{ "cells": [ { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:44.258823Z", "start_time": "2024-06-26T08:40:43.100949Z" } }, "source": [ "## 因子计算分析\n", " \n", "import datetime\n", "\n", "from tqsdk import TqApi, TqAuth\n", "from tqsdk.tafunc import get_t, get_bs_price\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import plotly.express as px\n", "\n", "pd.options.display.max_rows= None\n", "pd.options.display.max_columns = None\n", "pd.options.display.width = 0\n", "pd.options.display.float_format = '{:.6f}'.format" ], "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "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/\n" ] } ], "execution_count": 1 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:45.867748Z", "start_time": "2024-06-26T08:40:44.259725Z" } }, "source": [ "# 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\n", "api = TqApi(auth=TqAuth('快期账户', '快期密码'))\n", "quote = api.get_quote('CFFEX.IO2405-C-3550')\n", "underlying = quote.underlying_symbol\n", "exp = datetime.datetime.fromtimestamp(quote.expire_datetime)" ], "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "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\n" ] } ], "execution_count": 2 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.202661Z", "start_time": "2024-06-26T08:40:45.870485Z" } }, "source": [ "# 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\n", "csi = api.get_kline_data_series(symbol=underlying, duration_seconds=300, start_dt=exp-datetime.timedelta(days=365), end_dt=exp)\n", "# 将 unix time 转换成 pandas.Datetime 并获得周几及时间信息\n", "csi[\"dt\"] = pd.to_datetime(csi[\"datetime\"], utc=True).dt.tz_convert('Asia/Shanghai')\n", "csi[\"time\"] = csi[\"dt\"].dt.time\n", "csi[\"week\"] = csi[\"dt\"].dt.weekday+1\n", "# 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\n", "csi[\"p\"] = np.log(csi[\"close\"]/csi[\"open\"])" ], "outputs": [], "execution_count": 3 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.362044Z", "start_time": "2024-06-26T08:40:46.203294Z" } }, "source": [ "# 可以看到周一到周五的波动率有显著性的差异\n", "px.bar(csi.groupby(\"week\").std(numeric_only=True), y=\"p\")\n" ], "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "data": [ { "alignmentgroup": "True", "hovertemplate": "week=%{x}
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"domain": [ 0.0, 1.0 ], "title": { "text": "time" } }, "yaxis": { "anchor": "x", "domain": [ 0.0, 1.0 ], "title": { "text": "p" } }, "legend": { "title": { "text": "week" }, "tracegroupgap": 0 }, "margin": { "t": 60 } }, "config": { "plotlyServerURL": "https://plot.ly" } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "execution_count": 6 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.509194Z", "start_time": "2024-06-26T08:40:46.498478Z" } }, "source": [ "# 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\n", "# Tσ² = ∫σ²(dt)\n", "# 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\n", "# 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\n", "csi[\"r\"] = np.log(csi[\"close\"].shift(1)/csi[\"close\"])\n", "# 得到周一~五不同时间段的周期性收益率方差\n", "csiv = csi.groupby([\"week\",\"time\"]).var(numeric_only=True).reset_index()[[\"week\", \"time\", \"r\"]]" ], "outputs": [], "execution_count": 7 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.892108Z", "start_time": "2024-06-26T08:40:46.510015Z" } }, "source": [ "# 只关注期权最后一周的行情数据\n", "serial = api.get_kline_serial(symbol=[underlying, quote.instrument_id], duration_seconds=300, data_length=48*5)\n", "serial[\"dt\"] = pd.to_datetime(serial[\"datetime\"], utc=True).dt.tz_convert('Asia/Shanghai')\n", "serial[\"time\"] = serial[\"dt\"].dt.time\n", "serial[\"week\"] = serial[\"dt\"].dt.weekday+1\n", "# 