22%	156	10.91%	16.15%
-2.22% to 0.13%	510	35.66%	51.82%
0.13% to 2.48%	443	30.98%	82.80%
2.48% to 4.83%	165	11.54%	94.34%
4.83% to 7.18%	55	3.85%	98.18%
7.18% to 9.53%	15	1.05%	99.23%
Greater than 9.53%	11	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.00%	3.26%	77.69%	68.27%
±2σ	-6.14%	6.40%	95.38%	95.45%
±3σ	-9.27%	9.53%	98.39%	99.73%

Descriptive Statistics

Mean	0.129%
Standard Error	0.083%
Median	0.041%
Mode	0.000%
Standard Deviation	3.134%
Sample Variance	9.819%
Kurtosis	6.42
Skewness	-0.09
Range	41.567%
Minimum	-22.481%
Maximum	19.086%
Count	1430

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.245%	730	51.05%	1.146%
Negative	-2.093%	695	48.60%	-1.017%
Zero	0.000%	5	0.35%	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 1.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.97%	1	0.34%	0.34%
-20.97% to -15.80%	4	1.35%	1.69%
-15.80% to -10.63%	14	4.73%	6.42%
-10.63% to -5.46%	36	12.16%	18.58%
-5.46% to -0.29%	89	30.07%	48.65%
-0.29% to 4.88%	95	32.09%	80.74%
4.88% to 10.05%	37	12.50%	93.24%
10.05% to 15.22%	13	4.39%	97.64%
15.22% to 20.39%	6	2.03%	99.66%
Greater than 20.39%	1	0.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.18%	6.61%	75.00%	68.27%
±2σ	-14.08%	13.50%	94.59%	95.45%
±3σ	-20.97%	20.39%	99.32%	99.73%

Descriptive Statistics

Mean	-0.289%
Standard Error	0.401%
Median	-0.217%
Mode	-0.634%
Standard Deviation	6.894%
Sample Variance	47.521%
Kurtosis	1.61
Skewness	0.10
Range	51.766%
Minimum	-23.829%
Maximum	27.937%
Count	296

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.960%	141	47.63%	2.363%
Negative	-5.097%	154	52.03%	-2.652%
Zero	0.000%	1	0.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.00%
12	1 Quarter	11.70%
52	1 Year	9.44%
156	3 Years	8.57%
260	5 Years	10.27%
520	10 Years	10.60%
1,040	20 Years	10.60%
2,600	50 Years	10.60%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.10. Further, an Excess Kurtosis of 5.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.16%	0	0.00%	0.00%
-11.16% to -5.50%	0	0.00%	0.00%
-5.50% to 0.17%	0	0.00%	0.00%
0.17% to 5.83%	55	18.52%	18.52%
5.83% to 11.49%	132	44.44%	62.96%
11.49% to 17.16%	60	20.20%	83.16%
17.16% to 22.82%	32	10.77%	93.94%
22.82% to 28.49%	6	2.02%	95.96%
28.49% to 34.15%	2	0.67%	96.63%
Greater than 34.15%	10	3.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.94%	19.05%	84.18%	68.27%
±2σ	-3.61%	26.60%	95.96%	95.45%
±3σ	-11.16%	34.15%	96.63%	99.73%

Descriptive Statistics

Mean	11.495%
Standard Error	0.438%
Median	9.236%
Mode	8.186%
Standard Deviation	7.552%
Sample Variance	57.027%
Kurtosis	5.78
Skewness	2.10
Range	48.860%
Minimum	2.233%
Maximum	51.093%
Count	297

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.495%	297	100.00%	11.495%
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 0.72. Further, an Excess Kurtosis of 2.25 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.57%	1	0.34%	0.34%
-20.57% to -15.23%	1	0.34%	0.67%
-15.23% to -9.89%	12	4.04%	4.71%
-9.89% to -4.54%	40	13.47%	18.18%
-4.54% to 0.80%	108	36.36%	54.55%
0.80% to 6.15%	85	28.62%	83.16%
6.15% to 11.49%	27	9.09%	92.26%
11.49% to 16.84%	16	5.39%	97.64%
16.84% to 22.18%	3	1.01%	98.65%
Greater than 22.18%	4	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.32%	7.93%	75.08%	68.27%
±2σ	-13.45%	15.06%	93.94%	95.45%
±3σ	-20.57%	22.18%	98.32%	99.73%

