<no title>

[1]:

## 因子计算分析

import datetime

from tqsdk import TqApi, TqAuth
from tqsdk.tafunc import get_t, get_bs_price

import numpy as np
import pandas as pd
import plotly.express as px

pd.options.display.max_rows= None
pd.options.display.max_columns = None
pd.options.display.width = 0
pd.options.display.float_format = '{:.6f}'.format

在使用天勤量化之前，默认您已经知晓并同意以下免责条款，如果不同意请立即停止使用：https://www.shinnytech.com/blog/disclaimer/

[2]:

# 标准 BS 定价模型假设波动律为常量, 但是波动率实际和时间相关, 这里扩展 BS 定价模型引入时间相关波动率并与标准模型进行对比
api = TqApi(auth=TqAuth('快期账户', '快期密码'))
quote = api.get_quote('CFFEX.IO2405-C-3550')
underlying = quote.underlying_symbol
exp = datetime.datetime.fromtimestamp(quote.expire_datetime)

2024-06-26 16:40:45 -     INFO - 通知 : 与 wss://api.shinnytech.com/t/nfmd/front/mobile 的网络连接已建立

[3]:

# 获取沪深300指数过去一年的5分钟现数据，用来分析波动率
csi = api.get_kline_data_series(symbol=underlying, duration_seconds=300, start_dt=exp-datetime.timedelta(days=365), end_dt=exp)
# 将 unix time 转换成 pandas.Datetime 并获得周几及时间信息
csi["dt"] = pd.to_datetime(csi["datetime"], utc=True).dt.tz_convert('Asia/Shanghai')
csi["time"] = csi["dt"].dt.time
csi["week"] = csi["dt"].dt.weekday+1
# p 为每五分钟的波动率, 不计算跨交易时段的波动, 用来分析波动率的周期性
csi["p"] = np.log(csi["close"]/csi["open"])

[4]:

# 可以看到周一到周五的波动率有显著性的差异
px.bar(csi.groupby("week").std(numeric_only=True), y="p")

[5]:

# 每天不同时间段的波动率也有显著性的差异
# 早上及下午开盘的波动率显著偏高
# 注意这里的波动率是收盘价对比开盘价, 而不是收盘价对比上个收盘价, 因此 9:30 开盘的高波动率只包含集合竞价之后的价格波动, 不包含相对昨天收盘的波动
px.bar(csi.groupby("time").std(numeric_only=True), y="p")

[6]:

# 按周一~五绘制出不同时段的波动率, 可以观察到周一的 9:30 又显著高于周二~五
px.line(csi.groupby(["week","time"]).std(numeric_only=True).reset_index(), x="time", y="p", color="week")

[7]:

# 上述信息验证了波动率实际和时间相关的假设, 接下来基于该假设计算改进版的 BS 定价
# Tσ² = ∫σ²(dt)
# 其中 T 是距离到期时间, 按照波动率的周期性积分出改进版波动率
# 这里计算的 r 是使用当前周期的收盘价对比上一周期的收盘价, 使得积分的结果能够完整的覆盖 T
csi["r"] = np.log(csi["close"].shift(1)/csi["close"])
# 得到周一~五不同时间段的周期性收益率方差
csiv = csi.groupby(["week","time"]).var(numeric_only=True).reset_index()[["week", "time", "r"]]

[8]:

# 只关注期权最后一周的行情数据
serial = api.get_kline_serial(symbol=[underlying, quote.instrument_id], duration_seconds=300, data_length=48*5)
serial["dt"] = pd.to_datetime(serial["datetime"], utc=True).dt.tz_convert('Asia/Shanghai')
serial["time"] = serial["dt"].dt.time
serial["week"] = serial["dt"].dt.weekday+1
# 最后一个交易日使用最后两小时的算数平均数作为交割结算价
serial["close_avg"] = serial["close"]
serial.iloc[-24:, serial.columns.get_loc("close_avg")] = serial["close"].iloc[-24:].expanding().mean()

[9]:

# 将 csi 周期性收益率方差 join 期权价量信息, 计算出改进版波动率
serial = serial.merge(csiv, on=["week", "time"])

[10]:

# v 为年化后的改进版波动率
serial["v"] = np.sqrt(serial["r"].iloc[::-1].expanding().mean()*48*250)

[11]:

# 无风险利率 1.5%
rf = 0.015
# 距离到期的时间序列
t = get_t(serial, quote.expire_datetime)
# 行权价格的折现, 用于计算时间价值
serial["present_k"] = quote.strike_price * np.exp(-rf * t)
serial["time_value"] = (serial["close_avg"] - serial["present_k"]) - serial["close1"]
# 计算标准和改进版 BS 模型价格, 以及和实际期权价格的差
# 最后两小时使用算数平均作为交割结算价导致不能简单的使用波动率来估计交割结算价的变化, 因此跳过最后两小时
# v 为标准 BS 模型所用到的波动率
v = np.sqrt(np.var(csi["r"]) * 250*48)
serial["bs"] = get_bs_price(serial["close"].iloc[:-24], k=quote.strike_price, r=rf, v=v, t=t.iloc[:-24], option_class=quote.option_class)
serial["bs_diff"] = serial["bs"] - serial["close1"]
serial["tdbs"] = get_bs_price(serial["close"].iloc[:-24], k=quote.strike_price, r=rf, v=serial["v"].iloc[:-24], t=t.iloc[:-24], option_class=quote.option_class)
serial["tdbs_diff"] = serial["tdbs"] - serial["close1"]