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\n", "serial[\"close_avg\"] = serial[\"close\"]\n", "serial.iloc[-24:, serial.columns.get_loc(\"close_avg\")] = serial[\"close\"].iloc[-24:].expanding().mean()" ], "outputs": [], "execution_count": 8 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.902375Z", "start_time": "2024-06-26T08:40:46.893850Z" } }, "source": [ "# 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\n", "serial = serial.merge(csiv, on=[\"week\", \"time\"])" ], "outputs": [], "execution_count": 9 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.912369Z", "start_time": "2024-06-26T08:40:46.905272Z" } }, "source": [ "# v 为年化后的改进版波动率\n", "serial[\"v\"] = np.sqrt(serial[\"r\"].iloc[::-1].expanding().mean()*48*250)" ], "outputs": [], "execution_count": 10 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.934819Z", "start_time": "2024-06-26T08:40:46.913737Z" } }, "source": [ "# 无风险利率 1.5%\n", "rf = 0.015\n", "# 距离到期的时间序列\n", "t = get_t(serial, quote.expire_datetime)\n", "# 行权价格的折现, 用于计算时间价值\n", "serial[\"present_k\"] = quote.strike_price * np.exp(-rf * t)\n", "serial[\"time_value\"] = (serial[\"close_avg\"] - serial[\"present_k\"]) - serial[\"close1\"]\n", "# 计算标准和改进版 BS 模型价格, 以及和实际期权价格的差\n", "# 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\n", "# v 为标准 BS 模型所用到的波动率\n", "v = np.sqrt(np.var(csi[\"r\"]) * 250*48)\n", "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)\n", "serial[\"bs_diff\"] = serial[\"bs\"] - serial[\"close1\"]\n", "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)\n", "serial[\"tdbs_diff\"] = serial[\"tdbs\"] - serial[\"close1\"]" ], "outputs": [], "execution_count": 11 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:46.989359Z", "start_time": "2024-06-26T08:40:46.942388Z" } }, "source": [ "# 计算结果\n", "serial[[\"dt\", \"close_avg\", \"time_value\", \"close1\", \"bs\", \"bs_diff\", \"tdbs\", \"tdbs_diff\"]]" ], "outputs": [ { "data": { "text/plain": [ " dt close_avg time_value close1 bs \\\n", "0 2024-05-13 09:30:00+08:00 3642.430000 1.654996 91.400000 94.055250 \n", "1 2024-05-13 09:35:00+08:00 3642.540000 0.764482 92.400000 94.157842 \n", "2 2024-05-13 09:40:00+08:00 3640.660000 0.083969 91.200000 92.360068 \n", "3 2024-05-13 09:45:00+08:00 3642.880000 -0.096545 93.600000 94.477975 \n", "4 2024-05-13 09:50:00+08:00 3644.590000 -0.387058 95.600000 96.114526 \n", "5 2024-05-13 09:55:00+08:00 3644.780000 0.602428 94.800000 96.294486 \n", "6 2024-05-13 10:00:00+08:00 3643.400000 0.021915 94.000000 94.968284 \n", "7 2024-05-13 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dtclose_avgtime_valueclose1bsbs_difftdbstdbs_diff
02024-05-13 09:30:00+08:003642.4300001.65499691.40000094.0552502.65525094.0534672.653467
12024-05-13 09:35:00+08:003642.5400000.76448292.40000094.1578421.75784293.8178401.417840
22024-05-13 09:40:00+08:003640.6600000.08396991.20000092.3600681.16006891.9902690.790269
32024-05-13 09:45:00+08:003642.880000-0.09654593.60000094.4779750.87797594.1274350.527435
42024-05-13 09:50:00+08:003644.590000-0.38705895.60000096.1145260.51452695.7796020.179602
52024-05-13 09:55:00+08:003644.7800000.60242894.80000096.2944861.49448695.9541761.154176
62024-05-13 10:00:00+08:003643.4000000.02191594.00000094.9682840.96828494.6078890.607889
72024-05-13 10:05:00+08:003649.690000-1.288599101.600000101.022761-0.577239100.730440-0.869560
82024-05-13 10:10:00+08:003653.4900000.710888103.400000104.7060171.306017104.4472851.047285
