TTWO - 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	3.21%	3.11%	2.89%	2.69%	—	2.76%	194.73	204.84	189.86	210.09
Weekly	6.77%	7.46%	6.69%	6.35%	—	6.07%	188.90	211.16	178.66	223.26
Monthly	13.94%	16.40%	14.72%	13.58%	—	12.63%	177.85	224.28	158.38	251.85
Quarterly	21.85%	30.74%	22.62%	22.93%	—	21.88%	163.38	244.15	133.65	298.46
Annual	—	—	—	—	—	43.75%	133.65	298.46	89.43	446.00
Option Time Horizon	—	—	—	—	—	14.30%	175.14	227.74	153.59	259.70

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $199.72 | Strike (K): $200.00 (first OTM call ≥ spot) | Observed Mid-Price: $10.7000 (Bid $10.0000 / Ask $11.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 0.00% (CRR binomial tree, American, n=20 steps) | BS IV: 40.17% (European Black-Scholes) | Yahoo IV (Annual): 43.75% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2008-09-25	$0.0010

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 22.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.54%	48	0.66%	0.66%
-9.54% to -7.13%	64	0.89%	1.55%
-7.13% to -4.72%	198	2.74%	4.29%
-4.72% to -2.31%	729	10.09%	14.39%
-2.31% to 0.11%	2742	37.97%	52.35%
0.11% to 2.52%	2403	33.27%	85.63%
2.52% to 4.93%	680	9.42%	95.04%
4.93% to 7.34%	211	2.92%	97.96%
7.34% to 9.75%	86	1.19%	99.16%
Greater than 9.75%	61	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.11%	3.32%	80.63%	68.27%
±2σ	-6.32%	6.54%	95.06%	95.45%
±3σ	-9.54%	9.75%	98.49%	99.73%

Descriptive Statistics

Mean	0.106%
Standard Error	0.038%
Median	0.000%
Mode	0.000%
Standard Deviation	3.215%
Sample Variance	10.336%
Kurtosis	22.06
Skewness	0.86
Range	86.258%
Minimum	-31.362%
Maximum	54.896%
Count	7222

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.204%	3572	49.46%	1.090%
Negative	-2.047%	3473	48.09%	-0.984%
Zero	0.000%	177	2.45%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.94%
20	1 Month	4.39%
60	1 Quarter	2.77%
250	1 Year	2.66%
750	3 Years	2.36%
1,250	5 Years	2.69%
2,500	10 Years	2.86%
5,000	20 Years	3.37%
12,500	50 Years	4.10%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.58. Further, an Excess Kurtosis of 49.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.31%	0	0.00%	0.00%
-5.31% to -2.98%	0	0.00%	0.00%
-2.98% to -0.65%	0	0.00%	0.00%
-0.65% to 1.68%	841	11.64%	11.64%
1.68% to 4.01%	3905	54.06%	65.71%
4.01% to 6.35%	1446	20.02%	85.73%
6.35% to 8.68%	548	7.59%	93.31%
8.68% to 11.01%	257	3.56%	96.87%
11.01% to 13.34%	120	1.66%	98.53%
Greater than 13.34%	106	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.91%	7.12%	88.27%	68.27%
±2σ	-2.20%	10.23%	95.85%	95.45%
±3σ	-5.31%	13.34%	98.53%	99.73%

Descriptive Statistics

Mean	4.015%
Standard Error	0.037%
Median	3.127%
Mode	5.000%
Standard Deviation	3.109%
Sample Variance	9.666%
Kurtosis	49.07
Skewness	4.58
Range	63.840%
Minimum	0.569%
Maximum	64.409%
Count	7223

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.015%	7223	100.00%	4.015%
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 0.77. Further, an Excess Kurtosis of 17.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.60%	39	0.54%	0.54%
-8.60% to -6.43%	87	1.20%	1.74%
-6.43% to -4.27%	242	3.35%	5.09%
-4.27% to -2.10%	731	10.12%	15.22%
-2.10% to 0.07%	2675	37.03%	52.25%
0.07% to 2.24%	2344	32.45%	84.70%
2.24% to 4.41%	730	10.11%	94.81%
4.41% to 6.58%	219	3.03%	97.84%
6.58% to 8.74%	92	1.27%	99.11%
Greater than 8.74%	64	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.82%	2.96%	79.65%	68.27%
±2σ	-5.71%	5.85%	94.75%	95.45%
±3σ	-8.60%	8.74%	98.57%	99.73%