[12]:

# 计算结果
serial[["dt", "close_avg", "time_value", "close1", "bs", "bs_diff", "tdbs", "tdbs_diff"]]

[12]:

	dt	close_avg	time_value	close1	bs	bs_diff	tdbs	tdbs_diff
0	2024-05-13 09:30:00+08:00	3642.430000	1.654996	91.400000	94.055250	2.655250	94.053467	2.653467
1	2024-05-13 09:35:00+08:00	3642.540000	0.764482	92.400000	94.157842	1.757842	93.817840	1.417840
2	2024-05-13 09:40:00+08:00	3640.660000	0.083969	91.200000	92.360068	1.160068	91.990269	0.790269
3	2024-05-13 09:45:00+08:00	3642.880000	-0.096545	93.600000	94.477975	0.877975	94.127435	0.527435
4	2024-05-13 09:50:00+08:00	3644.590000	-0.387058	95.600000	96.114526	0.514526	95.779602	0.179602
5	2024-05-13 09:55:00+08:00	3644.780000	0.602428	94.800000	96.294486	1.494486	95.954176	1.154176
6	2024-05-13 10:00:00+08:00	3643.400000	0.021915	94.000000	94.968284	0.968284	94.607889	0.607889
7	2024-05-13 10:05:00+08:00	3649.690000	-1.288599	101.600000	101.022761	-0.577239	100.730440	-0.869560
8	2024-05-13 10:10:00+08:00	3653.490000	0.710888	103.400000	104.706017	1.306017	104.447285	1.047285
9	2024-05-13 10:15:00+08:00	3658.290000	-0.289626	109.200000	109.383127	0.183127	109.167791	-0.032209
10	2024-05-13 10:20:00+08:00	3659.020000	1.039861	108.600000	110.095092	1.495092	109.884757	1.284757
11	2024-05-13 10:25:00+08:00	3658.620000	2.239347	107.000000	109.702235	2.702235	109.490768	2.490768
12	2024-05-13 10:30:00+08:00	3660.600000	1.818833	109.400000	111.638249	2.238249	111.443192	2.043192
13	2024-05-13 10:35:00+08:00	3659.830000	1.248320	109.200000	110.882588	1.682588	110.683323	1.483323
14	2024-05-13 10:40:00+08:00	3660.470000	1.487806	109.600000	111.507632	1.907632	111.313157	1.713157
15	2024-05-13 10:45:00+08:00	3667.410000	-0.172707	118.200000	118.323862	0.123862	118.178861	-0.021139
16	2024-05-13 10:50:00+08:00	3669.310000	-1.873221	121.800000	120.195245	-1.604755	120.062026	-1.737974
17	2024-05-13 10:55:00+08:00	3667.370000	0.986266	117.000000	118.281704	1.281704	118.138850	1.138850
18	2024-05-13 11:00:00+08:00	3663.970000	0.585752	114.000000	114.935195	0.935195	114.772008	0.772008
19	2024-05-13 11:05:00+08:00	3663.260000	1.475239	112.400000	114.236226	1.836226	114.067249	1.667249
20	2024-05-13 11:10:00+08:00	3659.890000	1.104725	109.400000	110.929702	1.529702	110.736729	1.336729
21	2024-05-13 11:15:00+08:00	3661.100000	1.714212	110.000000	112.113643	2.113643	111.928860	1.928860
22	2024-05-13 11:20:00+08:00	3663.910000	1.123698	113.400000	114.870255	1.470255	114.705511	1.305511
23	2024-05-13 11:25:00+08:00	3665.520000	1.133185	115.000000	116.451949	1.451949	116.299429	1.299429
24	2024-05-13 13:00:00+08:00	3666.680000	0.883428	116.400000	117.567562	1.167562	117.430678	1.030678
25	2024-05-13 13:05:00+08:00	3669.440000	0.842915	119.200000	120.288497	1.088497	120.165952	0.965952
26	2024-05-13 13:10:00+08:00	3666.950000	0.952401	116.600000	117.830932	1.230932	117.694601	1.094601
27	2024-05-13 13:15:00+08:00	3664.050000	1.251888	113.400000	114.973967	1.573967	114.818286	1.418286
28	2024-05-13 13:20:00+08:00	3668.220000	0.821374	118.000000	119.080619	1.080619	118.950184	0.950184
29	2024-05-13 13:25:00+08:00	3671.950000	0.750861	121.800000	122.763406	0.963406	122.653171	0.853171
30	2024-05-13 13:30:00+08:00	3672.090000	0.490347	122.200000	122.900642	0.700642	122.792195	0.592195
31	2024-05-13 13:35:00+08:00	3670.360000	1.359834	119.600000	121.189497	1.589497	121.072959	1.472959
32	2024-05-13 13:40:00+08:00	3669.600000	1.399320	118.800000	120.437575	1.637575	120.318341	1.518341
