【50ETF期權】 5. 日內即時監控 Greeks 和隱含波動率微笑 · Python 量化交易教程

# 【50ETF期權】 5. 日內即時監控 Greeks 和隱含波動率微笑 > 來源：https://uqer.io/community/share/5615d10ff9f06c4ca72fb5be 和上一篇類似，計算上證50ETF期權的隱含波動率微笑，但這里通過DataAPI提供的高頻數據，在交易時間實時監控Greeks 和隱含波動率變化！ ```py from CAL.PyCAL import * import numpy as np import pandas as pd import matplotlib.pyplot as plt from matplotlib import rc rc('mathtext', default='regular') import seaborn as sns sns.set_style('white') import math from scipy import interpolate from scipy.stats import mstats from pandas import Series, DataFrame, concat import time from matplotlib import dates ``` 上海銀行間同業拆借利率 SHIBOR，用來作為無風險利率參考 ```py ## 銀行間質押式回購利率 def getHistDayInterestRateInterbankRepo(date): cal = Calendar('China.SSE') period = Period('-10B') begin = cal.advanceDate(date, period) begin_str = begin.toISO().replace('-', '') date_str = date.toISO().replace('-', '') # 以下的indicID分別對應的銀行間質押式回購利率周期為： # 1D, 7D, 14D, 21D, 1M, 3M, 4M, 6M, 9M, 1Y indicID = [u"M120000067", u"M120000068", u"M120000069", u"M120000070", u"M120000071", u"M120000072", u"M120000073", u"M120000074", u"M120000075", u"M120000076"] period = np.asarray([1.0, 7.0, 14.0, 21.0, 30.0, 90.0, 120.0, 180.0, 270.0, 360.0]) / 360.0 period_matrix = pd.DataFrame(index=indicID, data=period, columns=['period']) field = u"indicID,indicName,publishTime,periodDate,dataValue,unit" interbank_repo = DataAPI.ChinaDataInterestRateInterbankRepoGet(indicID=indicID,beginDate=begin_str,endDate=date_str,field=field,pandas="1") interbank_repo = interbank_repo.groupby('indicID').first() interbank_repo = concat([interbank_repo, period_matrix], axis=1, join='inner').sort_index() return interbank_repo ## 銀行間同業拆借利率 def getHistDaySHIBOR(date): cal = Calendar('China.SSE') period = Period('-10B') begin = cal.advanceDate(date, period) begin_str = begin.toISO().replace('-', '') date_str = date.toISO().replace('-', '') # 以下的indicID分別對應的SHIBOR周期為： # 1D, 7D, 14D, 1M, 3M, 6M, 9M, 1Y indicID = [u"M120000057", u"M120000058", u"M120000059", u"M120000060", u"M120000061", u"M120000062", u"M120000063", u"M120000064"] period = np.asarray([1.0, 7.0, 14.0, 30.0, 90.0, 180.0, 270.0, 360.0]) / 360.0 period_matrix = pd.DataFrame(index=indicID, data=period, columns=['period']) field = u"indicID,indicName,publishTime,periodDate,dataValue,unit" interest_shibor = DataAPI.ChinaDataInterestRateSHIBORGet(indicID=indicID,beginDate=begin_str,endDate=date_str,field=field,pandas="1") interest_shibor = interest_shibor.groupby('indicID').first() interest_shibor = concat([interest_shibor, period_matrix], axis=1, join='inner').sort_index() return interest_shibor ## 插值得到給定的周期的無風險利率 def periodsSplineRiskFreeInterestRate(date, periods): # 此處使用SHIBOR來插值 init_shibor = getHistDaySHIBOR(date) shibor = {} min_period = min(init_shibor.period.values) min_period = 10.0/360.0 max_period = max(init_shibor.period.values) for p in periods.keys(): tmp = periods[p] if periods[p] > max_period: tmp = max_period * 0.99999 elif periods[p] < min_period: tmp = min_period * 1.00001 sh = interpolate.spline(init_shibor.period.values, init_shibor.dataValue.values, [tmp], order=3) shibor[p] = sh[0]/100.0 return shibor ``` ## 1. Greeks 和隱含波動率本文中計算的Greeks包括： + `delta` 期權價格關于標的價格的一階導數 + `gamma` 期權價格關于標的價格的二階導數 + `rho` 期權價格關于無風險利率的一階導數 + `theta` 期權價格關于到期時間的一階導數 + `vega` 期權價格關于波動率的一階導數注意： + 計算隱含波動率，我們采用Black-Scholes-Merton模型，此模型在平臺Python包CAL中已有實現 + 無風險利率使用SHIBOR + 期權的時間價值為負時(此種情況在50ETF期權里時有發生)，沒法通過BSM模型計算隱含波動率，故此時將期權隱含波動率設為0.0，實際上，此時的隱含波動率和各風險指標并無實際參考價值 + 此處計算即時隱含波動率和Greeks時候，我們使用買一和賣一的中間價作為期權價格 ```py ## 使用DataAPI.OptGet, DataAPI.MktOptionTickRTSnapshotGet 拿到計算所需數據 def getOptTickSnapshot(opt_var_sec, date): date_str = date.toISO().replace('-', '') #使用DataAPI.OptGet，拿到已退市和上市的所有期權的基本信息 info_fields = [u'optID', u'varSecID', u'varShortName', u'varTicker', u'varExchangeCD', u'varType', u'contractType', u'strikePrice', u'contMultNum', u'contractStatus', u'listDate', u'expYear', u'expMonth', u'expDate', u'lastTradeDate', u'exerDate', u'deliDate', u'delistDate'] opt_info = DataAPI.OptGet(optID='', contractStatus=[u"DE",u"L"], field=info_fields, pandas="1") #使用DataAPI.MktOptionTickRTSnapshotGet，拿到期權實時成交數據 date_str = date.toISO().replace('-', '') fields_mkt = ['instrumentID', u'optionId', u'dataDate', u'lastPrice', u'preSettlePrice', u'bidBook_price1', u'bidBook_volume1', u'askBook_price1', u'askBook_volume1'] opt_mkt = DataAPI.MktOptionTickRTSnapshotGet(optionId=u"", field='', pandas="1") opt_mkt = opt_mkt[opt_mkt.dataDate == date.toISO()] opt_mkt['optID'] = map(int, opt_mkt['optionId']) opt_mkt[u"price"] = (opt_mkt['bidBook_price1'] + opt_mkt['askBook_price1'])/2.0 opt_info = opt_info.set_index(u"optID") opt_mkt = opt_mkt.set_index(u"optID") opt = concat([opt_info, opt_mkt], axis=1, join='inner').sort_index() return opt ## 分析期權即時交易信息，得到隱含波動率微笑和期權風險指標 def getOptAnalysisSnapshot(opt_var_sec): date = Date.todaysDate() opt = getOptTickSnapshot(opt_var_sec, date) #使用DataAPI.MktTickRTSnapshotGet 拿到期權標的的即時行情 date_str = date.toISO().replace('-', '') opt_var_mkt = DataAPI.MktTickRTSnapshotGet(securityID=opt_var_sec,field=u"lastPrice",pandas="1") # 計算shibor exp_dates_str = opt.expDate.unique() periods = {} for date_str in exp_dates_str: exp_date = Date.parseISO(date_str) periods[exp_date] = (exp_date - date)/360.0 shibor = periodsSplineRiskFreeInterestRate(date, periods) settle = opt.price.values # 期權 settle price close = opt.price.values # 期權 close price strike = opt.strikePrice.values # 期權 strike price option_type = opt.contractType.values # 期權類型 exp_date_str = opt.expDate.values # 期權行權日期 eval_date_str = opt.dataDate.values # 期權交易日期 mat_dates = [] eval_dates = [] spot = [] for epd, evd in zip(exp_date_str, eval_date_str): mat_dates.append(Date.parseISO(epd)) eval_dates.append(Date.parseISO(evd)) spot.append(opt_var_mkt.lastPrice[0]) time_to_maturity = [float(mat - eva + 1.0)/365.0 for (mat, eva) in zip(mat_dates, eval_dates)] risk_free = [] # 無風險利率 for s, mat, time in zip(spot, mat_dates, time_to_maturity): #rf = math.log(forward_price[mat] / s) / time rf = shibor[mat] risk_free.append(rf) opt_types = [] # 期權類型 for t in option_type: if t == 'CO': opt_types.append(1) else: opt_types.append(-1) # 使用通聯CAL包中 BSMImpliedVolatity 計算隱含波動率 calculated_vol = BSMImpliedVolatity(opt_types, strike, spot, risk_free, 0.0, time_to_maturity, settle) calculated_vol = calculated_vol.fillna(0.0) # 使用通聯CAL包中 BSMPrice 計算期權風險指標 greeks = BSMPrice(opt_types, strike, spot, risk_free, 0.0, calculated_vol.vol.values, time_to_maturity) # vega、rho、theta 的計量單位參照上交所的數據，以求統一對比 greeks.vega = greeks.vega #/ 100.0 greeks.rho = greeks.rho #/ 100.0 greeks.theta = greeks.theta #* 365.0 / 252.0 #/ 365.0 opt['strike'] = strike opt['optType'] = option_type opt['expDate'] = exp_date_str opt['spotPrice'] = spot opt['riskFree'] = risk_free opt['timeToMaturity'] = np.around(time_to_maturity, decimals=4) opt['settle'] = np.around(greeks.price.values.astype(np.double), decimals=4) opt['iv'] = np.around(calculated_vol.vol.values.astype(np.double), decimals=4) opt['delta'] = np.around(greeks.delta.values.astype(np.double), decimals=4) opt['vega'] = np.around(greeks.vega.values.astype(np.double), decimals=4) opt['gamma'] = np.around(greeks.gamma.values.astype(np.double), decimals=4) opt['theta'] = np.around(greeks.theta.values.astype(np.double), decimals=4) opt['rho'] = np.around(greeks.rho.values.astype(np.double), decimals=4) fields = [u'instrumentID', u'contractType', u'strikePrice', u'expDate', u'dataDate', u'dataTime', u'price', 'spotPrice', u'iv', u'delta', u'vega', u'gamma', u'theta', u'rho'] opt = opt[fields].reset_index().set_index('instrumentID').sort_index() #opt['iv'] = opt.iv.replace(to_replace=0.0, value=np.nan) return opt # 期權分析數據整理 def getOptSnapshotGreeksIV(): # Uqer 計算期權的風險數據 opt_var_sec = u"510050.XSHG" # 期權標的 opt = getOptAnalysisSnapshot(opt_var_sec) # 整理數據部分 opt.index = [index[-10:] for index in opt.index] opt = opt[['spotPrice', 'contractType','strikePrice','expDate','price','iv','delta','theta','gamma','vega','rho']] opt_call = opt[opt.contractType=='CO'] opt_put = opt[opt.contractType=='PO'] opt_call.columns = pd.MultiIndex.from_tuples([('Call', c) for c in opt_call.columns]) opt_call[('Call-Put', 'spotPrice')] = opt_call[('Call', 'spotPrice')] opt_call[('Call-Put', 'strikePrice')] = opt_call[('Call', 'strikePrice')] opt_put.columns = pd.MultiIndex.from_tuples([('Put', c) for c in opt_put.columns]) opt = concat([opt_call, opt_put], axis=1, join='inner').sort_index() opt = opt.set_index(('Call','expDate')).sort_index() opt = opt.drop([('Call','contractType'), ('Call','strikePrice'), ('Call','spotPrice')], axis=1) opt = opt.drop([('Put','expDate'), ('Put','contractType'), ('Put','strikePrice'), ('Put','spotPrice')], axis=1) opt.index.name = 'expDate' ## 以上得到完整的歷史某日數據，格式簡潔明了 return opt ``` 即時風險數據計算，其中的price就是買一、賣一價格的平均 ```py DataAPI.MktTickRTSnapshotGet(securityID="510050.XSHG",field=u"",pandas="1").columns Index([u'exchangeCD', u'ticker', u'timestamp', u'AggQty', u'amplitude', u'change', u'changePct', u'currencyCD', u'dataDate', u'dataTime', u'deal', u'extraLargeOrderValue', u'highPrice', u'IEP', u'largeOrderValue', u'lastPrice', u'localTimestamp', u'lowPrice', u'mediumOrderValue', u'negMarketValue', u'nominalPrice', u'openPrice', u'orderType', u'prevClosePrice', u'shortNM', u'smallOrderValue', u'staticPE', u'suspension', u'totalOrderValue', u'tradSessionID', u'tradSessionStatus', u'tradSessionSubID', u'tradStatus', u'tradType', u'turnoverRate', u'utcOffset', u'value', u'volume', u'VWAP', u'Yield', u'bidBook_price1', u'bidBook_volume1', u'bidBook_price2', u'bidBook_volume2', u'bidBook_price3', u'bidBook_volume3', u'bidBook_price4', u'bidBook_volume4', u'bidBook_price5', u'bidBook_volume5', u'askBook_price1', u'askBook_volume1', u'askBook_price2', u'askBook_volume2', u'askBook_price3', u'askBook_volume3', u'askBook_price4', u'askBook_volume4', u'askBook_price5', u'askBook_volume5'], dtype='object') ``` ```py opt = getOptSnapshotGreeksIV() opt.head(20) ``` | | Call | Call-Put | Put | | --- | --- | | price | iv | delta | theta | gamma | vega | rho | spotPrice | strikePrice | price | iv | delta | theta | gamma | vega | rho | | expDate | | | | | | | | | | | | | | | | | | 2015-10-28 | 0.35250 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.85 | 0.00265 | 0.4139 | -0.0300 | -0.1281 | 0.3097 | 0.0362 | -0.0040 | | 2015-10-28 | 0.30390 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.90 | 0.00490 | 0.4093 | -0.0517 | -0.1965 | 0.4868 | 0.0562 | -0.0069 | | 2015-10-28 | 0.25710 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.95 | 0.00810 | 0.3985 | -0.0810 | -0.2706 | 0.7086 | 0.0797 | -0.0108 | | 2015-10-28 | 0.20990 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 2.00 | 0.01130 | 0.3716 | -0.1133 | -0.3219 | 0.9729 | 0.1021 | -0.0151 | | 2015-10-28 | 0.16690 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 2.05 | 0.01710 | 0.3539 | -0.1649 | -0.3942 | 1.3199 | 0.1318 | -0.0220 | | 2015-10-28 | 0.12500 | 0.1998 | 0.8793 | -0.2390 | 1.8916 | 0.1067 | 0.1049 | 2.215 | 2.10 | 0.02605 | 0.3391 | -0.2367 | -0.4668 | 1.7125 | 0.1639 | -0.0317 | | 2015-10-28 | 0.09155 | 0.2392 | 0.7182 | -0.4171 | 2.6574 | 0.1794 | 0.0863 | 2.215 | 2.15 | 0.03965 | 0.3287 | -0.3305 | -0.5273 | 2.0746 | 0.1925 | -0.0444 | | 2015-10-28 | 0.06285 | 0.2510 | 0.5679 | -0.4908 | 2.9485 | 0.2089 | 0.0688 | 2.215 | 2.20 | 0.06060 | 0.3297 | -0.4416 | -0.5701 | 2.2532 | 0.2097 | -0.0598 | | 2015-10-28 | 0.04160 | 0.2615 | 0.4241 | -0.4994 | 2.8189 | 0.2081 | 0.0516 | 2.215 | 2.25 | 0.09095 | 0.3483 | -0.5500 | -0.5979 | 2.1391 | 0.2103 | -0.0753 | | 2015-10-28 | 0.02795 | 0.2780 | 0.3064 | -0.4697 | 2.3766 | 0.1865 | 0.0374 | 2.215 | 2.30 | 0.12510 | 0.3612 | -0.6450 | -0.5751 | 1.9401 | 0.1978 | -0.0894 | | 2015-10-28 | 0.01655 | 0.2793 | 0.2049 | -0.3791 | 1.9141 | 0.1509 | 0.0252 | 2.215 | 2.35 | 0.16490 | 0.3831 | -0.7188 | -0.5449 | 1.6571 | 0.1792 | -0.1011 | | 2015-11-25 | 0.17915 | 0.1663 | 0.9149 | -0.1371 | 1.1545 | 0.1264 | 0.2480 | 2.215 | 2.05 | 0.04815 | 0.3692 | -0.2509 | -0.3361 | 1.0627 | 0.2584 | -0.0811 | | 2015-11-25 | 0.14805 | 0.2196 | 0.7751 | -0.2490 | 1.6819 | 0.2433 | 0.2106 | 2.215 | 2.10 | 0.06685 | 0.3775 | -0.3136 | -0.3803 | 1.1574 | 0.2878 | -0.1022 | | 2015-11-25 | 0.12025 | 0.2438 | 0.6649 | -0.3116 | 1.8413 | 0.2957 | 0.1816 | 2.215 | 2.15 | 0.08985 | 0.3880 | -0.3780 | -0.4163 | 1.2072 | 0.3085 | -0.1245 | | 2015-11-25 | 0.09455 | 0.2541 | 0.5657 | -0.3391 | 1.9085 | 0.3194 | 0.1555 | 2.215 | 2.20 | 0.11335 | 0.3891 | -0.4408 | -0.4293 | 1.2495 | 0.3202 | -0.1463 | | 2015-11-25 | 0.07355 | 0.2631 | 0.4721 | -0.3475 | 1.8635 | 0.3230 | 0.1305 | 2.215 | 2.25 | 0.14205 | 0.3964 | -0.5023 | -0.4380 | 1.2402 | 0.3238 | -0.1684 | | 2015-11-25 | 0.05525 | 0.2667 | 0.3849 | -0.3335 | 1.7659 | 0.3102 | 0.1070 | 2.215 | 2.30 | 0.17425 | 0.4052 | -0.5598 | -0.4381 | 1.1993 | 0.3201 | -0.1899 | | 2015-12-23 | 0.38610 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.80 | 0.02025 | 0.3907 | -0.0997 | -0.1573 | 0.4406 | 0.1782 | -0.0509 | | 2015-12-23 | 0.34710 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.85 | 0.02735 | 0.3885 | -0.1280 | -0.1862 | 0.5295 | 0.2129 | -0.0656 | | 2015-12-23 | 0.30415 | 0.0000 | NaN | NaN | NaN | NaN | NaN | 2.215 | 1.90 | 0.03625 | 0.3865 | -0.1610 | -0.2152 | 0.6212 | 0.2485 | -0.0829 | ## 2. 隱含波動率微笑利用上一小節的代碼，給出隱含波動率微笑結構隱含波動率微笑 ```py # 做圖展示某一天的隱含波動率微笑 def plotSnapshotSmileVolatility(): # Uqer 計算期權的風險數據 opt = getOptSnapshotGreeksIV() # 下面展示波動率微笑 exp_dates = np.sort(opt.index.unique()) ## ---------------------------------------------- fig = plt.figure(figsize=(10,8)) fig.set_tight_layout(True) for i in range(exp_dates.shape[0]): date = exp_dates[i] ax = fig.add_subplot(2,2,i+1) opt_date = opt[opt.index==date].set_index(('Call-Put', 'strikePrice')) opt_date.index.name = 'strikePrice' ax.plot(opt_date.index, opt_date[('Call', 'iv')], '-o') ax.plot(opt_date.index, opt_date[('Put', 'iv')], '-s') ax.legend(['call', 'put'], loc=0) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Implied Volatility") plt.title(exp_dates[i]) ``` ```py plotSnapshotSmileVolatility() ``` ![](https://box.kancloud.cn/2016-07-30_579cbdbc03be3.png) 行權價和行權日期兩個方向上的隱含波動率微笑 ```py from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm # 做圖展示某一天的隱含波動率結構 def plotSnapshotSmileVolatilitySurface(): # Uqer 計算期權的風險數據 date = Date.todaysDate() opt = getOptSnapshotGreeksIV() # 下面展示波動率結構 exp_dates = np.sort(opt.index.unique()) strikes = np.sort(opt[('Call-Put', 'strikePrice')].unique()) risk_mt = {'Call': pd.DataFrame(index=strikes), 'Put': pd.DataFrame(index=strikes) } # 將數據整理成Call和Put分開來，分別的結構為： # 行為行權價，列為剩余到期天數（以自然天數計算） for epd in exp_dates: exp_days = Date.parseISO(epd) - date opt_date = opt[opt.index==epd].set_index(('Call-Put', 'strikePrice')) opt_date.index.name = 'strikePrice' for cp in risk_mt.keys(): risk_mt[cp][exp_days] = opt_date[(cp, 'iv')] for cp in risk_mt.keys(): for strike in risk_mt[cp].index: if np.sum(np.isnan(risk_mt[cp].ix[strike])) > 0: risk_mt[cp] = risk_mt[cp].drop(strike) # Call和Put分開顯示，行index為行權價，列index為剩余到期天數 #print risk_mt # 畫圖 for cp in ['Call', 'Put']: opt = risk_mt[cp] x = [] y = [] z = [] for xx in opt.index: for yy in opt.columns: x.append(xx) y.append(yy) z.append(opt[yy][xx]) fig = plt.figure(figsize=(10,8)) fig.suptitle(cp) ax = fig.gca(projection='3d') ax.plot_trisurf(x, y, z, cmap=cm.jet, linewidth=0.2) return risk_mt ``` 畫出某一天的波動率微笑曲面結構 ```py opt = plotSnapshotSmileVolatilitySurface() opt # Call和Put分開顯示，行index為行權價，列index為剩余到期天數 {'Call': 20 48 76 167 2.05 0.0000 0.1663 0.2027 0.2263 2.10 0.1998 0.2196 0.2283 0.2430 2.15 0.2392 0.2438 0.2446 0.2502 2.20 0.2510 0.2541 0.2570 0.2579 2.25 0.2615 0.2631 0.2646 0.2639 2.30 0.2780 0.2667 0.2763 0.2673, 'Put': 20 48 76 167 2.05 0.3535 0.3692 0.3965 0.3965 2.10 0.3391 0.3775 0.4002 0.4002 2.15 0.3287 0.3877 0.4116 0.4030 2.20 0.3297 0.3891 0.4185 0.4069 2.25 0.3483 0.3964 0.4228 0.4084 2.30 0.3612 0.4052 0.4287 0.4149} ``` ![](https://box.kancloud.cn/2016-07-30_579cbdbc1ff3d.png) ![](https://box.kancloud.cn/2016-07-30_579cbdbc433f6.png) 波動率曲面結構圖中： + 上圖為Call，下圖為Put，此處沒有進行任何插值處理，略顯粗糙 + Put的隱含波動率明顯大于Call + 期限結構來說，波動率呈現遠高近低的特征 + 切記：所有的隱含波動率為0代表著期權的時間價值為負，此時的風險數據實際上并無多大參考意義！！