Descriptive Statistics

Mean	0.803%
Standard Error	0.414%
Median	0.380%
Mode	-6.256%
Standard Deviation	7.126%
Sample Variance	50.786%
Kurtosis	2.25
Skewness	0.72
Range	51.180%
Minimum	-21.079%
Maximum	30.101%
Count	297

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.625%	156	52.52%	2.955%
Negative	-4.564%	140	47.14%	-2.151%
Zero	0.000%	1	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.28. Further, an Excess Kurtosis of -0.31 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.51%	0	0.00%	0.00%
-34.51% to -26.33%	0	0.00%	0.00%
-26.33% to -18.14%	3	4.41%	4.41%
-18.14% to -9.96%	14	20.59%	25.00%
-9.96% to -1.78%	19	27.94%	52.94%
-1.78% to 6.40%	18	26.47%	79.41%
6.40% to 14.59%	8	11.76%	91.18%
14.59% to 22.77%	5	7.35%	98.53%
22.77% to 30.95%	1	1.47%	100.00%
Greater than 30.95%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.69%	9.13%	67.65%	68.27%
±2σ	-23.60%	20.04%	95.59%	95.45%
±3σ	-34.51%	30.95%	100.00%	99.73%

Descriptive Statistics

Mean	-1.779%
Standard Error	1.323%
Median	-2.158%
Mode	-24.403%
Standard Deviation	10.910%
Sample Variance	119.028%
Kurtosis	-0.31
Skewness	0.28
Range	49.671%
Minimum	-24.403%
Maximum	25.268%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.988%	27	39.71%	3.569%
Negative	-8.868%	41	60.29%	-5.347%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	22.98%
12	1 Year	20.69%
36	3 Years	19.31%
60	5 Years	21.38%
120	10 Years	21.82%
240	20 Years	21.82%
600	50 Years	21.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.92. Further, an Excess Kurtosis of 0.29 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.68%	0	0.00%	0.00%
-12.68% to -3.10%	0	0.00%	0.00%
-3.10% to 6.46%	0	0.00%	0.00%
6.46% to 16.04%	21	30.43%	30.43%
16.04% to 25.61%	18	26.09%	56.52%
25.61% to 35.18%	17	24.64%	81.16%
35.18% to 44.75%	7	10.14%	91.30%
44.75% to 54.32%	3	4.35%	95.65%
54.32% to 63.89%	3	4.35%	100.00%
Greater than 63.89%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.85%	38.37%	69.57%	68.27%
±2σ	0.09%	51.13%	95.65%	95.45%
±3σ	-12.68%	63.89%	100.00%	99.73%

Descriptive Statistics

Mean	25.607%
Standard Error	1.536%
Median	22.785%
Mode	10.338%
Standard Deviation	12.761%
Sample Variance	162.842%
Kurtosis	0.29
Skewness	0.92
Range	52.193%
Minimum	10.338%
Maximum	62.531%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.607%	69	100.00%	25.607%
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 0.10. Further, an Excess Kurtosis of -0.14 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.07%	0	0.00%	0.00%
-33.07% to -24.15%	1	1.45%	1.45%
-24.15% to -15.24%	2	2.90%	4.35%
-15.24% to -6.33%	12	17.39%	21.74%
-6.33% to 2.59%	24	34.78%	56.52%
2.59% to 11.50%	14	20.29%	76.81%
11.50% to 20.42%	11	15.94%	92.75%
20.42% to 29.33%	4	5.80%	98.55%
29.33% to 38.24%	1	1.45%	100.00%
Greater than 38.24%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.30%	14.47%	65.22%	68.27%
±2σ	-21.18%	26.36%	97.10%	95.45%
±3σ	-33.07%	38.24%	100.00%	99.73%