33	2024-05-13 13:45:00+08:00	3669.570000	-0.231193	120.400000	120.406686	0.006686	120.289042	-0.110958
34	2024-05-13 13:50:00+08:00	3670.170000	0.568293	120.200000	120.998062	0.798062	120.885163	0.685163
35	2024-05-13 13:55:00+08:00	3670.580000	-1.622220	122.800000	121.401920	-1.398080	121.292969	-1.507031
36	2024-05-13 14:00:00+08:00	3673.590000	0.787266	123.400000	124.377621	0.977621	124.283658	0.883658
37	2024-05-13 14:05:00+08:00	3669.120000	0.316752	119.400000	119.957257	0.557257	119.842775	0.442775
38	2024-05-13 14:10:00+08:00	3665.720000	2.316239	114.000000	116.602395	2.602395	116.470472	2.470472
39	2024-05-13 14:15:00+08:00	3662.720000	1.715725	111.600000	113.648407	2.048407	113.500451	1.900451
40	2024-05-13 14:20:00+08:00	3660.120000	-0.284788	111.000000	111.093480	0.093480	110.929663	-0.070337
41	2024-05-13 14:25:00+08:00	3659.050000	0.244698	109.400000	110.042649	0.642649	109.871612	0.471612
42	2024-05-13 14:30:00+08:00	3658.900000	1.094185	108.400000	109.894002	1.494002	109.724688	1.324688
43	2024-05-13 14:35:00+08:00	3662.210000	0.803671	112.000000	113.141110	1.141110	112.993528	0.993528
44	2024-05-13 14:40:00+08:00	3664.110000	0.703158	114.000000	115.008462	1.008462	114.874169	0.874169
45	2024-05-13 14:45:00+08:00	3662.850000	-0.757356	114.200000	113.767335	-0.432665	113.626656	-0.573344
46	2024-05-13 14:50:00+08:00	3663.660000	0.452131	113.800000	114.562703	0.762703	114.426168	0.626168
47	2024-05-13 14:55:00+08:00	3664.690000	1.881617	113.400000	115.575260	2.175260	115.446259	2.046259
48	2024-05-14 09:30:00+08:00	3675.380000	-0.142898	126.000000	125.923052	-0.076948	125.888199	-0.111801
49	2024-05-14 09:35:00+08:00	3669.180000	0.856588	118.800000	119.754387	0.954387	119.693480	0.893480
50	2024-05-14 09:40:00+08:00	3668.870000	1.946075	117.400000	119.445348	2.045348	119.383071	1.983071
51	2024-05-14 09:45:00+08:00	3665.320000	1.995561	113.800000	115.919007	2.119007	115.843588	2.043588
52	2024-05-14 09:50:00+08:00	3660.910000	0.585048	110.800000	111.546159	0.746159	111.449895	0.649895
53	2024-05-14 09:55:00+08:00	3658.300000	0.774534	108.000000	108.962288	0.962288	108.851476	0.851476
54	2024-05-14 10:00:00+08:00	3651.790000	0.864021	101.400000	102.538132	1.138132	102.383731	0.983731
55	2024-05-14 10:05:00+08:00	3646.850000	-0.676493	98.000000	97.685160	-0.314840	97.488161	-0.511839
56	2024-05-14 10:10:00+08:00	3649.710000	0.582994	99.600000	100.489548	0.889548	100.318113	0.718113
57	2024-05-14 10:15:00+08:00	3651.900000	-0.627520	103.000000	102.641792	-0.358208	102.488000	-0.512000
58	2024-05-14 10:20:00+08:00	3652.970000	0.441967	103.000000	103.694095	0.694095	103.549219	0.549219
59	2024-05-14 10:25:00+08:00	3657.120000	3.391453	104.200000	107.788052	3.588052	107.671500	3.471500
60	2024-05-14 10:30:00+08:00	3652.390000	2.660940	100.200000	103.119731	2.919731	102.972943	2.772943
61	2024-05-14 10:35:00+08:00	3652.650000	1.920426	101.200000	103.374352	2.174352	103.229984	2.029984
62	2024-05-14 10:40:00+08:00	3652.450000	0.119912	102.800000	103.175829	0.375829	103.030603	0.230603
63	2024-05-14 10:45:00+08:00	3652.890000	2.159399	101.200000	103.607862	2.407862	103.467599	2.267599
64	2024-05-14 10:50:00+08:00	3654.460000	2.928885	102.000000	105.154556	3.154556	105.025329	3.025329
65	2024-05-14 10:55:00+08:00	3656.650000	1.518372	105.600000	107.315681	1.715681	107.201142	1.601142
66	2024-05-14 11:00:00+08:00	3656.350000	2.617858	104.200000	107.017923	2.817923	106.902754	2.702754