92024-05-13 10:15:00+08:003658.290000-0.289626109.200000109.3831270.183127109.167791-0.032209
102024-05-13 10:20:00+08:003659.0200001.039861108.600000110.0950921.495092109.8847571.284757
112024-05-13 10:25:00+08:003658.6200002.239347107.000000109.7022352.702235109.4907682.490768
122024-05-13 10:30:00+08:003660.6000001.818833109.400000111.6382492.238249111.4431922.043192
132024-05-13 10:35:00+08:003659.8300001.248320109.200000110.8825881.682588110.6833231.483323
142024-05-13 10:40:00+08:003660.4700001.487806109.600000111.5076321.907632111.3131571.713157
152024-05-13 10:45:00+08:003667.410000-0.172707118.200000118.3238620.123862118.178861-0.021139
162024-05-13 10:50:00+08:003669.310000-1.873221121.800000120.195245-1.604755120.062026-1.737974
172024-05-13 10:55:00+08:003667.3700000.986266117.000000118.2817041.281704118.1388501.138850
182024-05-13 11:00:00+08:003663.9700000.585752114.000000114.9351950.935195114.7720080.772008
192024-05-13 11:05:00+08:003663.2600001.475239112.400000114.2362261.836226114.0672491.667249
202024-05-13 11:10:00+08:003659.8900001.104725109.400000110.9297021.529702110.7367291.336729
212024-05-13 11:15:00+08:003661.1000001.714212110.000000112.1136432.113643111.9288601.928860
222024-05-13 11:20:00+08:003663.9100001.123698113.400000114.8702551.470255114.7055111.305511
232024-05-13 11:25:00+08:003665.5200001.133185115.000000116.4519491.451949116.2994291.299429
242024-05-13 13:00:00+08:003666.6800000.883428116.400000117.5675621.167562117.4306781.030678
252024-05-13 13:05:00+08:003669.4400000.842915119.200000120.2884971.088497120.1659520.965952
262024-05-13 13:10:00+08:003666.9500000.952401116.600000117.8309321.230932117.6946011.094601
272024-05-13 13:15:00+08:003664.0500001.251888113.400000114.9739671.573967114.8182861.418286
282024-05-13 13:20:00+08:003668.2200000.821374118.000000119.0806191.080619118.9501840.950184
292024-05-13 13:25:00+08:003671.9500000.750861121.800000122.7634060.963406122.6531710.853171
302024-05-13 13:30:00+08:003672.0900000.490347122.200000122.9006420.700642122.7921950.592195
312024-05-13 13:35:00+08:003670.3600001.359834119.600000121.1894971.589497121.0729591.472959
322024-05-13 13:40:00+08:003669.6000001.399320118.800000120.4375751.637575120.3183411.518341
332024-05-13 13:45:00+08:003669.570000-0.231193120.400000120.4066860.006686120.289042-0.110958
342024-05-13 13:50:00+08:003670.1700000.568293120.200000120.9980620.798062120.8851630.685163
352024-05-13 13:55:00+08:003670.580000-1.622220122.800000121.401920-1.398080121.292969-1.507031
362024-05-13 14:00:00+08:003673.5900000.787266123.400000124.3776210.977621124.2836580.883658
372024-05-13 14:05:00+08:003669.1200000.316752119.400000119.9572570.557257119.8427750.442775
382024-05-13 14:10:00+08:003665.7200002.316239114.000000116.6023952.602395116.4704722.470472
392024-05-13 14:15:00+08:003662.7200001.715725111.600000113.6484072.048407113.5004511.900451
402024-05-13 14:20:00+08:003660.120000-0.284788111.000000111.0934800.093480110.929663-0.070337
412024-05-13 14:25:00+08:003659.0500000.244698109.400000110.0426490.642649109.8716120.471612
422024-05-13 14:30:00+08:003658.9000001.094185108.400000109.8940021.494002109.7246881.324688
432024-05-13 14:35:00+08:003662.2100000.803671112.000000113.1411101.141110112.9935280.993528
442024-05-13 14:40:00+08:003664.1100000.703158114.000000115.0084621.008462114.8741690.874169
452024-05-13 14:45:00+08:003662.850000-0.757356114.200000113.767335-0.432665113.626656-0.573344
462024-05-13 14:50:00+08:003663.6600000.452131113.800000114.5627030.762703114.4261680.626168