Descriptive Statistics

Mean	0.071%
Standard Error	0.034%
Median	0.000%
Mode	0.000%
Standard Deviation	2.891%
Sample Variance	8.357%
Kurtosis	17.06
Skewness	0.77
Range	75.644%
Minimum	-28.016%
Maximum	47.628%
Count	7223

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.037%	3524	48.79%	0.994%
Negative	-1.895%	3518	48.71%	-0.923%
Zero	0.000%	181	2.51%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 10.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.82%	8	0.53%	0.53%
-19.82% to -14.74%	18	1.20%	1.73%
-14.74% to -9.67%	47	3.13%	4.86%
-9.67% to -4.59%	167	11.11%	15.97%
-4.59% to 0.48%	523	34.80%	50.77%
0.48% to 5.56%	507	33.73%	84.50%
5.56% to 10.64%	155	10.31%	94.81%
10.64% to 15.71%	50	3.33%	98.14%
15.71% to 20.79%	15	1.00%	99.14%
Greater than 20.79%	13	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.28%	7.25%	79.31%	68.27%
±2σ	-13.05%	14.02%	95.01%	95.45%
±3σ	-19.82%	20.79%	98.60%	99.73%

Descriptive Statistics

Mean	0.485%
Standard Error	0.175%
Median	0.332%
Mode	0.000%
Standard Deviation	6.768%
Sample Variance	45.807%
Kurtosis	10.53
Skewness	0.86
Range	102.220%
Minimum	-32.353%
Maximum	69.867%
Count	1503

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.788%	800	53.23%	2.549%
Negative	-4.501%	689	45.84%	-2.063%
Zero	0.000%	14	0.93%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.03%
12	1 Quarter	6.85%
52	1 Year	6.14%
156	3 Years	5.54%
260	5 Years	6.35%
520	10 Years	6.54%
1,040	20 Years	7.81%
2,600	50 Years	9.40%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.96. Further, an Excess Kurtosis of 14.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.41%	0	0.00%	0.00%
-12.41% to -6.82%	0	0.00%	0.00%
-6.82% to -1.23%	0	0.00%	0.00%
-1.23% to 4.37%	217	14.43%	14.43%
4.37% to 9.96%	757	50.33%	64.76%
9.96% to 15.55%	301	20.01%	84.77%
15.55% to 21.14%	121	8.05%	92.82%
21.14% to 26.73%	68	4.52%	97.34%
26.73% to 32.32%	10	0.66%	98.01%
Greater than 32.32%	30	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.50%	17.41%	87.17%	68.27%
±2σ	-4.95%	24.87%	96.34%	95.45%
±3σ	-12.41%	32.32%	98.01%	99.73%

Descriptive Statistics

Mean	9.956%
Standard Error	0.192%
Median	7.690%
Mode	5.000%
Standard Deviation	7.455%
Sample Variance	55.581%
Kurtosis	14.51
Skewness	2.96
Range	71.951%
Minimum	1.571%
Maximum	73.522%
Count	1504

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.956%	1504	100.00%	9.956%
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 0.97. Further, an Excess Kurtosis of 7.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.05%	6	0.40%	0.40%
-20.05% to -15.03%	14	0.93%	1.33%
-15.03% to -10.02%	52	3.46%	4.79%
-10.02% to -5.00%	169	11.24%	16.02%
-5.00% to 0.02%	558	37.10%	53.12%
0.02% to 5.04%	479	31.85%	84.97%
5.04% to 10.05%	146	9.71%	94.68%
10.05% to 15.07%	44	2.93%	97.61%
15.07% to 20.09%	17	1.13%	98.74%
Greater than 20.09%	19	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.67%	6.71%	78.66%	68.27%
±2σ	-13.36%	13.40%	94.88%	95.45%
±3σ	-20.05%	20.09%	98.34%	99.73%

Descriptive Statistics

Mean	0.019%
Standard Error	0.173%
Median	-0.320%
Mode	0.000%
Standard Deviation	6.690%
Sample Variance	44.758%
Kurtosis	7.40
Skewness	0.97
Range	87.268%
Minimum	-40.721%
Maximum	46.547%
Count	1504

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.834%	705	46.88%	2.266%
Negative	-4.300%	786	52.26%	-2.247%
Zero	0.000%	13	0.86%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.10. Further, an Excess Kurtosis of 8.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.81%	1	0.29%	0.29%
-39.81% to -29.36%	3	0.87%	1.16%
-29.36% to -18.91%	13	3.76%	4.91%
-18.91% to -8.45%	41	11.85%	16.76%
-8.45% to 2.00%	123	35.55%	52.31%
2.00% to 12.45%	108	31.21%	83.53%
12.45% to 22.90%	40	11.56%	95.09%
22.90% to 33.35%	10	2.89%	97.98%
33.35% to 43.81%	3	0.87%	98.84%
Greater than 43.81%	4	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.94%	15.93%	79.77%	68.27%
±2σ	-25.87%	29.87%	96.24%	95.45%
±3σ	-39.81%	43.81%	98.55%	99.73%

Descriptive Statistics

Mean	1.998%
Standard Error	0.749%
Median	1.310%
Mode	-7.662%
Standard Deviation	13.936%
Sample Variance	194.208%
Kurtosis	8.24
Skewness	1.10
Range	154.440%
Minimum	-57.410%
Maximum	97.030%
Count	346

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.466%	194	56.07%	5.868%
Negative	-8.868%	151	43.64%	-3.870%
Zero	0.000%	1	0.29%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	14.79%
12	1 Year	12.63%
36	3 Years	12.09%
60	5 Years	13.58%
120	10 Years	13.99%
240	20 Years	16.94%
600	50 Years	20.20%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.82. Further, an Excess Kurtosis of 12.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.03%	0	0.00%	0.00%
-26.03% to -13.73%	0	0.00%	0.00%
-13.73% to -1.42%	0	0.00%	0.00%
-1.42% to 10.88%	56	16.14%	16.14%
10.88% to 23.18%	167	48.13%	64.27%
23.18% to 35.48%	75	21.61%	85.88%
35.48% to 47.79%	24	6.92%	92.80%
47.79% to 60.09%	12	3.46%	96.25%
60.09% to 72.39%	8	2.31%	98.56%
Greater than 72.39%	5	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.78%	39.59%	88.18%	68.27%
±2σ	-9.63%	55.99%	95.68%	95.45%
±3σ	-26.03%	72.39%	98.56%	99.73%

Descriptive Statistics

Mean	23.182%
Standard Error	0.881%
Median	18.538%
Mode	32.000%
Standard Deviation	16.404%
Sample Variance	269.092%
Kurtosis	12.85
Skewness	2.82
Range	136.822%
Minimum	5.423%
Maximum	142.245%
Count	347

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.182%	347	100.00%	23.182%
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 2.42. Further, an Excess Kurtosis of 18.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.43%	1	0.29%	0.29%
-44.43% to -33.39%	1	0.29%	0.58%
-33.39% to -22.35%	8	2.31%	2.88%
-22.35% to -11.31%	53	15.27%	18.16%
-11.31% to -0.27%	130	37.46%	55.62%
-0.27% to 10.78%	102	29.39%	85.01%
10.78% to 21.82%	33	9.51%	94.52%
21.82% to 32.86%	13	3.75%	98.27%
32.86% to 43.90%	2	0.58%	98.85%
Greater than 43.90%	4	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.99%	14.46%	81.84%	68.27%
±2σ	-29.71%	29.18%	96.25%	95.45%
±3σ	-44.43%	43.90%	98.56%	99.73%