67	2024-05-14 11:05:00+08:00	3658.570000	1.837345	107.200000	109.211636	2.011636	109.110100	1.910100
68	2024-05-14 11:10:00+08:00	3657.860000	2.326831	106.000000	108.508019	2.508019	108.404232	2.404232
69	2024-05-14 11:15:00+08:00	3659.010000	-0.123682	109.600000	109.644577	0.044577	109.547984	-0.052016
70	2024-05-14 11:20:00+08:00	3654.440000	2.105804	102.800000	105.126397	2.326397	105.005914	2.205914
71	2024-05-14 11:25:00+08:00	3654.770000	0.835291	104.400000	105.450726	1.050726	105.333805	0.933805
72	2024-05-14 13:00:00+08:00	3652.710000	2.165534	101.000000	103.391106	2.391106	103.270910	2.270910
73	2024-05-14 13:05:00+08:00	3650.870000	1.525020	99.800000	101.575720	1.775720	101.439435	1.639435
74	2024-05-14 13:10:00+08:00	3652.930000	2.584506	100.800000	103.605310	2.805310	103.482591	2.682591
75	2024-05-14 13:15:00+08:00	3652.040000	1.293993	101.200000	102.725948	1.525948	102.599247	1.399247
76	2024-05-14 13:20:00+08:00	3651.300000	1.353479	100.400000	101.994935	1.594935	101.865638	1.465638
77	2024-05-14 13:25:00+08:00	3651.330000	1.182966	100.600000	102.023020	1.423020	101.896062	1.296062
78	2024-05-14 13:30:00+08:00	3653.810000	0.462452	103.800000	104.468396	0.668396	104.357940	0.557940
79	2024-05-14 13:35:00+08:00	3652.900000	1.751939	101.600000	103.568631	1.968631	103.454249	1.854249
80	2024-05-14 13:40:00+08:00	3652.170000	1.621425	101.000000	102.846928	1.846928	102.729466	1.729466
81	2024-05-14 13:45:00+08:00	3653.330000	1.180912	102.600000	103.990293	1.390293	103.880397	1.280397
82	2024-05-14 13:50:00+08:00	3655.620000	1.870398	104.200000	106.251688	2.051688	106.154887	1.954887
83	2024-05-14 13:55:00+08:00	3656.340000	1.389885	105.400000	106.962552	1.562552	106.871013	1.471013
84	2024-05-14 14:00:00+08:00	3658.040000	1.889371	106.600000	108.644041	2.044041	108.562048	1.962048
85	2024-05-14 14:05:00+08:00	3658.580000	3.628858	105.400000	109.177714	3.777714	109.097781	3.697781
86	2024-05-14 14:10:00+08:00	3654.920000	1.768344	103.600000	105.554367	1.954367	105.458036	1.858036
87	2024-05-14 14:15:00+08:00	3657.190000	2.637831	105.000000	107.798757	2.798757	107.713914	2.713914
88	2024-05-14 14:20:00+08:00	3657.730000	1.977317	106.200000	108.332210	2.132210	108.250726	2.050726
89	2024-05-14 14:25:00+08:00	3658.350000	3.796803	105.000000	108.945114	3.945114	108.867394	3.867394
90	2024-05-14 14:30:00+08:00	3658.450000	2.496290	106.400000	109.043001	2.643001	108.967213	2.567213
91	2024-05-14 14:35:00+08:00	3656.220000	2.665776	104.000000	106.833715	2.833715	106.749344	2.749344
92	2024-05-14 14:40:00+08:00	3656.810000	2.255263	105.000000	107.416414	2.416414	107.335882	2.335882
93	2024-05-14 14:45:00+08:00	3655.840000	1.884749	104.400000	106.455190	2.055190	106.372151	1.972151
94	2024-05-14 14:50:00+08:00	3656.660000	3.304236	103.800000	107.265454	3.465454	107.187130	3.387130
95	2024-05-14 14:55:00+08:00	3657.050000	2.693722	104.800000	107.650341	2.850341	107.575578	2.775578
96	2024-05-15 09:30:00+08:00	3646.770000	1.299202	95.800000	97.194105	1.394105	97.147714	1.347714
97	2024-05-15 09:35:00+08:00	3642.210000	1.738688	90.800000	92.671127	1.871127	92.596385	1.796385
98	2024-05-15 09:40:00+08:00	3638.550000	0.478175	88.400000	89.049836	0.649836	88.955822	0.555822
99	2024-05-15 09:45:00+08:00	3638.390000	-0.682339	89.400000	88.890298	-0.509702	88.795248	-0.604752
100	2024-05-15 09:50:00+08:00	3641.170000	-0.302852	91.800000	91.637479	-0.162521	91.557236	-0.242764
101	2024-05-15 09:55:00+08:00	3645.950000	-0.723366	97.000000	96.374352	-0.625648	96.315757	-0.684243
102	2024-05-15 10:00:00+08:00	3642.810000	-0.663879	93.800000	93.258960	-0.541040	93.187078	-0.612922
103	2024-05-15 10:05:00+08:00	3645.730000	0.055607	96.000000	96.153669	0.153669	96.094729	0.094729
104	2024-05-15 10:10:00+08:00	3644.640000	-1.034906	96.000000	95.070876	-0.929124	95.007886	-0.992114
105	2024-05-15 10:15:00+08:00	3640.620000	-2.055420	93.000000	91.086296	-1.913704	91.005444	-1.994556
106	2024-05-15 10:20:00+08:00	3641.790000	-1.085933	93.200000	92.243277	-0.956723	92.168346	-1.031654
107	2024-05-15 10:25:00+08:00	3639.600000	0.723553	89.200000	90.074408	0.874408	89.989087	0.789087
108	2024-05-15 10:30:00+08:00	3637.730000	-1.346961	89.400000	88.224799	-1.175201	88.129248	-1.270752
109	2024-05-15 10:35:00+08:00	3635.920000	0.042526	86.200000	86.436971	0.236971	86.331909	0.131909
110	2024-05-15 10:40:00+08:00	3640.400000	0.122012	90.600000	90.861687	0.261687	90.783249	0.183249
111	2024-05-15 10:45:00+08:00	3637.770000	-0.908501	89.000000	88.259755	-0.740245	88.168259	-0.831741
112	2024-05-15 10:50:00+08:00	3639.320000	-0.359015	90.000000	89.790361	-0.209639	89.709042	-0.290958
113	2024-05-15 10:55:00+08:00	3639.800000	-1.279528	91.400000	90.263787	-1.136213	90.186331	-1.213669
114	2024-05-15 11:00:00+08:00	3643.950000	-0.330042	94.600000	94.374352	-0.225648	94.316199	-0.283801
115	2024-05-15 11:05:00+08:00	3644.240000	-0.840555	95.400000	94.660888	-0.739112	94.604686	-0.795314
116	2024-05-15 11:10:00+08:00	3642.240000	1.158931	91.400000	92.676192	1.276192	92.613173	1.213173
117	2024-05-15 11:15:00+08:00	3642.710000	1.028417	92.000000	93.140862	1.140862	93.080868	1.080868
118	2024-05-15 11:20:00+08:00	3644.970000	0.087904	95.200000	95.381923	0.181923	95.331098	0.131098
119	2024-05-15 11:25:00+08:00	3647.190000	1.907390	95.600000	97.586002	1.986002	97.542763	1.942763
120	2024-05-15 13:00:00+08:00	3647.430000	2.137633	95.600000	97.804856	2.204856	97.767831	2.167831
121	2024-05-15 13:05:00+08:00	3646.080000	1.787119	94.600000	96.461464	1.861464	96.421280	1.821280
122	2024-05-15 13:10:00+08:00	3644.190000	1.496606	93.000000	94.582349	1.582349	94.537705	1.537705
123	2024-05-15 13:15:00+08:00	3644.680000	1.586092	93.400000	95.067990	1.667990	95.025518	1.625518
124	2024-05-15 13:20:00+08:00	3646.030000	0.535579	95.800000	96.408594	0.608594	96.370221	0.570221
125	2024-05-15 13:25:00+08:00	3645.340000	2.045065	93.600000	95.721655	2.121655	95.682533	2.082533
126	2024-05-15 13:30:00+08:00	3645.340000	0.644551	95.000000	95.720582	0.720582	95.681256	0.681256
127	2024-05-15 13:35:00+08:00	3642.780000	1.284038	91.800000	93.176505	1.376505	93.130829	1.330829
128	2024-05-15 13:40:00+08:00	3641.380000	-0.516476	92.200000	91.785984	-0.414016	91.737070	-0.462930
129	2024-05-15 13:45:00+08:00	3638.450000	0.753011	88.000000	88.880616	0.880616	88.821418	0.821418
130	2024-05-15 13:50:00+08:00	3639.240000	1.542497	88.000000	89.661794	1.661794	89.607325	1.607325
131	2024-05-15 13:55:00+08:00	3636.810000	0.511984	86.600000	87.254671	0.654671	87.191674	0.591674
132	2024-05-15 14:00:00+08:00	3635.040000	-0.658530	86.000000	85.503476	-0.496524	85.434319	-0.565681
133	2024-05-15 14:05:00+08:00	3633.420000	-1.279043	85.000000	83.902615	-1.097385	83.827834	-1.172166
134	2024-05-15 14:10:00+08:00	3632.060000	-1.839557	84.200000	82.560063	-1.639937	82.479929	-1.720071
135	2024-05-15 14:15:00+08:00	3631.760000	-3.540071	85.600000	82.262768	-3.337232	82.182892	-3.417108
136	2024-05-15 14:20:00+08:00	3637.500000	0.599416	87.200000	87.930403	0.730403	87.875313	0.675313
137	2024-05-15 14:25:00+08:00	3634.630000	0.128902	84.800000	85.090744	0.290744	85.026059	0.226059
138	2024-05-15 14:30:00+08:00	3633.040000	0.138389	83.200000	83.519539	0.319539	83.451494	0.251494
139	2024-05-15 14:35:00+08:00	3631.900000	-0.202125	82.400000	82.393800	-0.006200	82.322468	-0.077532
140	2024-05-15 14:40:00+08:00	3628.880000	-0.022638	79.200000	79.420272	0.220272	79.336179	0.136179
141	2024-05-15 14:45:00+08:00	3624.750000	-0.353152	75.400000	75.371095	-0.028905	75.269562	-0.130438
142	2024-05-15 14:50:00+08:00	3624.610000	-0.093665	75.000000	75.232007	0.232007	75.133333	0.133333
143	2024-05-15 14:55:00+08:00	3626.060000	-1.644179	78.000000	76.648150	-1.351850	76.561502	-1.438498
144	2024-05-16 09:30:00+08:00	3629.820000	-2.798704	82.800000	80.030639	-2.769361	80.019019	-2.780981
145	2024-05-16 09:35:00+08:00	3629.060000	-1.359218	80.600000	79.272244	-1.327756	79.253133	-1.346867
146	2024-05-16 09:40:00+08:00	3630.650000	-1.969731	82.800000	80.856281	-1.943719	80.839893	-1.960107
147	2024-05-16 09:45:00+08:00	3631.720000	-2.900245	84.800000	81.922489	-2.877511	81.907561	-2.892439
148	2024-05-16 09:50:00+08:00	3637.050000	-1.570758	88.800000	87.241325	-1.558675	87.232759	-1.567241
149	2024-05-16 09:55:00+08:00	3637.740000	-0.081272	88.000000	87.929678	-0.070322	87.921758	-0.078242
150	2024-05-16 10:00:00+08:00	3638.460000	0.838215	87.800000	88.648092	0.848092	88.640824	0.840824
151	2024-05-16 10:05:00+08:00	3639.940000	0.117701	90.000000	90.125815	0.125815	90.119747	0.119747
152	2024-05-16 10:10:00+08:00	3637.540000	-0.282813	88.000000	87.727853	-0.272147	87.719887	-0.280113
153	2024-05-16 10:15:00+08:00	3640.410000	0.386674	90.200000	90.594068	0.394068	90.588425	0.388425
154	2024-05-16 10:20:00+08:00	3638.140000	0.916160	87.400000	88.325749	0.925749	88.318639	0.918639
155	2024-05-16 10:25:00+08:00	3639.060000	1.435647	87.800000	89.244071	1.444071	89.237722	1.437722
156	2024-05-16 10:30:00+08:00	3642.220000	-0.404867	92.800000	92.400720	-0.399280	92.396434	-0.403566
157	2024-05-16 10:35:00+08:00	3642.200000	0.774620	91.600000	92.380117	0.780117	92.375872	0.775872
158	2024-05-16 10:40:00+08:00	3640.410000	1.384106	89.200000	90.590861	1.390861	90.585770	1.385770
159	2024-05-16 10:45:00+08:00	3639.900000	-0.126408	90.200000	90.080661	-0.119339	90.075368	-0.124632
160	2024-05-16 10:50:00+08:00	3640.220000	1.793079	88.600000	90.399747	1.799747	90.394782	1.794782
161	2024-05-16 10:55:00+08:00	3642.800000	0.772565	92.200000	92.977284	0.777284	92.973720	0.773720
162	2024-05-16 11:00:00+08:00	3641.620000	0.392052	91.400000	91.797433	0.397433	91.793466	0.393466
163	2024-05-16 11:05:00+08:00	3645.460000	1.231538	94.400000	95.634748	1.234748	95.632318	1.232318
164	2024-05-16 11:10:00+08:00	3646.390000	0.961025	95.600000	96.563804	0.963804	96.561696	0.961696
165	2024-05-16 11:15:00+08:00	3648.620000	0.990511	97.800000	98.792528	0.992528	98.790995	0.990995
166	2024-05-16 11:20:00+08:00	3652.170000	1.139997	101.200000	102.341208	1.141208	102.340249	1.140249
167	2024-05-16 11:25:00+08:00	3654.520000	2.889484	101.800000	104.690332	2.890332	104.689648	2.889648
168	2024-05-16 13:00:00+08:00	3656.080000	1.839726	104.400000	106.240137	1.840137	106.239800	1.839800
169	2024-05-16 13:05:00+08:00	3654.280000	0.839212	103.600000	104.439737	0.839737	104.439308	0.839308
170	2024-05-16 13:10:00+08:00	3651.510000	1.268699	100.400000	101.669471	1.269471	101.668847	1.268847
171	2024-05-16 13:15:00+08:00	3653.600000	1.758185	102.000000	103.758736	1.758736	103.758286	1.758286
172	2024-05-16 13:20:00+08:00	3652.570000	1.127672	101.600000	102.728297	1.128297	102.727793	1.127793
173	2024-05-16 13:25:00+08:00	3654.140000	1.697158	102.600000	104.297638	1.697638	104.297255	1.697255
174	2024-05-16 13:30:00+08:00	3652.530000	1.886644	100.800000	102.687240	1.887240	102.686771	1.886771
175	2024-05-16 13:35:00+08:00	3654.270000	1.826131	102.600000	104.426576	1.826576	104.426223	1.826223
176	2024-05-16 13:40:00+08:00	3656.340000	1.895617	104.600000	106.495931	1.895931	106.495684	1.895684
177	2024-05-16 13:45:00+08:00	3652.980000	2.735104	100.400000	103.135616	2.735616	103.135228	2.735228
178	2024-05-16 13:50:00+08:00	3652.960000	1.714590	101.400000	103.115090	1.715090	103.114721	1.714721
179	2024-05-16 13:55:00+08:00	3649.600000	2.354077	97.400000	99.754884	2.354884	99.754307	2.354307
180	2024-05-16 14:00:00+08:00	3649.650000	2.203563	97.600000	99.804344	2.204344	99.803801	2.203801
181	2024-05-16 14:05:00+08:00	3652.960000	2.313049	100.800000	103.113508	2.313508	103.113172	2.313172
182	2024-05-16 14:10:00+08:00	3648.120000	3.272536	95.000000	98.273466	3.273466	98.272807	3.272807
183	2024-05-16 14:15:00+08:00	3644.350000	2.502022	92.000000	94.503601	2.503601	94.502497	2.502497
184	2024-05-16 14:20:00+08:00	3644.000000	2.951509	91.200000	94.153129	2.953129	94.151956	2.951956
185	2024-05-16 14:25:00+08:00	3641.850000	2.000995	90.000000	92.003150	2.003150	92.001681	2.001681
186	2024-05-16 14:30:00+08:00	3635.850000	2.200481	83.800000	86.005358	2.205358	86.002381	2.202381
187	2024-05-16 14:35:00+08:00	3636.370000	3.519968	83.000000	86.524409	3.524409	86.521721	3.521721
188	2024-05-16 14:40:00+08:00	3636.190000	3.939454	82.400000	86.343906	3.943906	86.341310	3.941310
189	2024-05-16 14:45:00+08:00	3638.770000	4.318941	84.600000	88.921976	4.321976	88.920233	4.320233
190	2024-05-16 14:50:00+08:00	3641.200000	5.548427	85.800000	91.350520	5.550520	91.349336	5.549336
191	2024-05-16 14:55:00+08:00	3640.360000	4.107914	86.400000	90.510219	4.110219	90.509041	4.109041
192	2024-05-17 09:30:00+08:00	3636.920000	-0.246616	87.200000	86.953384	-0.246616	86.953384	-0.246616
193	2024-05-17 09:35:00+08:00	3644.450000	-0.317130	94.800000	94.482870	-0.317130	94.482870	-0.317130
194	2024-05-17 09:40:00+08:00	3647.620000	-1.347643	99.000000	97.652357	-1.347643	97.652357	-1.347643
195	2024-05-17 09:45:00+08:00	3645.080000	-2.288157	97.400000	95.111843	-2.288157	95.111843	-2.288157
196	2024-05-17 09:50:00+08:00	3644.230000	-1.138671	95.400000	94.261329	-1.138671	94.261329	-1.138671
197	2024-05-17 09:55:00+08:00	3648.570000	-1.799184	100.400000	98.600816	-1.799184	98.600816	-1.799184
198	2024-05-17 10:00:00+08:00	3640.520000	-1.249698	91.800000	90.550302	-1.249698	90.550302	-1.249698
199	2024-05-17 10:05:00+08:00	3638.290000	-0.680211	89.000000	88.319789	-0.680211	88.319789	-0.680211
200	2024-05-17 10:10:00+08:00	3639.280000	-1.690725	91.000000	89.309275	-1.690725	89.309275	-1.690725
201	2024-05-17 10:15:00+08:00	3635.060000	-0.511239	85.600000	85.088761	-0.511239	85.088761	-0.511239
202	2024-05-17 10:20:00+08:00	3638.010000	-0.161752	88.200000	88.038248	-0.161752	88.038248	-0.161752
203	2024-05-17 10:25:00+08:00	3632.990000	-1.182266	84.200000	83.017734	-1.182266	83.017734	-1.182266
204	2024-05-17 10:30:00+08:00	3628.510000	-0.462779	79.000000	78.537221	-0.462779	78.537221	-0.462779