Descriptive Statistics

Mean	2.589%
Standard Error	1.431%
Median	1.813%
Mode	-26.826%
Standard Deviation	11.885%
Sample Variance	141.263%
Kurtosis	-0.14
Skewness	0.10
Range	59.602%
Minimum	-26.826%
Maximum	32.776%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.426%	40	57.97%	6.044%
Negative	-8.220%	29	42.03%	-3.455%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.24. Further, an Excess Kurtosis of -0.16 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.95%	0	0.00%	0.00%
-55.95% to -43.31%	0	0.00%	0.00%
-43.31% to -30.68%	2	8.70%	8.70%
-30.68% to -18.04%	3	13.04%	21.74%
-18.04% to -5.41%	8	34.78%	56.52%
-5.41% to 7.23%	4	17.39%	73.91%
7.23% to 19.87%	4	17.39%	91.30%
19.87% to 32.50%	2	8.70%	100.00%
32.50% to 45.14%	0	0.00%	100.00%
Greater than 45.14%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.25%	11.44%	60.87%	68.27%
±2σ	-39.10%	28.29%	95.65%	95.45%
±3σ	-55.95%	45.14%	100.00%	99.73%

Descriptive Statistics

Mean	-5.405%
Standard Error	3.513%
Median	-8.801%
Mode	-36.925%
Standard Deviation	16.847%
Sample Variance	283.822%
Kurtosis	-0.16
Skewness	0.24
Range	67.738%
Minimum	-36.925%
Maximum	30.813%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.055%	7	30.43%	4.582%
Negative	-14.356%	16	69.56%	-9.987%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	34.68%
12	3 Years	33.21%
20	5 Years	35.38%
40	10 Years	35.97%
80	20 Years	35.97%
200	50 Years	35.97%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.39. Further, an Excess Kurtosis of 2.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.72%	0	0.00%	0.00%
-8.72% to 5.07%	0	0.00%	0.00%
5.07% to 18.86%	0	0.00%	0.00%
18.86% to 32.65%	4	16.67%	16.67%
32.65% to 46.44%	11	45.83%	62.50%
46.44% to 60.23%	5	20.83%	83.33%
60.23% to 74.02%	2	8.33%	91.67%
74.02% to 87.81%	1	4.17%	95.83%
87.81% to 101.60%	1	4.17%	100.00%
Greater than 101.60%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	28.05%	64.83%	83.33%	68.27%
±2σ	9.67%	83.22%	91.67%	95.45%
±3σ	-8.72%	101.60%	100.00%	99.73%

Descriptive Statistics

Mean	46.442%
Standard Error	3.753%
Median	42.638%
Mode	19.333%
Standard Deviation	18.387%
Sample Variance	338.084%
Kurtosis	2.55
Skewness	1.39
Range	81.759%
Minimum	19.333%
Maximum	101.092%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.442%	24	100.00%	46.442%
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 0.73. Further, an Excess Kurtosis of 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.54%	0	0.00%	0.00%
-50.54% to -35.91%	0	0.00%	0.00%
-35.91% to -21.28%	1	4.17%	4.17%
-21.28% to -6.65%	6	25.00%	29.17%
-6.65% to 7.97%	4	16.67%	45.83%
7.97% to 22.60%	9	37.50%	83.33%
22.60% to 37.23%	1	4.17%	87.50%
37.23% to 51.86%	2	8.33%	95.83%
51.86% to 66.49%	1	4.17%	100.00%
Greater than 66.49%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.53%	27.48%	70.83%	68.27%
±2σ	-31.03%	46.98%	95.83%	95.45%
±3σ	-50.54%	66.49%	100.00%	99.73%

Descriptive Statistics

Mean	7.975%
Standard Error	3.981%
Median	9.197%
Mode	-24.080%
Standard Deviation	19.505%
Sample Variance	380.438%
Kurtosis	0.77
Skewness	0.73
Range	83.277%
Minimum	-24.080%
Maximum	59.197%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.036%	16	66.67%	12.024%
Negative	-12.148%	8	33.33%	-4.049%
Zero	0.000%	0	0.00%	0.000%

NCNO Deep Analytical Report