【50ETF期權】 4. Greeks 和隱含波動率微笑 · Python 量化交易教程

# 【50ETF期權】 4. Greeks 和隱含波動率微笑 > 來源：https://uqer.io/community/share/560769faf9f06c597165ef75 在本文中，我們將通過量化實驗室提供的數據，計算上證50ETF期權的隱含波動率微笑。 ```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 和隱含波動率計算本文中計算的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 ```py ## 使用DataAPI.OptGet, DataAPI.MktOptdGet拿到計算所需數據 def getOptDayData(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.MktOptdGet，拿到歷史上某一天的期權成交信息 mkt_fields = [u'ticker', u'optID', u'secShortName', u'exchangeCD', u'tradeDate', u'preSettlePrice', u'preClosePrice', u'openPrice', u'highestPrice', u'lowestPrice', u'closePrice', u'settlPrice', u'turnoverVol', u'turnoverValue', u'openInt'] opt_mkt = DataAPI.MktOptdGet(tradeDate=date_str, field=mkt_fields, pandas = "1") 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 ## 分析歷史某一日的期權收盤價信息，得到隱含波動率微笑和期權風險指標 def getOptDayAnalysis(opt_var_sec, date): opt = getOptDayData(opt_var_sec, date) #使用DataAPI.MktFunddGet拿到期權標的的日行情 date_str = date.toISO().replace('-', '') opt_var_mkt = DataAPI.MktFunddGet(secID=opt_var_sec,tradeDate=date_str,beginDate=u"",endDate=u"",field=u"",pandas="1") #opt_var_mkt = DataAPI.MktFunddAdjGet(secID=opt_var_sec,beginDate=date_str,endDate=date_str,field=u"",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.settlPrice.values # 期權 settle price close = opt.closePrice.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.tradeDate.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.closePrice[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) 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'ticker', u'contractType', u'strikePrice', u'expDate', u'tradeDate', u'closePrice', u'settlPrice', 'spotPrice', u'iv', u'delta', u'vega', u'gamma', u'theta', u'rho'] opt = opt[fields].reset_index().set_index('ticker').sort_index() #opt['iv'] = opt.iv.replace(to_replace=0.0, value=np.nan) return opt ``` 嘗試用 `getOptDayAnalysis` 計算 2015-09-24 這一天的風險指標 ```py # Uqer 計算期權的風險數據 opt_var_sec = u"510050.XSHG" # 期權標的 date = Date(2015, 9, 24) option_risk = getOptDayAnalysis(opt_var_sec, date) option_risk.head(2) ``` | | optID | contractType | strikePrice | expDate | tradeDate | closePrice | settlPrice | spotPrice | iv | delta | vega | gamma | theta | rho | | --- | --- | | ticker | | | | | | | | | | | | | | | | 510050C1510M01850 | 10000405 | CO | 1.85 | 2015-10-28 | 2015-09-24 | 0.3268 | 0.3555 | 2.187 | 0.4317 | 0.9101 | 0.1099 | 0.5550 | -0.2992 | 0.1568 | | 510050C1510M01900 | 10000406 | CO | 1.90 | 2015-10-28 | 2015-09-24 | 0.2791 | 0.3102 | 2.187 | 0.4161 | 0.8810 | 0.1347 | 0.7058 | -0.3435 | 0.1550 | 進一步，我們和上交所給出的對應日期的風險指標參考數據對比一下 + 上交所的數據需要自行下載，注意選擇日期下載相應csv文件，http://www.sse.com.cn/assortment/derivatives/options/risk/ + 下載完后，不做內容改動，請上傳到UQER平臺的 Data 中；文件名請相應修改，此處我設為了 `option_risk_sse_0924.csv` + 為了避免冗余，下面我們僅僅對比近月期權的各個風險指標 ```py # 讀取上交所數據 def readRiskDataSSE(file_str): # 按照上交所下載到的risk數據排版格式，做以處理 opt = pd.read_csv(file_str, encoding='gb2312').reset_index() opt.columns = [['tradeDate','optID','ticker','secShortName','delta','theta','gamma','vega','rho','margin']] opt = opt[['tradeDate','optID','ticker','delta','theta','gamma','vega','rho']] opt['ticker'] = [tic[1:-2] for tic in opt['ticker']] opt['tradeDate'] = [td[0:-1] for td in opt['tradeDate']] #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") # 上交所的數據和期權基本信息合并，得到比較完整的期權數據 opt_info = opt_info.set_index(u"optID") opt = opt.set_index(u"optID") opt = concat([opt_info, opt], axis=1, join='inner').sort_index() fields = [u'ticker', u'contractType', u'strikePrice', u'expDate', u'tradeDate', u'delta', u'vega', u'gamma', u'theta', u'rho'] opt = opt[fields].reset_index().set_index('ticker').sort_index() return opt ``` 讀取 2015-09-24 上交所數據 ```py option_risk_sse = readRiskDataSSE('option_risk_sse_0924.csv') option_risk_sse.head(2) ``` | | optID | contractType | strikePrice | expDate | tradeDate | delta | vega | gamma | theta | rho | | --- | --- | | ticker | | | | | | | | | | | | 510050C1510M01850 | 10000405 | CO | 1.85 | 2015-10-28 | 2015-09-24 | 0.910 | 0.109 | 0.555 | -0.303 | 0.154 | | 510050C1510M01900 | 10000406 | CO | 1.90 | 2015-10-28 | 2015-09-24 | 0.881 | 0.134 | 0.706 | -0.349 | 0.153 | `getOptDayAnalysis` 函數計算結果和上交所數據的對比 ```py # 對比本文計算結果 option_risk 和上交所結果 option_risk_sse 中的近月期權風險指標 near_exp = np.sort(option_risk.expDate.unique())[0] # 近月期權行權日 opt_call_uqer = option_risk[option_risk.expDate==near_exp][option_risk.contractType=='CO'].set_index('strikePrice') opt_call_sse = option_risk_sse[option_risk_sse.expDate==near_exp][option_risk_sse.contractType=='CO'].set_index('strikePrice') opt_put_uqer = option_risk[option_risk.expDate==near_exp][option_risk.contractType=='PO'].set_index('strikePrice') opt_put_sse = option_risk_sse[option_risk_sse.expDate==near_exp][option_risk_sse.contractType=='PO'].set_index('strikePrice') ## ---------------------------------------------- ## 風險指標對比 fig = plt.figure(figsize=(10,12)) fig.set_tight_layout(True) # ------ Delta ------ ax = fig.add_subplot(321) ax.plot(opt_call_uqer.index, opt_call_uqer['delta'], '-') ax.plot(opt_call_sse.index, opt_call_sse['delta'], 's') ax.plot(opt_put_uqer.index, opt_put_uqer['delta'], '-') ax.plot(opt_put_sse.index, opt_put_sse['delta'], 's') ax.legend(['call-uqer', 'call-sse', 'put-uqer', 'put-sse']) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Delta") plt.title('Delta Comparison') # ------ Theta ------ ax = fig.add_subplot(322) ax.plot(opt_call_uqer.index, opt_call_uqer['theta'], '-') ax.plot(opt_call_sse.index, opt_call_sse['theta'], 's') ax.plot(opt_put_uqer.index, opt_put_uqer['theta'], '-') ax.plot(opt_put_sse.index, opt_put_sse['theta'], 's') ax.legend(['call-uqer', 'call-sse', 'put-uqer', 'put-sse']) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Theta") plt.title('Theta Comparison') # ------ Gamma ------ ax = fig.add_subplot(323) ax.plot(opt_call_uqer.index, opt_call_uqer['gamma'], '-') ax.plot(opt_call_sse.index, opt_call_sse['gamma'], 's') ax.plot(opt_put_uqer.index, opt_put_uqer['gamma'], '-') ax.plot(opt_put_sse.index, opt_put_sse['gamma'], 's') ax.legend(['call-uqer', 'call-sse', 'put-uqer', 'put-sse'], loc=0) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Gamma") plt.title('Gamma Comparison') # # ------ Vega ------ ax = fig.add_subplot(324) ax.plot(opt_call_uqer.index, opt_call_uqer['vega'], '-') ax.plot(opt_call_sse.index, opt_call_sse['vega'], 's') ax.plot(opt_put_uqer.index, opt_put_uqer['vega'], '-') ax.plot(opt_put_sse.index, opt_put_sse['vega'], 's') ax.legend(['call-uqer', 'call-sse', 'put-uqer', 'put-sse'], loc=4) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Vega") plt.title('Vega Comparison') # ------ Rho ------ ax = fig.add_subplot(325) ax.plot(opt_call_uqer.index, opt_call_uqer['rho'], '-') ax.plot(opt_call_sse.index, opt_call_sse['rho'], 's') ax.plot(opt_put_uqer.index, opt_put_uqer['rho'], '-') ax.plot(opt_put_sse.index, opt_put_sse['rho'], 's') ax.legend(['call-uqer', 'call-sse', 'put-uqer', 'put-sse'], loc=3) ax.grid() ax.set_xlabel(u"strikePrice") ax.set_ylabel(r"Rho") plt.title('Rho Comparison') <matplotlib.text.Text at 0x535d0d0> ``` ![](https://box.kancloud.cn/2016-07-30_579cbdbb7928c.png) 上述五張圖中，對于近月期權，我們分別對比了五個Greeks風險指標：`Delta`， `Theta`， `Gamma`， `Vega`， `Rho`： + 每張圖中，`Call` 和 `Put` 分開比較，橫軸為行權價 + 可以看出，本文中的計算結果和上交所的參考數值符合的比較好 + 在接下來的50ETF期權分析中，我們將使用本文中的計算方法來計算期權隱含波動率和Greeks風險指標把上面的數據整理整理，格式更簡潔一點 ```py # 每日期權分析數據整理 def getOptDayGreeksIV(date): # Uqer 計算期權的風險數據 opt_var_sec = u"510050.XSHG" # 期權標的 opt = getOptDayAnalysis(opt_var_sec, date) # 整理數據部分 opt.index = [index[-10:] for index in opt.index] opt = opt[['contractType','strikePrice','expDate','closePrice','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', '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')], axis=1) opt = opt.drop([('Put','expDate'), ('Put','contractType'), ('Put','strikePrice')], 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 ``` ```py date = Date(2015, 9, 24) option_risk = getOptDayGreeksIV(date) option_risk.head(10) ``` | | Call | Call-Put | Put | | --- | --- | | closePrice | iv | delta | theta | gamma | vega | rho | strikePrice | closePrice | iv | delta | theta | gamma | vega | rho | | expDate | | | | | | | | | | | | | | | | | 2015-10-28 | 0.3268 | 0.4317 | 0.9101 | -0.2992 | 0.5550 | 0.1099 | 0.1568 | 1.85 | 0.0129 | 0.4319 | -0.0900 | -0.2410 | 0.5551 | 0.1100 | -0.0201 | | 2015-10-28 | 0.2791 | 0.4161 | 0.8810 | -0.3435 | 0.7058 | 0.1347 | 0.1550 | 1.90 | 0.0176 | 0.4174 | -0.1197 | -0.2854 | 0.7063 | 0.1352 | -0.0268 | | 2015-10-28 | 0.2360 | 0.3990 | 0.8449 | -0.3862 | 0.8823 | 0.1615 | 0.1517 | 1.95 | 0.0232 | 0.3992 | -0.1552 | -0.3247 | 0.8822 | 0.1615 | -0.0348 | | 2015-10-28 | 0.1955 | 0.1811 | 0.9532 | -0.1225 | 0.7980 | 0.0663 | 0.1811 | 2.00 | 0.0345 | 0.4020 | -0.2105 | -0.3940 | 1.0601 | 0.1954 | -0.0474 | | 2015-10-28 | 0.1599 | 0.2453 | 0.8237 | -0.2764 | 1.5588 | 0.1754 | 0.1574 | 2.05 | 0.0474 | 0.3975 | -0.2703 | -0.4441 | 1.2290 | 0.2241 | -0.0612 | | 2015-10-28 | 0.1275 | 0.2698 | 0.7137 | -0.3696 | 1.8625 | 0.2304 | 0.1374 | 2.10 | 0.0643 | 0.3952 | -0.3381 | -0.4847 | 1.3660 | 0.2476 | -0.0771 | | 2015-10-28 | 0.0990 | 0.2814 | 0.6081 | -0.4208 | 2.0162 | 0.2602 | 0.1180 | 2.15 | 0.0869 | 0.4013 | -0.4114 | -0.5200 | 1.4317 | 0.2635 | -0.0946 | | 2015-10-28 | 0.0768 | 0.2955 | 0.5057 | -0.4489 | 1.9934 | 0.2701 | 0.0987 | 2.20 | 0.1146 | 0.4121 | -0.4836 | -0.5428 | 1.4284 | 0.2699 | -0.1124 | | 2015-10-28 | 0.0584 | 0.3068 | 0.4132 | -0.4487 | 1.8746 | 0.2637 | 0.0810 | 2.25 | 0.1450 | 0.4200 | -0.5517 | -0.5438 | 1.3908 | 0.2679 | -0.1296 | | 2015-10-28 | 0.0470 | 0.3264 | 0.3381 | -0.4434 | 1.6538 | 0.2476 | 0.0664 | 2.30 | 0.1826 | 0.4426 | -0.6091 | -0.5520 | 1.2809 | 0.2600 | -0.1452 | ## 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 plotSmileVolatility(date): # Uqer 計算期權的風險數據 opt = getOptDayGreeksIV(date) # 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 plotSmileVolatility(Date(2015,9,24)) ``` ![](https://box.kancloud.cn/2016-07-30_579cbdbb989ed.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 plotSmileVolatilitySurface(date): # Uqer 計算期權的風險數據 opt = getOptDayGreeksIV(date) # 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 = plotSmileVolatilitySurface(Date(2015,9,24)) opt # Call和Put分開顯示，行index為行權價，列index為剩余到期天數 {'Call': 34 62 90 181 2.10 0.2698 0.2817 0.2823 0.3042 2.15 0.2814 0.2888 0.2916 0.3063 2.20 0.2955 0.3008 0.2922 0.3237 2.25 0.3068 0.3067 0.3093 0.3157 2.30 0.3264 0.3155 0.3128 0.3172, 'Put': 34 62 90 181 2.10 0.3952 0.4403 0.4740 0.4449 2.15 0.4013 0.4442 0.4794 0.4632 2.20 0.4121 0.4498 0.4802 0.4451 2.25 0.4200 0.4581 0.4863 0.4547 2.30 0.4426 0.4673 0.4893 0.4691} ``` ![](https://box.kancloud.cn/2016-07-30_579cbdbbb5536.png) ![](https://box.kancloud.cn/2016-07-30_579cbdbbd80e3.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，所以略顯粗糙 + 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