472024-05-13 14:55:00+08:003664.6900001.881617113.400000115.5752602.175260115.4462592.046259
482024-05-14 09:30:00+08:003675.380000-0.142898126.000000125.923052-0.076948125.888199-0.111801
492024-05-14 09:35:00+08:003669.1800000.856588118.800000119.7543870.954387119.6934800.893480
502024-05-14 09:40:00+08:003668.8700001.946075117.400000119.4453482.045348119.3830711.983071
512024-05-14 09:45:00+08:003665.3200001.995561113.800000115.9190072.119007115.8435882.043588
522024-05-14 09:50:00+08:003660.9100000.585048110.800000111.5461590.746159111.4498950.649895
532024-05-14 09:55:00+08:003658.3000000.774534108.000000108.9622880.962288108.8514760.851476
542024-05-14 10:00:00+08:003651.7900000.864021101.400000102.5381321.138132102.3837310.983731
552024-05-14 10:05:00+08:003646.850000-0.67649398.00000097.685160-0.31484097.488161-0.511839
562024-05-14 10:10:00+08:003649.7100000.58299499.600000100.4895480.889548100.3181130.718113
572024-05-14 10:15:00+08:003651.900000-0.627520103.000000102.641792-0.358208102.488000-0.512000
582024-05-14 10:20:00+08:003652.9700000.441967103.000000103.6940950.694095103.5492190.549219
592024-05-14 10:25:00+08:003657.1200003.391453104.200000107.7880523.588052107.6715003.471500
602024-05-14 10:30:00+08:003652.3900002.660940100.200000103.1197312.919731102.9729432.772943
612024-05-14 10:35:00+08:003652.6500001.920426101.200000103.3743522.174352103.2299842.029984
622024-05-14 10:40:00+08:003652.4500000.119912102.800000103.1758290.375829103.0306030.230603
632024-05-14 10:45:00+08:003652.8900002.159399101.200000103.6078622.407862103.4675992.267599
642024-05-14 10:50:00+08:003654.4600002.928885102.000000105.1545563.154556105.0253293.025329
652024-05-14 10:55:00+08:003656.6500001.518372105.600000107.3156811.715681107.2011421.601142
662024-05-14 11:00:00+08:003656.3500002.617858104.200000107.0179232.817923106.9027542.702754
672024-05-14 11:05:00+08:003658.5700001.837345107.200000109.2116362.011636109.1101001.910100
682024-05-14 11:10:00+08:003657.8600002.326831106.000000108.5080192.508019108.4042322.404232
692024-05-14 11:15:00+08:003659.010000-0.123682109.600000109.6445770.044577109.547984-0.052016
702024-05-14 11:20:00+08:003654.4400002.105804102.800000105.1263972.326397105.0059142.205914
712024-05-14 11:25:00+08:003654.7700000.835291104.400000105.4507261.050726105.3338050.933805
722024-05-14 13:00:00+08:003652.7100002.165534101.000000103.3911062.391106103.2709102.270910
732024-05-14 13:05:00+08:003650.8700001.52502099.800000101.5757201.775720101.4394351.639435
742024-05-14 13:10:00+08:003652.9300002.584506100.800000103.6053102.805310103.4825912.682591
752024-05-14 13:15:00+08:003652.0400001.293993101.200000102.7259481.525948102.5992471.399247
762024-05-14 13:20:00+08:003651.3000001.353479100.400000101.9949351.594935101.8656381.465638
772024-05-14 13:25:00+08:003651.3300001.182966100.600000102.0230201.423020101.8960621.296062
782024-05-14 13:30:00+08:003653.8100000.462452103.800000104.4683960.668396104.3579400.557940
792024-05-14 13:35:00+08:003652.9000001.751939101.600000103.5686311.968631103.4542491.854249
802024-05-14 13:40:00+08:003652.1700001.621425101.000000102.8469281.846928102.7294661.729466
812024-05-14 13:45:00+08:003653.3300001.180912102.600000103.9902931.390293103.8803971.280397
822024-05-14 13:50:00+08:003655.6200001.870398104.200000106.2516882.051688106.1548871.954887
832024-05-14 13:55:00+08:003656.3400001.389885105.400000106.9625521.562552106.8710131.471013
842024-05-14 14:00:00+08:003658.0400001.889371106.600000108.6440412.044041108.5620481.962048
852024-05-14 14:05:00+08:003658.5800003.628858105.400000109.1777143.777714109.0977813.697781
862024-05-14 14:10:00+08:003654.9200001.768344103.600000105.5543671.954367105.4580361.858036
872024-05-14 14:15:00+08:003657.1900002.637831105.000000107.7987572.798757107.7139142.713914
882024-05-14 14:20:00+08:003657.7300001.977317106.200000108.3322102.132210108.2507262.050726
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912024-05-14 14:35:00+08:003656.2200002.665776104.000000106.8337152.833715106.7493442.749344
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\n", "
" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 12 }, { "cell_type": "code", "metadata": { "scrolled": true, "ExecuteTime": { "end_time": "2024-06-26T08:40:47.033548Z", "start_time": "2024-06-26T08:40:46.990381Z" } }, "source": [ "# 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)\n", "px.line(serial, x=\"dt\", y=[\"time_value\", \"bs_diff\", \"tdbs_diff\"])" ], "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "hovertemplate": "variable=time_value
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"standoff": 15 }, "zerolinecolor": "white", "automargin": true, "zerolinewidth": 2 }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white", "gridwidth": 2 }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white", "gridwidth": 2 }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white", "gridwidth": 2 } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "geo": { "bgcolor": "white", "landcolor": "#E5ECF6", "subunitcolor": "white", "showland": true, "showlakes": true, "lakecolor": "white" }, "title": { "x": 0.05 }, "mapbox": { "style": "light" } } }, "xaxis": { "anchor": "y", "domain": [ 0.0, 1.0 ], "title": { "text": "dt" } }, "yaxis": { "anchor": "x", "domain": [ 0.0, 1.0 ], "title": { "text": "value" } }, "legend": { "title": { "text": "variable" }, "tracegroupgap": 0 }, "margin": { "t": 60 } }, "config": { "plotlyServerURL": "https://plot.ly" } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "execution_count": 13 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:47.046480Z", "start_time": "2024-06-26T08:40:47.034819Z" } }, "source": [ "# 残差均值\n", "serial[[\"bs_diff\", \"tdbs_diff\"]].mean()" ], "outputs": [ { "data": { "text/plain": [ "bs_diff 0.873137\n", "tdbs_diff 0.793846\n", "dtype: float64" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 14 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:47.052412Z", "start_time": "2024-06-26T08:40:47.047743Z" } }, "source": [ "# 标准模型的残差标准差\n", "np.log(serial[\"bs\"]/serial[\"close1\"]).std()" ], "outputs": [ { "data": { "text/plain": [ "0.016289936725434342" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 15 }, { "cell_type": "code", "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:47.059764Z", "start_time": "2024-06-26T08:40:47.054422Z" } }, "source": [ "# 改进模型的残差标准差\n", "np.log(serial[\"tdbs\"]/serial[\"close1\"]).std()" ], "outputs": [ { "data": { "text/plain": [ "0.016233962768335282" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "execution_count": 16 }, { "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:47.086281Z", "start_time": "2024-06-26T08:40:47.062006Z" } }, "cell_type": "code", "source": "api.close()", "outputs": [], "execution_count": 17 }, { "metadata": { "ExecuteTime": { "end_time": "2024-06-26T08:40:47.091103Z", "start_time": "2024-06-26T08:40:47.087680Z" } }, "cell_type": "code", "source": "", "outputs": [], "execution_count": 17 } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }