LITE - 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	3.46%	2.70%	2.84%	4.48%	6.63%	6.52%	672.91	768.25	629.77	820.87
Weekly	7.64%	7.28%	7.35%	10.89%	14.58%	14.35%	621.42	831.90	537.09	962.53
Monthly	16.29%	13.19%	14.88%	24.60%	30.36%	29.87%	530.73	974.06	391.76	1319.60
Quarterly	30.89%	26.38%	26.04%	52.42%	52.59%	51.74%	424.96	1216.50	251.17	2058.22
Annual	—	—	—	—	105.17%	103.48%	251.17	2058.22	87.74	5891.89
Option Time Horizon	—	—	—	—	39.70%	39.06%	483.42	1069.38	325.03	1590.51

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $719.00 | Strike (K): $720.00 (first OTM call ≥ spot) | Observed Mid-Price: $113.0000 (Bid $109.0000 / Ask $117.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 105.17% (CRR binomial tree, American, n=20 steps) | BS IV: 103.93% (European Black-Scholes) | Yahoo IV (Annual): 103.48% → 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 -0.19. Further, an Excess Kurtosis of 8.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.20%	20	0.75%	0.75%
-10.20% to -7.60%	26	0.97%	1.72%
-7.60% to -5.00%	74	2.76%	4.48%
-5.00% to -2.40%	296	11.05%	15.53%
-2.40% to 0.20%	954	35.61%	51.14%
0.20% to 2.80%	877	32.74%	83.87%
2.80% to 5.40%	294	10.97%	94.85%
5.40% to 8.00%	86	3.21%	98.06%
8.00% to 10.60%	33	1.23%	99.29%
Greater than 10.60%	19	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.26%	3.67%	79.40%	68.27%
±2σ	-6.73%	7.13%	94.74%	95.45%
±3σ	-10.20%	10.59%	98.54%	99.73%

Descriptive Statistics

Mean	0.200%
Standard Error	0.067%
Median	0.132%
Mode	0.000%
Standard Deviation	3.465%
Sample Variance	12.005%
Kurtosis	8.98
Skewness	-0.19
Range	56.543%
Minimum	-32.976%
Maximum	23.567%
Count	2679

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.474%	1393	52.00%	1.286%
Negative	-2.302%	1264	47.18%	-1.086%
Zero	0.000%	22	0.82%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	13.30%
20	1 Month	10.93%
60	1 Quarter	9.85%
250	1 Year	7.21%
750	3 Years	5.32%
1,250	5 Years	4.48%
2,500	10 Years	4.46%
5,000	20 Years	4.49%
12,500	50 Years	4.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.38. Further, an Excess Kurtosis of 21.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.85%	0	0.00%	0.00%
-3.85% to -1.83%	0	0.00%	0.00%
-1.83% to 0.20%	0	0.00%	0.00%
0.20% to 2.22%	370	13.81%	13.81%
2.22% to 4.25%	1350	50.37%	64.18%
4.25% to 6.28%	570	21.27%	85.45%
6.28% to 8.30%	214	7.99%	93.43%
8.30% to 10.33%	94	3.51%	96.94%
10.33% to 12.35%	37	1.38%	98.32%
Greater than 12.35%	45	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.55%	6.95%	86.83%	68.27%
±2σ	-1.15%	9.65%	96.08%	95.45%
±3σ	-3.85%	12.35%	98.32%	99.73%

Descriptive Statistics

Mean	4.249%
Standard Error	0.052%
Median	3.550%
Mode	2.276%
Standard Deviation	2.701%
Sample Variance	7.295%
Kurtosis	21.35
Skewness	3.38
Range	33.552%
Minimum	0.855%
Maximum	34.407%
Count	2680

