BILL 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	4.62%	3.60%	3.63%	5.47%	4.48%	4.57%	35.56	38.90	34.00	40.68
周度	9.76%	10.67%	10.26%	12.93%	9.87%	10.07%	33.70	41.05	30.53	45.30
月度	19.70%	25.80%	20.17%	26.86%	20.54%	20.96%	30.28	45.67	24.66	56.09
季度	31.94%	38.44%	34.24%	47.45%	35.58%	36.30%	26.06	53.08	18.25	75.77
Annual	—	—	—	—	71.16%	72.61%	18.25	75.77	8.96	154.36
Option Time Horizon	—	—	—	—	27.12%	27.67%	28.36	48.77	21.62	63.97

Calculation Notes: Computed at 2026-04-26T02:49 UTC | Reference Contract: Call option expiring 2026-06-18 (53 days) | Spot 价格 (S): $37.19 | Strike (K): $40.00 (first OTM call ≥ spot) | Observed Mid-价格: $3.0250 (Bid $2.5500 / Ask $3.5000) | Risk-Free Rate (r): 3.69% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 71.16% (CRR binomial tree, American, n=20 steps) | BS IV: 71.97% (European Black-Scholes) | Yahoo IV (Annual): 72.61% → 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 0.83. Further, an Excess 峰度 of 12.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -13.74%	6	0.38%	0.38%
-13.74% to -10.28%	9	0.56%	0.94%
-10.28% to -6.82%	51	3.19%	4.13%
-6.82% to -3.35%	199	12.45%	16.58%
-3.35% to 0.11%	555	34.73%	51.31%
0.11% to 3.57%	533	33.35%	84.67%
3.57% to 7.03%	178	11.14%	95.81%
7.03% to 10.49%	37	2.32%	98.12%
10.49% to 13.95%	14	0.88%	99.00%
Greater than 13.95%	16	1.00%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.51%	4.72%	79.66%	68.27%
±2σ	-9.12%	9.34%	95.93%	95.45%
±3σ	-13.74%	13.95%	98.62%	99.73%

Descriptive Statistics

均值	0.108%
Standard Error	0.115%
中位数	0.010%
Mode	0.000%
Standard Deviation	4.615%
Sample Variance	21.294%
峰度	12.07
偏度	0.83
Range	72.680%
Minimum	-35.516%
Maximum	37.164%
Count	1598

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	3.172%	800	50.06%	1.588%
负向	-2.982%	793	49.62%	-1.480%
Zero	0.000%	5	0.31%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average 日度 True Range %
5	1 Week	4.38%
20	1 Month	4.99%
60	1 Quarter	6.01%
250	1 Year	4.36%
750	3 Years	4.55%
1,250	5 Years	5.47%
2,500	10 Years	5.81%
5,000	20 Years	5.81%
12,500	50 Years	5.81%

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 3.56. Further, an Excess 峰度 of 24.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -5.21%	0	0.00%	0.00%
-5.21% to -2.51%	0	0.00%	0.00%
-2.51% to 0.18%	0	0.00%	0.00%
0.18% to 2.88%	240	15.01%	15.01%
2.88% to 5.58%	754	47.15%	62.16%
5.58% to 8.28%	377	23.58%	85.74%
8.28% to 10.97%	130	8.13%	93.87%
10.97% to 13.67%	47	2.94%	96.81%
13.67% to 16.37%	25	1.56%	98.37%
Greater than 16.37%	26	1.63%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.98%	9.18%	86.80%	68.27%
±2σ	-1.61%	12.77%	96.44%	95.45%
±3σ	-5.21%	16.37%	98.37%	99.73%

Descriptive Statistics

均值	5.579%
Standard Error	0.090%
中位数	4.639%
Mode	2.442%
Standard Deviation	3.596%
Sample Variance	12.932%
峰度	24.80
偏度	3.56
Range	45.080%
Minimum	0.950%
Maximum	46.030%
Count	1599

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	5.579%	1599	100.00%	5.579%
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 -0.13. Further, an Excess 峰度 of 3.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -10.80%	14	0.88%	0.88%
-10.80% to -8.08%	13	0.81%	1.69%
-8.08% to -5.36%	49	3.06%	4.75%
-5.36% to -2.64%	222	13.88%	18.64%
-2.64% to 0.07%	513	32.08%	50.72%
0.07% to 2.79%	502	31.39%	82.11%
2.79% to 5.51%	183	11.44%	93.56%
5.51% to 8.23%	71	4.44%	98.00%
8.23% to 10.95%	22	1.38%	99.37%
Greater than 10.95%	10	0.63%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.55%	3.70%	76.05%	68.27%
±2σ	-7.18%	7.33%	95.18%	95.45%
±3σ	-10.80%	10.95%	98.50%	99.73%

Descriptive Statistics

均值	0.075%
Standard Error	0.091%
中位数	0.026%
Mode	-1.261%
Standard Deviation	3.626%
Sample Variance	13.148%
峰度	3.84
偏度	-0.13
Range	43.220%
Minimum	-22.948%
Maximum	20.272%
Count	1599

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	2.681%	806	50.41%	1.351%
负向	-2.579%	791	49.47%	-1.276%
Zero	0.000%	2	0.12%	0.000%

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a 偏度 factor of 0.35. Further, an Excess 峰度 of 3.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -28.78%	3	0.90%	0.90%
-28.78% to -21.47%	4	1.20%	2.11%
-21.47% to -14.15%	10	3.01%	5.12%
-14.15% to -6.83%	45	13.55%	18.67%
-6.83% to 0.48%	104	31.33%	50.00%
0.48% to 7.80%	109	32.83%	82.83%
7.80% to 15.11%	43	12.95%	95.78%
15.11% to 22.43%	8	2.41%	98.19%
22.43% to 29.75%	2	0.60%	98.80%
Greater than 29.75%	4	1.20%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.27%	10.24%	78.92%	68.27%
±2σ	-19.03%	19.99%	95.18%	95.45%
±3σ	-28.78%	29.75%	97.89%	99.73%

Descriptive Statistics

均值	0.482%
Standard Error	0.535%
中位数	0.495%
Mode	-6.571%
Standard Deviation	9.755%
Sample Variance	95.153%
峰度	3.97
偏度	0.35
Range	85.773%
Minimum	-38.600%
Maximum	47.173%
Count	332

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	7.089%	174	52.41%	3.715%
负向	-6.794%	158	47.59%	-3.233%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average 周度 True Range %
4	1 Month	10.87%
12	1 Quarter	13.63%
52	1 Year	10.23%
156	3 Years	10.93%
260	5 Years	12.93%
520	10 Years	13.75%
1,040	20 Years	13.75%
2,600	50 Years	13.75%

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 2.57. Further, an Excess 峰度 of 8.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -16.86%	0	0.00%	0.00%
-16.86% to -8.86%	0	0.00%	0.00%
-8.86% to -0.85%	0	0.00%	0.00%
-0.85% to 7.15%	45	13.51%	13.51%
7.15% to 15.15%	177	53.15%	66.67%
15.15% to 23.16%	67	20.12%	86.79%
23.16% to 31.16%	19	5.71%	92.49%
31.16% to 39.17%	11	3.30%	95.80%
39.17% to 47.17%	6	1.80%	97.60%
Greater than 47.17%	8	2.40%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.48%	25.83%	88.89%	68.27%
±2σ	-6.19%	36.50%	94.89%	95.45%
±3σ	-16.86%	47.17%	97.60%	99.73%

Descriptive Statistics

均值	15.154%
Standard Error	0.585%
中位数	11.674%
Mode	8.182%
Standard Deviation	10.673%
Sample Variance	113.916%
峰度	8.71
偏度	2.57
Range	71.151%
Minimum	3.252%
Maximum	74.403%
Count	333

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	15.154%	333	100.00%	15.154%
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 1.42. Further, an Excess 峰度 of 6.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -30.15%	1	0.30%	0.30%
-30.15% to -22.46%	2	0.60%	0.90%
-22.46% to -14.76%	6	1.80%	2.70%
-14.76% to -7.07%	48	14.41%	17.12%
-7.07% to 0.62%	128	38.44%	55.56%
0.62% to 8.32%	97	29.13%	84.68%
8.32% to 16.01%	33	9.91%	94.59%
16.01% to 23.71%	9	2.70%	97.30%
23.71% to 31.40%	4	1.20%	98.50%
Greater than 31.40%	5	1.50%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.63%	10.88%	79.28%	68.27%
±2σ	-19.89%	21.14%	95.50%	95.45%
±3σ	-30.15%	31.40%	98.20%	99.73%