Descriptive Statistics

Mean	-0.265%
Standard Error	0.790%
Median	-1.508%
Mode	-49.103%
Standard Deviation	14.723%
Sample Variance	216.776%
Kurtosis	18.52
Skewness	2.42
Range	179.089%
Minimum	-49.103%
Maximum	129.986%
Count	347

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.041%	151	43.52%	4.805%
Negative	-9.021%	195	56.20%	-5.069%
Zero	0.000%	1	0.29%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.55. Further, an Excess Kurtosis of 2.39 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.08%	0	0.00%	0.00%
-60.08% to -43.69%	1	0.86%	0.86%
-43.69% to -27.30%	5	4.31%	5.17%
-27.30% to -10.91%	21	18.10%	23.28%
-10.91% to 5.48%	29	25.00%	48.28%
5.48% to 21.87%	35	30.17%	78.45%
21.87% to 38.26%	20	17.24%	95.69%
38.26% to 54.65%	3	2.59%	98.28%
54.65% to 71.04%	1	0.86%	99.14%
Greater than 71.04%	1	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.38%	27.33%	71.55%	68.27%
±2σ	-38.23%	49.19%	96.55%	95.45%
±3σ	-60.08%	71.04%	99.14%	99.73%

Descriptive Statistics

Mean	5.479%
Standard Error	2.029%
Median	6.220%
Mode	-47.979%
Standard Deviation	21.854%
Sample Variance	477.591%
Kurtosis	2.39
Skewness	0.55
Range	148.941%
Minimum	-47.979%
Maximum	100.962%
Count	116

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.695%	71	61.21%	11.443%
Negative	-15.373%	45	38.79%	-5.964%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.30%
12	3 Years	20.95%
20	5 Years	22.93%
40	10 Years	24.57%
80	20 Years	29.60%
200	50 Years	34.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.99. Further, an Excess Kurtosis of 13.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.75%	0	0.00%	0.00%
-48.75% to -25.69%	0	0.00%	0.00%
-25.69% to -2.63%	0	0.00%	0.00%
-2.63% to 20.42%	15	12.82%	12.82%
20.42% to 43.48%	64	54.70%	67.52%
43.48% to 66.54%	20	17.09%	84.62%
66.54% to 89.60%	10	8.55%	93.16%
89.60% to 112.65%	4	3.42%	96.58%
112.65% to 135.71%	1	0.85%	97.44%
Greater than 135.71%	3	2.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.74%	74.22%	88.03%	68.27%
±2σ	-18.00%	104.97%	95.73%	95.45%
±3σ	-48.75%	135.71%	97.44%	99.73%

Descriptive Statistics

Mean	43.481%
Standard Error	2.842%
Median	33.112%
Mode	15.220%
Standard Deviation	30.743%
Sample Variance	945.142%
Kurtosis	13.49
Skewness	2.99
Range	220.494%
Minimum	15.220%
Maximum	235.714%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.481%	117	100.00%	43.481%
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 1.23. Further, an Excess Kurtosis of 2.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.17%	0	0.00%	0.00%
-69.17% to -52.20%	0	0.00%	0.00%
-52.20% to -35.23%	3	2.56%	2.56%
-35.23% to -18.26%	23	19.66%	22.22%
-18.26% to -1.29%	46	39.32%	61.54%
-1.29% to 15.68%	23	19.66%	81.20%
15.68% to 32.65%	14	11.97%	93.16%
32.65% to 49.62%	4	3.42%	96.58%
49.62% to 66.58%	2	1.71%	98.29%
Greater than 66.58%	2	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.92%	21.33%	78.63%	68.27%
±2σ	-46.54%	43.96%	95.73%	95.45%
±3σ	-69.17%	66.58%	98.29%	99.73%

Descriptive Statistics

Mean	-1.291%
Standard Error	2.092%
Median	-5.520%
Mode	-50.957%
Standard Deviation	22.625%
Sample Variance	511.912%
Kurtosis	2.73
Skewness	1.23
Range	144.296%
Minimum	-50.957%
Maximum	93.339%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.206%	42	35.90%	7.971%
Negative	-14.449%	75	64.10%	-9.262%
Zero	0.000%	0	0.00%	0.000%

TTWO Deep Analytical Report