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.249%	2680	100.00%	4.249%
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 0.63. Further, an Excess Kurtosis of 5.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.47%	15	0.56%	0.56%
-8.47% to -6.35%	20	0.75%	1.31%
-6.35% to -4.22%	86	3.21%	4.51%
-4.22% to -2.09%	363	13.54%	18.06%
-2.09% to 0.04%	902	33.66%	51.72%
0.04% to 2.16%	842	31.42%	83.13%
2.16% to 4.29%	303	11.31%	94.44%
4.29% to 6.42%	89	3.32%	97.76%
6.42% to 8.55%	34	1.27%	99.03%
Greater than 8.55%	26	0.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.80%	2.87%	77.31%	68.27%
±2σ	-5.64%	5.71%	94.89%	95.45%
±3σ	-8.48%	8.55%	98.47%	99.73%

Descriptive Statistics

Mean	0.036%
Standard Error	0.055%
Median	-0.043%
Mode	0.000%
Standard Deviation	2.837%
Sample Variance	8.047%
Kurtosis	5.33
Skewness	0.63
Range	37.319%
Minimum	-17.271%
Maximum	20.048%
Count	2680

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.095%	1306	48.73%	1.021%
Negative	-1.949%	1354	50.52%	-0.985%
Zero	0.000%	20	0.75%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.50. Further, an Excess Kurtosis of 2.92 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.01%	1	0.18%	0.18%
-22.01% to -16.27%	8	1.44%	1.62%
-16.27% to -10.54%	19	3.42%	5.04%
-10.54% to -4.81%	79	14.21%	19.24%
-4.81% to 0.92%	175	31.47%	50.72%
0.92% to 6.66%	172	30.94%	81.65%
6.66% to 12.39%	70	12.59%	94.24%
12.39% to 18.12%	20	3.60%	97.84%
18.12% to 23.86%	6	1.08%	98.92%
Greater than 23.86%	6	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.72%	8.57%	75.54%	68.27%
±2σ	-14.36%	16.21%	95.32%	95.45%
±3σ	-22.01%	23.86%	98.74%	99.73%

Descriptive Statistics

Mean	0.924%
Standard Error	0.324%
Median	0.849%
Mode	0.000%
Standard Deviation	7.644%
Sample Variance	58.423%
Kurtosis	2.92
Skewness	0.50
Range	66.043%
Minimum	-29.736%
Maximum	36.307%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.054%	302	54.32%	3.288%
Negative	-5.238%	251	45.14%	-2.365%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	25.50%
12	1 Quarter	24.11%
52	1 Year	17.76%
156	3 Years	13.16%
260	5 Years	10.89%
520	10 Years	10.63%
1,040	20 Years	10.65%
2,600	50 Years	10.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.59. Further, an Excess Kurtosis of 9.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.62%	0	0.00%	0.00%
-10.62% to -5.17%	0	0.00%	0.00%
-5.17% to 0.29%	0	0.00%	0.00%
0.29% to 5.75%	85	15.26%	15.26%
5.75% to 11.21%	258	46.32%	61.58%
11.21% to 16.68%	138	24.78%	86.36%
16.68% to 22.14%	41	7.36%	93.72%
22.14% to 27.59%	15	2.69%	96.41%
27.59% to 33.05%	6	1.08%	97.49%
Greater than 33.05%	14	2.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.93%	18.50%	86.89%	68.27%
±2σ	-3.35%	25.77%	95.69%	95.45%
±3σ	-10.62%	33.05%	97.49%	99.73%

Descriptive Statistics

Mean	11.215%
Standard Error	0.308%
Median	9.563%
Mode	4.811%
Standard Deviation	7.280%
Sample Variance	53.003%
Kurtosis	9.65
Skewness	2.59
Range	56.542%
Minimum	2.620%
Maximum	59.162%
Count	557

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.215%	557	100.00%	11.215%
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 0.59. Further, an Excess Kurtosis of 3.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.41%	2	0.36%	0.36%
-22.41% to -16.90%	8	1.44%	1.80%
-16.90% to -11.38%	14	2.51%	4.31%
-11.38% to -5.87%	83	14.90%	19.21%
-5.87% to -0.36%	189	33.93%	53.14%
-0.36% to 5.15%	154	27.65%	80.79%
5.15% to 10.66%	81	14.54%	95.33%
10.66% to 16.17%	14	2.51%	97.85%
16.17% to 21.68%	5	0.90%	98.74%
Greater than 21.68%	7	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.71%	6.98%	75.04%	68.27%
±2σ	-15.06%	14.33%	95.15%	95.45%
±3σ	-22.41%	21.68%	98.38%	99.73%

Descriptive Statistics

Mean	-0.363%
Standard Error	0.311%
Median	-0.947%
Mode	-9.664%
Standard Deviation	7.348%
Sample Variance	53.990%
Kurtosis	3.58
Skewness	0.59
Range	70.486%
Minimum	-27.739%
Maximum	42.747%
Count	557

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.661%	250	44.88%	2.541%
Negative	-5.268%	307	55.12%	-2.904%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.15. Further, an Excess Kurtosis of 3.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.84%	0	0.00%	0.00%
-44.84% to -32.63%	1	0.78%	0.78%
-32.63% to -20.41%	2	1.56%	2.34%
-20.41% to -8.19%	23	17.97%	20.31%
-8.19% to 4.03%	46	35.94%	56.25%
4.03% to 16.25%	31	24.22%	80.47%
16.25% to 28.46%	16	12.50%	92.97%
28.46% to 40.68%	7	5.47%	98.44%
40.68% to 52.90%	0	0.00%	98.44%
Greater than 52.90%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.26%	20.32%	74.22%	68.27%
±2σ	-28.55%	36.61%	96.88%	95.45%
±3σ	-44.85%	52.90%	98.44%	99.73%

Descriptive Statistics

Mean	4.028%
Standard Error	1.440%
Median	1.411%
Mode	-5.294%
Standard Deviation	16.291%
Sample Variance	265.405%
Kurtosis	3.45
Skewness	1.15
Range	113.571%
Minimum	-34.694%
Maximum	78.877%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.839%	70	54.69%	8.115%
Negative	-9.179%	57	44.53%	-4.088%
Zero	0.000%	1	0.78%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	52.88%
12	1 Year	42.38%
36	3 Years	30.44%
60	5 Years	24.60%
120	10 Years	23.78%
240	20 Years	23.84%
600	50 Years	23.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.67. Further, an Excess Kurtosis of 4.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.64%	0	0.00%	0.00%
-12.64% to -2.75%	0	0.00%	0.00%
-2.75% to 7.14%	0	0.00%	0.00%
7.14% to 17.03%	27	20.93%	20.93%
17.03% to 26.93%	52	40.31%	61.24%
26.93% to 36.82%	28	21.71%	82.95%
36.82% to 46.71%	12	9.30%	92.25%
46.71% to 56.60%	6	4.65%	96.90%
56.60% to 66.50%	2	1.55%	98.45%
Greater than 66.50%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.74%	40.12%	77.52%	68.27%
±2σ	0.55%	53.30%	95.35%	95.45%
±3σ	-12.64%	66.50%	98.45%	99.73%

Descriptive Statistics

Mean	26.925%
Standard Error	1.161%
Median	24.274%
Mode	7.298%
Standard Deviation	13.190%
Sample Variance	173.966%
Kurtosis	4.31
Skewness	1.67
Range	81.596%
Minimum	7.298%
Maximum	88.894%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.925%	129	100.00%	26.925%
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 0.38. Further, an Excess Kurtosis of 1.25 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.80%	0	0.00%	0.00%
-45.80% to -34.64%	2	1.55%	1.55%
-34.64% to -23.48%	5	3.88%	5.43%
-23.48% to -12.32%	25	19.38%	24.81%
-12.32% to -1.16%	31	24.03%	48.84%
-1.16% to 10.00%	40	31.01%	79.84%
10.00% to 21.16%	19	14.73%	94.57%
21.16% to 32.32%	4	3.10%	97.67%
32.32% to 43.48%	2	1.55%	99.22%
Greater than 43.48%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.04%	13.72%	73.64%	68.27%
±2σ	-30.92%	28.60%	96.12%	95.45%
±3σ	-45.80%	43.48%	99.22%	99.73%

Descriptive Statistics

Mean	-1.159%
Standard Error	1.310%
Median	-0.592%
Mode	-42.148%
Standard Deviation	14.881%
Sample Variance	221.458%
Kurtosis	1.25
Skewness	0.38
Range	97.695%
Minimum	-42.148%
Maximum	55.547%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.056%	61	47.29%	5.228%
Negative	-12.117%	68	52.71%	-6.387%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.08. Further, an Excess Kurtosis of 1.10 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.23%	0	0.00%	0.00%
-80.23% to -57.06%	0	0.00%	0.00%
-57.06% to -33.90%	0	0.00%	0.00%
-33.90% to -10.73%	10	23.26%	23.26%
-10.73% to 12.44%	14	32.56%	55.81%
12.44% to 35.61%	12	27.91%	83.72%
35.61% to 58.78%	3	6.98%	90.70%
58.78% to 81.95%	0	0.00%	90.70%
81.95% to 105.12%	4	9.30%	100.00%
Greater than 105.12%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.45%	43.34%	69.77%	68.27%
±2σ	-49.34%	74.23%	90.70%	95.45%
±3σ	-80.23%	105.12%	100.00%	99.73%

Descriptive Statistics

Mean	12.443%
Standard Error	4.711%
Median	10.648%
Mode	-30.590%
Standard Deviation	30.892%
Sample Variance	954.299%
Kurtosis	1.10
Skewness	1.08
Range	124.994%
Minimum	-30.590%
Maximum	94.404%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.998%	28	65.12%	18.231%
Negative	-16.594%	15	34.88%	-5.789%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	105.43%
12	3 Years	69.05%
20	5 Years	52.42%
40	10 Years	45.93%
80	20 Years	46.17%
200	50 Years	46.17%

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 2.10 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.03%	0	0.00%	0.00%
-25.03% to -5.24%	0	0.00%	0.00%
-5.24% to 14.55%	0	0.00%	0.00%
14.55% to 34.34%	13	29.55%	29.55%
34.34% to 54.12%	12	27.27%	56.82%
54.12% to 73.91%	11	25.00%	81.82%
73.91% to 93.70%	4	9.09%	90.91%
93.70% to 113.48%	3	6.82%	97.73%
113.48% to 133.27%	0	0.00%	97.73%
Greater than 133.27%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.74%	80.51%	75.00%	68.27%
±2σ	1.36%	106.89%	93.18%	95.45%
±3σ	-25.03%	133.27%	97.73%	99.73%

Descriptive Statistics

Mean	54.123%
Standard Error	3.977%
Median	50.840%
Mode	15.947%
Standard Deviation	26.383%
Sample Variance	696.054%
Kurtosis	2.10
Skewness	1.35
Range	127.267%
Minimum	15.947%
Maximum	143.214%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.123%	44	100.00%	54.123%
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 0.93. Further, an Excess Kurtosis of 2.20 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.93%	0	0.00%	0.00%
-81.93% to -62.40%	0	0.00%	0.00%
-62.40% to -42.87%	4	9.09%	9.09%
-42.87% to -23.33%	4	9.09%	18.18%
-23.33% to -3.80%	18	40.91%	59.09%
-3.80% to 15.73%	9	20.45%	79.55%
15.73% to 35.27%	7	15.91%	95.45%
35.27% to 54.80%	1	2.27%	97.73%
54.80% to 74.33%	0	0.00%	97.73%
Greater than 74.33%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.84%	22.24%	70.45%	68.27%
±2σ	-55.89%	48.29%	97.73%	95.45%
±3σ	-81.93%	74.33%	97.73%	99.73%

Descriptive Statistics

Mean	-3.800%
Standard Error	3.926%
Median	-8.959%
Mode	-48.482%
Standard Deviation	26.044%
Sample Variance	678.273%
Kurtosis	2.20
Skewness	0.93
Range	135.930%
Minimum	-48.482%
Maximum	87.448%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.434%	15	34.09%	8.330%
Negative	-18.403%	29	65.91%	-12.129%
Zero	0.000%	0	0.00%	0.000%

LITE Deep Analytical Report