Descriptive Statistics

均值	0.625%
Standard Error	0.562%
中位数	-0.397%
Mode	0.000%
Standard Deviation	10.259%
Sample Variance	105.245%
峰度	6.28
偏度	1.42
Range	92.932%
Minimum	-31.890%
Maximum	61.042%
Count	333

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	8.143%	157	47.15%	3.839%
负向	-6.187%	173	51.95%	-3.214%
Zero	0.000%	3	0.90%	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 0.67. Further, an Excess 峰度 of 1.71 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -57.29%	0	0.00%	0.00%
-57.29% to -42.51%	1	1.32%	1.32%
-42.51% to -27.74%	3	3.95%	5.26%
-27.74% to -12.96%	10	13.16%	18.42%
-12.96% to 1.81%	29	38.16%	56.58%
1.81% to 16.59%	19	25.00%	81.58%
16.59% to 31.36%	8	10.53%	92.11%
31.36% to 46.14%	4	5.26%	97.37%
46.14% to 60.91%	1	1.32%	98.68%
Greater than 60.91%	1	1.32%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.89%	21.51%	71.05%	68.27%
±2σ	-37.59%	41.21%	94.74%	95.45%
±3σ	-57.29%	60.91%	98.68%	99.73%

Descriptive Statistics

均值	1.811%
Standard Error	2.260%
中位数	-0.503%
Mode	-42.958%
Standard Deviation	19.700%
Sample Variance	388.086%
峰度	1.71
偏度	0.67
Range	115.151%
Minimum	-42.958%
Maximum	72.193%
Count	76

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	16.900%	37	48.68%	8.228%
负向	-12.504%	39	51.32%	-6.417%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average 月度 True Range %
3	1 Quarter	26.71%
12	1 Year	20.73%
36	3 Years	24.05%
60	5 Years	26.86%
120	10 Years	29.73%
240	20 Years	29.73%
600	50 Years	29.73%

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 2.68. Further, an Excess 峰度 of 9.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -40.93%	0	0.00%	0.00%
-40.93% to -21.58%	0	0.00%	0.00%
-21.58% to -2.23%	0	0.00%	0.00%
-2.23% to 17.13%	14	18.18%	18.18%
17.13% to 36.48%	37	48.05%	66.23%
36.48% to 55.83%	16	20.78%	87.01%
55.83% to 75.19%	4	5.19%	92.21%
75.19% to 94.54%	3	3.90%	96.10%
94.54% to 113.89%	1	1.30%	97.40%
Greater than 113.89%	2	2.60%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.68%	62.28%	89.61%	68.27%
±2σ	-15.13%	88.09%	94.81%	95.45%
±3σ	-40.93%	113.89%	97.40%	99.73%

Descriptive Statistics

均值	36.481%
Standard Error	2.941%
中位数	29.963%
Mode	12.416%
Standard Deviation	25.804%
Sample Variance	665.838%
峰度	9.29
偏度	2.68
Range	153.869%
Minimum	12.416%
Maximum	166.285%
Count	77

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	36.481%	77	100.00%	36.481%
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 Right Skewed (正向 Asymmetry) with a 偏度 factor of 0.92. Further, an Excess 峰度 of 2.12 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -58.86%	0	0.00%	0.00%
-58.86% to -43.73%	1	1.30%	1.30%
-43.73% to -28.59%	1	1.30%	2.60%
-28.59% to -13.46%	14	18.18%	20.78%
-13.46% to 1.67%	23	29.87%	50.65%
1.67% to 16.80%	25	32.47%	83.12%
16.80% to 31.93%	7	9.09%	92.21%
31.93% to 47.06%	4	5.19%	97.40%
47.06% to 62.19%	0	0.00%	97.40%
Greater than 62.19%	2	2.60%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.51%	21.84%	74.03%	68.27%
±2σ	-38.68%	42.01%	94.81%	95.45%
±3σ	-58.86%	62.19%	97.40%	99.73%

Descriptive Statistics

均值	1.666%
Standard Error	2.299%
中位数	0.439%
Mode	-45.441%
Standard Deviation	20.174%
Sample Variance	407.008%
峰度	2.12
偏度	0.92
Range	115.532%
Minimum	-45.441%
Maximum	70.091%
Count	77

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	15.730%	40	51.95%	8.171%
负向	-13.539%	37	48.05%	-6.506%
Zero	0.000%	0	0.00%	0.000%

收盘-to-收盘收益

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a 偏度 factor of 0.48. Further, an Excess 峰度 of -0.48 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -92.32%	0	0.00%	0.00%
-92.32% to -68.37%	0	0.00%	0.00%
-68.37% to -44.41%	1	4.00%	4.00%
-44.41% to -20.46%	4	16.00%	20.00%
-20.46% to 3.49%	9	36.00%	56.00%
3.49% to 27.44%	6	24.00%	80.00%
27.44% to 51.39%	2	8.00%	88.00%
51.39% to 75.34%	3	12.00%	100.00%
75.34% to 99.30%	0	0.00%	100.00%
Greater than 99.30%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.45%	35.42%	72.00%	68.27%
±2σ	-60.38%	67.36%	100.00%	95.45%
±3σ	-92.32%	99.30%	100.00%	99.73%

Descriptive Statistics

均值	3.489%
Standard Error	6.387%
中位数	-5.969%
Mode	-52.909%
Standard Deviation	31.936%
Sample Variance	1019.915%
峰度	-0.48
偏度	0.48
Range	118.725%
Minimum	-52.909%
Maximum	65.816%
Count	25

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	33.550%	11	44.00%	14.762%
负向	-20.130%	14	56.00%	-11.273%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average 季度 True Range %
4	1 Year	32.06%
12	3 Years	43.77%
20	5 Years	47.45%
40	10 Years	51.01%
80	20 Years	51.01%
200	50 Years	51.01%

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 1.51. Further, an Excess 峰度 of 2.02 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -44.55%	0	0.00%	0.00%
-44.55% to -15.73%	0	0.00%	0.00%
-15.73% to 13.10%	0	0.00%	0.00%
13.10% to 41.93%	4	15.38%	15.38%
41.93% to 70.75%	12	46.15%	61.54%
70.75% to 99.58%	7	26.92%	88.46%
99.58% to 128.41%	0	0.00%	88.46%
128.41% to 157.23%	1	3.85%	92.31%
157.23% to 186.06%	2	7.69%	100.00%
Greater than 186.06%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	32.32%	109.19%	84.62%	68.27%
±2σ	-6.12%	147.62%	92.31%	95.45%
±3σ	-44.55%	186.06%	100.00%	99.73%

Descriptive Statistics

均值	70.753%
Standard Error	7.538%
中位数	59.756%
Mode	19.494%
Standard Deviation	38.435%
Sample Variance	1477.213%
峰度	2.02
偏度	1.51
Range	152.086%
Minimum	19.494%
Maximum	171.580%
Count	26

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	70.753%	26	100.00%	70.753%
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 Right Skewed (正向 Asymmetry) with a 偏度 factor of 0.99. Further, an Excess 峰度 of 1.57 proves the distribution possesses Fat Tails (高er Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	频率	Prob	Cum. Prob
Less than -97.89%	0	0.00%	0.00%
-97.89% to -72.21%	0	0.00%	0.00%
-72.21% to -46.53%	0	0.00%	0.00%
-46.53% to -20.85%	6	23.08%	23.08%
-20.85% to 4.83%	7	26.92%	50.00%
4.83% to 30.50%	9	34.62%	84.62%
30.50% to 56.18%	3	11.54%	96.15%
56.18% to 81.86%	0	0.00%	96.15%
81.86% to 107.54%	1	3.85%	100.00%
Greater than 107.54%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	低er Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.41%	39.06%	73.08%	68.27%
±2σ	-63.65%	73.30%	96.15%	95.45%
±3σ	-97.89%	107.54%	100.00%	99.73%

Descriptive Statistics

均值	4.826%
Standard Error	6.715%
中位数	5.018%
Mode	-40.844%
Standard Deviation	34.239%
Sample Variance	1172.303%
峰度	1.57
偏度	0.99
Range	146.879%
Minimum	-40.844%
Maximum	106.035%
Count	26

频率 Breakdown

分类	Avg 收益	Count	概率	Freq Adj 收益
正向	29.547%	14	53.85%	15.910%
负向	-24.014%	12	46.15%	-11.083%
Zero	0.000%	0	0.00%	0.000%

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