TWLO 资产分析 - DOR 信号与波动率

Quick 总览

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 低er (68.27%)	1σ Upper	2σ 低er (95.45%)	2σ Upper
日度	3.79%	2.55%	3.04%	4.64%	4.05%	4.09%	138.08	149.73	132.60	155.93
周度	8.81%	8.45%	8.99%	11.11%	8.92%	9.00%	131.52	157.20	120.30	171.87
月度	17.19%	17.52%	17.82%	23.29%	18.56%	18.74%	119.43	173.12	99.19	208.44
季度	36.27%	28.81%	29.86%	42.76%	32.15%	32.46%	104.25	198.32	75.59	273.54
Annual	—	—	—	—	64.31%	64.92%	75.59	273.54	39.73	520.37
Option Time Horizon	—	—	—	—	24.51%	24.74%	112.54	183.72	88.08	234.74

Calculation Notes: Computed at 2026-04-26T02:49 UTC | Reference Contract: Call option expiring 2026-06-18 (53 days) | Spot 价格 (S): $143.79 | Strike (K): $145.00 (first OTM call ≥ spot) | Observed Mid-价格: $13.7500 (Bid $13.4000 / Ask $14.1000) | Risk-Free Rate (r): 3.69% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 64.31% (CRR binomial tree, American, n=20 steps) | BS IV: 63.96% (European Black-Scholes) | Yahoo IV (Annual): 64.92% → period-scaled as σ_period = σ_annual·√h | 价格 bands: Upper = S·e^+σ√h, 低er = S·e^−σ√h

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Right Skewed (正向 Asymmetry) with a 偏度 factor of 0.60. Further, an Excess 峰度 of 14.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -11.23%	10	0.40%	0.40%
-11.23% to -8.39%	21	0.85%	1.25%
-8.39% to -5.55%	100	4.05%	5.30%
-5.55% to -2.71%	278	11.25%	16.55%
-2.71% to 0.14%	820	33.17%	49.72%
0.14% to 2.98%	862	34.87%	84.59%
2.98% to 5.82%	265	10.72%	95.31%
5.82% to 8.66%	71	2.87%	98.18%
8.66% to 11.51%	24	0.97%	99.15%
Greater than 11.51%	21	0.85%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.65%	3.93%	78.68%	68.27%
±2σ	-7.44%	7.72%	95.75%	95.45%
±3σ	-11.23%	11.51%	98.75%	99.73%

Descriptive Statistics

均值	0.137%
Standard Error	0.076%
中位数	0.150%
Mode	0.000%
Standard Deviation	3.790%
Sample Variance	14.367%
峰度	14.12
偏度	0.60
Range	74.224%
Minimum	-34.608%
Maximum	39.616%
Count	2472

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	2.582%	1290	52.18%	1.347%
负向	-2.543%	1177	47.61%	-1.211%
Zero	0.000%	5	0.20%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average 日度 True Range %
5	1 Week	5.22%
20	1 Month	5.42%
60	1 Quarter	5.26%
250	1 Year	4.18%
750	3 Years	3.86%
1,250	5 Years	4.64%
2,500	10 Years	4.81%
5,000	20 Years	4.81%
12,500	50 Years	4.81%

高-to-低收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.92. Further, an Excess 峰度 of 6.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -3.04%	0	0.00%	0.00%
-3.04% to -1.13%	0	0.00%	0.00%
-1.13% to 0.78%	0	0.00%	0.00%
0.78% to 2.69%	525	21.23%	21.23%
2.69% to 4.60%	998	40.36%	61.59%
4.60% to 6.51%	533	21.55%	83.14%
6.51% to 8.41%	227	9.18%	92.32%
8.41% to 10.32%	96	3.88%	96.20%
10.32% to 12.23%	55	2.22%	98.42%
Greater than 12.23%	39	1.58%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.05%	7.14%	78.37%	68.27%
±2σ	-0.50%	9.69%	95.19%	95.45%
±3σ	-3.04%	12.23%	98.42%	99.73%

Descriptive Statistics

均值	4.596%
Standard Error	0.051%
中位数	3.949%
Mode	4.394%
Standard Deviation	2.546%
Sample Variance	6.480%
峰度	6.34
偏度	1.92
Range	24.307%
Minimum	0.841%
Maximum	25.148%
Count	2473

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	4.596%	2473	100.00%	4.596%
负向	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

开盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a 偏度 factor of 0.07. Further, an Excess 峰度 of 2.22 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -9.09%	16	0.65%	0.65%
-9.09% to -6.81%	26	1.05%	1.70%
-6.81% to -4.53%	82	3.32%	5.01%
-4.53% to -2.24%	340	13.75%	18.76%
-2.24% to 0.04%	806	32.59%	51.35%
0.04% to 2.32%	754	30.49%	81.84%
2.32% to 4.60%	282	11.40%	93.25%
4.60% to 6.88%	109	4.41%	97.65%
6.88% to 9.16%	40	1.62%	99.27%
Greater than 9.16%	18	0.73%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.00%	3.08%	74.24%	68.27%
±2σ	-6.05%	6.12%	94.74%	95.45%
±3σ	-9.09%	9.16%	98.63%	99.73%

Descriptive Statistics

均值	0.038%
Standard Error	0.061%
中位数	-0.051%
Mode	0.000%
Standard Deviation	3.042%
Sample Variance	9.252%
峰度	2.22
偏度	0.07
Range	32.407%
Minimum	-16.672%
Maximum	15.735%
Count	2473

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	2.309%	1215	49.13%	1.134%
负向	-2.168%	1251	50.59%	-1.097%
Zero	0.000%	7	0.28%	0.000%

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Right Skewed (正向 Asymmetry) with a 偏度 factor of 0.68. Further, an Excess 峰度 of 6.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -25.74%	3	0.58%	0.58%
-25.74% to -19.13%	4	0.78%	1.36%
-19.13% to -12.52%	25	4.87%	6.24%
-12.52% to -5.91%	56	10.92%	17.15%
-5.91% to 0.71%	174	33.92%	51.07%
0.71% to 7.32%	161	31.38%	82.46%
7.32% to 13.93%	62	12.09%	94.54%
13.93% to 20.54%	19	3.70%	98.25%
20.54% to 27.15%	6	1.17%	99.42%
Greater than 27.15%	3	0.58%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.11%	9.52%	76.22%	68.27%
±2σ	-16.92%	18.34%	95.71%	95.45%
±3σ	-25.74%	27.15%	98.83%	99.73%

Descriptive Statistics

均值	0.706%
Standard Error	0.389%
中位数	0.551%
Mode	-7.307%
Standard Deviation	8.815%
Sample Variance	77.710%
峰度	6.82
偏度	0.68
Range	103.354%
Minimum	-38.577%
Maximum	64.777%
Count	513

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	6.265%	280	54.58%	3.419%
负向	-5.974%	233	45.42%	-2.713%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average 周度 True Range %
4	1 Month	15.39%
12	1 Quarter	11.80%
52	1 Year	10.10%
156	3 Years	9.41%
260	5 Years	11.11%
520	10 Years	11.59%
1,040	20 Years	11.59%
2,600	50 Years	11.59%

高-to-低收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 3.44. Further, an Excess 峰度 of 21.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -12.93%	0	0.00%	0.00%
-12.93% to -6.59%	0	0.00%	0.00%
-6.59% to -0.25%	0	0.00%	0.00%
-0.25% to 6.09%	76	14.79%	14.79%
6.09% to 12.43%	254	49.42%	64.20%
12.43% to 18.77%	104	20.23%	84.44%
18.77% to 25.10%	50	9.73%	94.16%
25.10% to 31.44%	19	3.70%	97.86%
31.44% to 37.78%	3	0.58%	98.44%
Greater than 37.78%	8	1.56%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.98%	20.88%	85.99%	68.27%
±2σ	-4.48%	29.33%	96.69%	95.45%
±3σ	-12.93%	37.78%	98.44%	99.73%

Descriptive Statistics

均值	12.427%
Standard Error	0.373%
中位数	10.193%
Mode	4.509%
Standard Deviation	8.451%
Sample Variance	71.412%
峰度	21.84
偏度	3.44
Range	90.470%
Minimum	2.506%
Maximum	92.976%
Count	514

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	12.427%	514	100.00%	12.427%
负向	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

开盘-to-收盘收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.40. Further, an Excess 峰度 of 8.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -26.72%	1	0.19%	0.19%
-26.72% to -19.98%	2	0.39%	0.58%
-19.98% to -13.24%	17	3.31%	3.89%
-13.24% to -6.50%	65	12.65%	16.54%
-6.50% to 0.24%	198	38.52%	55.06%
0.24% to 6.98%	149	28.99%	84.05%
6.98% to 13.72%	48	9.34%	93.39%
13.72% to 20.46%	24	4.67%	98.05%
20.46% to 27.20%	5	0.97%	99.03%
Greater than 27.20%	5	0.97%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.75%	9.23%	77.82%	68.27%
±2σ	-17.74%	18.22%	94.94%	95.45%
±3σ	-26.72%	27.20%	98.83%	99.73%

Descriptive Statistics

均值	0.240%
Standard Error	0.396%
中位数	-0.374%
Mode	-3.875%
Standard Deviation	8.988%
Sample Variance	80.784%
峰度	8.57
偏度	1.40
Range	106.854%
Minimum	-38.224%
Maximum	68.630%
Count	514

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	6.674%	245	47.66%	3.181%
负向	-5.640%	268	52.14%	-2.941%
Zero	0.000%	1	0.20%	0.000%

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Right Skewed (正向 Asymmetry) with a 偏度 factor of 0.60. Further, an Excess 峰度 of 2.26 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -48.99%	0	0.00%	0.00%
-48.99% to -36.10%	1	0.85%	0.85%
-36.10% to -23.21%	3	2.54%	3.39%
-23.21% to -10.31%	20	16.95%	20.34%
-10.31% to 2.58%	37	31.36%	51.69%
2.58% to 15.48%	35	29.66%	81.36%
15.48% to 28.37%	14	11.86%	93.22%
28.37% to 41.26%	7	5.93%	99.15%
41.26% to 54.16%	0	0.00%	99.15%
Greater than 54.16%	1	0.85%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.61%	19.77%	68.64%	68.27%
±2σ	-31.80%	36.97%	95.76%	95.45%
±3σ	-48.99%	54.16%	99.15%	99.73%

Descriptive Statistics

均值	2.582%
Standard Error	1.583%
中位数	1.564%
Mode	-46.986%
Standard Deviation	17.192%
Sample Variance	295.574%
峰度	2.26
偏度	0.60
Range	122.943%
Minimum	-46.986%
Maximum	75.957%
Count	118

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	14.477%	63	53.39%	7.729%
负向	-11.043%	55	46.61%	-5.147%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average 月度 True Range %
3	1 Quarter	19.35%
12	1 Year	20.77%
36	3 Years	20.47%
60	5 Years	23.29%
120	10 Years	24.80%
240	20 Years	24.80%
600	50 Years	24.80%

高-to-低收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.88. Further, an Excess 峰度 of 4.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -23.20%	0	0.00%	0.00%
-23.20% to -10.05%	0	0.00%	0.00%
-10.05% to 3.09%	0	0.00%	0.00%
3.09% to 16.23%	24	20.17%	20.17%
16.23% to 29.37%	51	42.86%	63.03%
29.37% to 42.51%	26	21.85%	84.87%
42.51% to 55.66%	10	8.40%	93.28%
55.66% to 68.80%	3	2.52%	95.80%
68.80% to 81.94%	2	1.68%	97.48%
Greater than 81.94%	3	2.52%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.85%	46.89%	81.51%	68.27%
±2σ	-5.67%	64.42%	94.96%	95.45%
±3σ	-23.20%	81.94%	97.48%	99.73%

Descriptive Statistics

均值	29.372%
Standard Error	1.606%
中位数	24.701%
Mode	9.172%
Standard Deviation	17.523%
Sample Variance	307.073%
峰度	4.35
偏度	1.88
Range	88.443%
Minimum	9.172%
Maximum	97.615%
Count	119

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	29.372%	119	100.00%	29.372%
负向	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

开盘-to-收盘收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.10. Further, an Excess 峰度 of 3.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -53.18%	0	0.00%	0.00%
-53.18% to -39.82%	1	0.84%	0.84%
-39.82% to -26.46%	2	1.68%	2.52%
-26.46% to -13.09%	21	17.65%	20.17%
-13.09% to 0.27%	41	34.45%	54.62%
0.27% to 13.63%	33	27.73%	82.35%
13.63% to 26.99%	14	11.76%	94.12%
26.99% to 40.35%	4	3.36%	97.48%
40.35% to 53.72%	1	0.84%	98.32%
Greater than 53.72%	2	1.68%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.55%	18.08%	71.43%	68.27%
±2σ	-35.36%	35.90%	95.80%	95.45%
±3σ	-53.18%	53.72%	98.32%	99.73%

Descriptive Statistics

均值	0.268%
Standard Error	1.633%
中位数	-1.634%
Mode	-44.641%
Standard Deviation	17.816%
Sample Variance	317.406%
峰度	3.93
偏度	1.10
Range	127.818%
Minimum	-44.641%
Maximum	83.177%
Count	119

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	14.208%	55	46.22%	6.567%
负向	-11.712%	64	53.78%	-6.299%
Zero	0.000%	0	0.00%	0.000%

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.66. Further, an Excess 峰度 of 4.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -100.53%	0	0.00%	0.00%
-100.53% to -73.33%	0	0.00%	0.00%
-73.33% to -46.13%	0	0.00%	0.00%
-46.13% to -18.94%	8	20.51%	20.51%
-18.94% to 8.26%	15	38.46%	58.97%
8.26% to 35.46%	9	23.08%	82.05%
35.46% to 62.66%	5	12.82%	94.87%
62.66% to 89.86%	1	2.56%	97.44%
89.86% to 117.06%	0	0.00%	97.44%
Greater than 117.06%	1	2.56%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.00%	44.53%	79.49%	68.27%
±2σ	-64.27%	80.80%	94.87%	95.45%
±3σ	-100.53%	117.06%	97.44%	99.73%

Descriptive Statistics

均值	8.264%
Standard Error	5.807%
中位数	1.436%
Mode	-45.750%
Standard Deviation	36.266%
Sample Variance	1315.242%
峰度	4.50
偏度	1.66
Range	192.785%
Minimum	-45.750%
Maximum	147.035%
Count	39

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	32.001%	21	53.85%	17.231%
负向	-19.428%	18	46.15%	-8.967%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average 季度 True Range %
4	1 Year	34.97%
12	3 Years	41.69%
20	5 Years	42.76%
40	10 Years	46.67%
80	20 Years	46.67%
200	50 Years	46.67%

高-to-低收益

Gram-Charlier Analysis: Data reveals 高ly Right Skewed (Extreme 正向 Tail Risk) with a 偏度 factor of 1.41. Further, an Excess 峰度 of 2.68 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -26.89%	0	0.00%	0.00%
-26.89% to -5.28%	0	0.00%	0.00%
-5.28% to 16.33%	0	0.00%	0.00%
16.33% to 37.94%	9	22.50%	22.50%
37.94% to 59.55%	20	50.00%	72.50%
59.55% to 81.15%	1	2.50%	75.00%
81.15% to 102.76%	7	17.50%	92.50%
102.76% to 124.37%	2	5.00%	97.50%
124.37% to 145.97%	0	0.00%	97.50%
Greater than 145.97%	1	2.50%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	30.74%	88.36%	67.50%	68.27%
±2σ	1.93%	117.16%	97.50%	95.45%
±3σ	-26.88%	145.97%	97.50%	99.73%

Descriptive Statistics

均值	59.545%
Standard Error	4.555%
中位数	55.043%
Mode	21.710%
Standard Deviation	28.810%
Sample Variance	829.997%
峰度	2.68
偏度	1.41
Range	139.423%
Minimum	21.710%
Maximum	161.133%
Count	40

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	59.545%	40	100.00%	59.545%
负向	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

开盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a 偏度 factor of 0.41. Further, an Excess 峰度 of 0.39 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -89.17%	0	0.00%	0.00%
-89.17% to -66.77%	0	0.00%	0.00%
-66.77% to -44.38%	2	5.00%	5.00%
-44.38% to -21.98%	10	25.00%	30.00%
-21.98% to 0.41%	8	20.00%	50.00%
0.41% to 22.81%	12	30.00%	80.00%
22.81% to 45.21%	6	15.00%	95.00%
45.21% to 67.60%	1	2.50%	97.50%
67.60% to 90.00%	1	2.50%	100.00%
Greater than 90.00%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.45%	30.28%	75.00%	68.27%
±2σ	-59.31%	60.14%	95.00%	95.45%
±3σ	-89.17%	90.00%	100.00%	99.73%

Descriptive Statistics

均值	0.415%
Standard Error	4.721%
中位数	0.181%
Mode	-60.569%
Standard Deviation	29.861%
Sample Variance	891.659%
峰度	0.39
偏度	0.41
Range	146.788%
Minimum	-60.569%
Maximum	86.219%
Count	40

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	24.451%	20	50.00%	12.226%
负向	-23.621%	20	50.00%	-11.810%
Zero	0.000%	0	0.00%	0.000%

TWLO 深度分析报告