205	2024-05-17 10:35:00+08:00	3631.370000	0.996707	80.400000	81.396707	0.996707	81.396707	0.996707
206	2024-05-17 10:40:00+08:00	3630.080000	-0.893807	81.000000	80.106193	-0.893807	80.106193	-0.893807
207	2024-05-17 10:45:00+08:00	3627.830000	-1.144320	79.000000	77.855680	-1.144320	77.855680	-1.144320
208	2024-05-17 10:50:00+08:00	3629.340000	-2.234834	81.600000	79.365166	-2.234834	79.365166	-2.234834
209	2024-05-17 10:55:00+08:00	3633.450000	-1.325347	84.800000	83.474653	-1.325347	83.474653	-1.325347
210	2024-05-17 11:00:00+08:00	3633.490000	-2.685861	86.200000	83.514139	-2.685861	83.514139	-2.685861
211	2024-05-17 11:05:00+08:00	3631.800000	-2.176374	84.000000	81.823626	-2.176374	81.823626	-2.176374
212	2024-05-17 11:10:00+08:00	3630.470000	-3.106888	83.600000	80.493112	-3.106888	80.493112	-3.106888
213	2024-05-17 11:15:00+08:00	3631.300000	-1.277402	82.600000	81.322598	-1.277402	81.322598	-1.277402
214	2024-05-17 11:20:00+08:00	3630.860000	-2.317915	83.200000	80.882085	-2.317915	80.882085	-2.317915
215	2024-05-17 11:25:00+08:00	3633.040000	1.461571	81.600000	83.061571	1.461571	83.061571	1.461571
216	2024-05-17 13:00:00+08:00	3634.530000	-0.458187	85.000000	NaN	NaN	NaN	NaN
217	2024-05-17 13:05:00+08:00	3635.565000	0.576299	85.000000	NaN	NaN	NaN	NaN
218	2024-05-17 13:10:00+08:00	3635.070000	-0.319214	85.400000	NaN	NaN	NaN	NaN
219	2024-05-17 13:15:00+08:00	3634.500000	-0.089728	84.600000	NaN	NaN	NaN	NaN
220	2024-05-17 13:20:00+08:00	3634.216000	0.025758	84.200000	NaN	NaN	NaN	NaN
221	2024-05-17 13:25:00+08:00	3633.796667	-0.394089	84.200000	NaN	NaN	NaN	NaN
222	2024-05-17 13:30:00+08:00	3633.867143	-0.324126	84.200000	NaN	NaN	NaN	NaN
223	2024-05-17 13:35:00+08:00	3634.633750	-3.558032	88.200000	NaN	NaN	NaN	NaN
224	2024-05-17 13:40:00+08:00	3635.740000	-5.652296	91.400000	NaN	NaN	NaN	NaN
225	2024-05-17 13:45:00+08:00	3636.584000	-4.208810	90.800000	NaN	NaN	NaN	NaN
226	2024-05-17 13:50:00+08:00	3637.460909	-3.532414	91.000000	NaN	NaN	NaN	NaN
227	2024-05-17 13:55:00+08:00	3638.371667	-5.622170	94.000000	NaN	NaN	NaN	NaN
228	2024-05-17 14:00:00+08:00	3639.120000	-2.674350	91.800000	NaN	NaN	NaN	NaN
229	2024-05-17 14:05:00+08:00	3639.754286	-2.440578	92.200000	NaN	NaN	NaN	NaN
230	2024-05-17 14:10:00+08:00	3640.271333	-1.524044	91.800000	NaN	NaN	NaN	NaN
231	2024-05-17 14:15:00+08:00	3640.685000	-1.110891	91.800000	NaN	NaN	NaN	NaN
232	2024-05-17 14:20:00+08:00	3641.273529	-1.922875	93.200000	NaN	NaN	NaN	NaN
233	2024-05-17 14:25:00+08:00	3641.865556	-2.131363	94.000000	NaN	NaN	NaN	NaN
234	2024-05-17 14:30:00+08:00	3642.788421	-3.209011	96.000000	NaN	NaN	NaN	NaN
235	2024-05-17 14:35:00+08:00	3643.980500	-2.817446	96.800000	NaN	NaN	NaN	NaN
236	2024-05-17 14:40:00+08:00	3645.153333	-1.045126	96.200000	NaN	NaN	NaN	NaN
237	2024-05-17 14:45:00+08:00	3646.353636	-1.245336	97.600000	NaN	NaN	NaN	NaN
238	2024-05-17 14:50:00+08:00	3647.678696	-0.320791	98.000000	NaN	NaN	NaN	NaN
239	2024-05-17 14:55:00+08:00	3648.940833	1.540833	97.400000	NaN	NaN	NaN	NaN

[13]:

# 绘制出时间价值(time_value), 标准 BS 定价与期权价格的差(bs_diff), 改进版 BS 定价与期权价格的差(tdbs_diff)
px.line(serial, x="dt", y=["time_value", "bs_diff", "tdbs_diff"])

[14]:

# 残差均值
serial[["bs_diff", "tdbs_diff"]].mean()

[14]:

bs_diff     0.873137
tdbs_diff   0.793846
dtype: float64

[15]:

# 标准模型的残差标准差
np.log(serial["bs"]/serial["close1"]).std()

[15]:

0.016289936725434342

[16]:

# 改进模型的残差标准差
np.log(serial["tdbs"]/serial["close1"]).std()

[16]:

0.016233962768335282

[17]:

api.close()

[17]: