如何獲取期權市場數據快照 · Python 量化交易教程

# 如何獲取期權市場數據快照 > 來源：https://uqer.io/community/share/550274e4f9f06c7a9ae9a535 在本文中，我們將通過實際的市場的例子，展示如何在量化實驗室中計算和展示期權的隱含波動率微笑。 ```py import pandas as pd from matplotlib import pylab pd.options.display.float_format = '{:,>.4f}'.format ``` ## 1. 獲取市場數據在本節中，我們使用數據API獲取數據，并進行一些必要的數據轉換。這里我們獲取的是實時報價，是本 notebook 運行時的市場快照。 + `dataDate` 交易日 + `dataTime` 快照時間戳 + `optionId` 期權代碼 + `instrumentID` 期權交易代碼 + `contractType` 期權類型，CO為看著，PO為看跌 + `strikePrice` 行權價 + `expDate` 到期日 + `lastPrice` 最新價 ```py optionSnapShot = OptionsDataSnapShot() optionSnapShot[optionSnapShot.expDate == Date(2015,9,23)] ``` | | dataDate | dataTime | optionId | instrumentID | contractType | strikePrice | expDate | lastPrice | | --- | --- | | 30 | 2015-03-13 | 13:24:12 | 10000031 | 510050C1509M02200 | CO | 2.2000 | September 23rd, 2015 | 0.3388 | | 31 | 2015-03-13 | 13:24:17 | 10000032 | 510050C1509M02250 | CO | 2.2500 | September 23rd, 2015 | 0.3019 | | 32 | 2015-03-13 | 13:24:22 | 10000033 | 510050C1509M02300 | CO | 2.3000 | September 23rd, 2015 | 0.2816 | | 33 | 2015-03-13 | 13:24:27 | 10000034 | 510050C1509M02350 | CO | 2.3500 | September 23rd, 2015 | 0.2484 | | 34 | 2015-03-13 | 13:24:32 | 10000035 | 510050C1509M02400 | CO | 2.4000 | September 23rd, 2015 | 0.2070 | | 35 | 2015-03-13 | 13:24:36 | 10000036 | 510050P1509M02200 | PO | 2.2000 | September 23rd, 2015 | 0.0690 | | 36 | 2015-03-13 | 13:24:41 | 10000037 | 510050P1509M02250 | PO | 2.2500 | September 23rd, 2015 | 0.0804 | | 37 | 2015-03-13 | 13:24:47 | 10000038 | 510050P1509M02300 | PO | 2.3000 | September 23rd, 2015 | 0.0955 | | 38 | 2015-03-13 | 13:24:52 | 10000039 | 510050P1509M02350 | PO | 2.3500 | September 23rd, 2015 | 0.1194 | | 39 | 2015-03-13 | 13:24:58 | 10000040 | 510050P1509M02400 | PO | 2.4000 | September 23rd, 2015 | 0.1322 | | 46 | 2015-03-13 | 13:24:52 | 10000047 | 510050C1509M02450 | CO | 2.4500 | September 23rd, 2015 | 0.1889 | | 47 | 2015-03-13 | 13:24:58 | 10000048 | 510050P1509M02450 | PO | 2.4500 | September 23rd, 2015 | 0.1555 | | 54 | 2015-03-13 | 13:24:32 | 10000055 | 510050C1509M02500 | CO | 2.5000 | September 23rd, 2015 | 0.1629 | | 55 | 2015-03-13 | 13:24:36 | 10000056 | 510050P1509M02500 | PO | 2.5000 | September 23rd, 2015 | 0.1900 | | 62 | 2015-03-13 | 13:24:32 | 10000063 | 510050C1509M02550 | CO | 2.5500 | September 23rd, 2015 | 0.1443 | | 63 | 2015-03-13 | 13:24:36 | 10000064 | 510050P1509M02550 | PO | 2.5500 | September 23rd, 2015 | 0.2169 | ## 2. 計算隱含波動率以及相關Greeks 接著我們可以方便的使用內置函數 BSMImpliedVolatity 計算期權的隱含波動率。 + `price` 市場報價或者模型價格 + `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（每日） + `vega` 期權價格關于波動率的一階導數 ```py analyticResult = OptionsAnalyticResult() analyticResult.loc[:10, ['optionId', 'contractType', 'strikePrice', 'expDate', 'lastPrice', 'vol', 'delta', 'gamma', 'rho', 'theta', 'vega']] ``` | | optionId | contractType | strikePrice | expDate | lastPrice | vol | delta | gamma | rho | theta | vega | | --- | --- | | 1 | 10000002 | CO | 2.2500 | March 25th, 2015 | 0.2184 | 0.2259 | 0.9886 | 0.2947 | 0.0730 | -0.0458 | 0.0133 | | 2 | 10000003 | CO | 2.3000 | March 25th, 2015 | 0.1730 | 0.2867 | 0.9165 | 1.1965 | 0.0687 | -0.2996 | 0.0687 | | 3 | 10000004 | CO | 2.3500 | March 25th, 2015 | 0.1229 | 0.2177 | 0.8963 | 1.8495 | 0.0687 | -0.2670 | 0.0806 | | 4 | 10000005 | CO | 2.4000 | March 25th, 2015 | 0.0814 | 0.2166 | 0.7676 | 3.1504 | 0.0596 | -0.4503 | 0.1367 | | 8 | 10000009 | PO | 2.3500 | March 25th, 2015 | 0.0076 | 0.2482 | -0.1332 | 1.9373 | -0.0111 | -0.3633 | 0.0963 | | 9 | 10000010 | PO | 2.4000 | March 25th, 2015 | 0.0159 | 0.2346 | -0.2488 | 3.0197 | -0.0207 | -0.5061 | 0.1419 | | 10 | 10000011 | CO | 2.2000 | April 22nd, 2015 | 0.2778 | 0.2703 | 0.9081 | 0.7466 | 0.2152 | -0.1661 | 0.1347 | ## 3. 構造波動率曲面但是對于市場參與者而言，像剛才這樣僅僅觀察的線的結構不夠。他們需要看到整個市場以到期時間，行權價為軸的波動率曲面（Volatility Surface）。除此之外，他們更想知道，波動率曲面上，那些并不是市場報價點的值，至少是個估計。這樣的波動率曲面構造，往往需要依賴某種模型，或者某種插值方法。在這一節中，我們將介紹使用 CAL 中的波動率曲面構造函數。以下的例子基于 CAL 函數: `VolatilitySurfaceSnapShot` ### 3.1 基于SABR模型的波動率曲面 ```py volInterpolatorSABR = VolatilitySurfaceSnapShot(optionType = 'CALL', interpType = 'SABR') volInterpolatorSABR.plotSurface(startStrike = 2.2,endStrike = 2.6) volInterpolatorSABR.volalitltyProfileFromPeriods([2.2, 2.3, 2.4, 2.5, 2.6], ['1M', '2M', '3M', '6M', '9M']) ``` | | 1M | 2M | 3M | 6M | 9M | | --- | --- | | 2.2000 | 0.2720 | 0.2406 | 0.2327 | 0.2531 | 0.2545 | | 2.3000 | 0.2048 | 0.2207 | 0.2345 | 0.2546 | 0.2557 | | 2.4000 | 0.2245 | 0.2341 | 0.2389 | 0.2525 | 0.2533 | | 2.5000 | 0.2241 | 0.2328 | 0.2381 | 0.2479 | 0.2484 | | 2.6000 | 0.2311 | 0.2356 | 0.2362 | 0.2425 | 0.2429 | ![](https://box.kancloud.cn/2016-07-30_579cbdb8b73a6.png) ### 3.2 基于SVI模型的波動率曲面 ```py volInterpolatorSVI = VolatilitySurfaceSnapShot(optionType = 'CALL', interpType = 'SVI') volInterpolatorSVI.plotSurface(startStrike = 2.2,endStrike = 2.6) volInterpolatorSVI.volalitltyProfileFromPeriods([2.2, 2.3, 2.4, 2.5, 2.6], ['1M', '2M', '3M', '6M', '9M']) ``` | | 1M | 2M | 3M | 6M | 9M | | --- | --- | | 2.2000 | 0.2769 | 0.2476 | 0.2369 | 0.2566 | 0.2580 | | 2.3000 | 0.2121 | 0.2223 | 0.2340 | 0.2535 | 0.2545 | | 2.4000 | 0.2170 | 0.2292 | 0.2365 | 0.2504 | 0.2512 | | 2.5000 | 0.2290 | 0.2357 | 0.2389 | 0.2474 | 0.2479 | | 2.6000 | 0.2401 | 0.2417 | 0.2413 | 0.2508 | 0.2514 | ![](https://box.kancloud.cn/2016-07-30_579cbdb8eda62.png) ### 3.3 基于Balck波動率插值的波動率曲面 ```py volInterpolatorVariance = VolatilitySurfaceSnapShot(optionType = 'CALL', interpType = 'BlackVariance') volInterpolatorVariance.plotSurface(startStrike = 2.2,endStrike = 2.6) volInterpolatorVariance.volalitltyProfileFromPeriods([2.2, 2.3, 2.4, 2.5, 2.6], ['1M', '2M', '3M', '6M', '9M']) ``` | | 1M | 2M | 3M | 6M | 9M | | --- | --- | | 2.2000 | 0.2676 | 0.2380 | 0.2202 | 0.2516 | 0.2537 | | 2.3000 | 0.2082 | 0.2270 | 0.2441 | 0.2660 | 0.2672 | | 2.4000 | 0.2277 | 0.2325 | 0.2341 | 0.2404 | 0.2408 | | 2.5000 | 0.2278 | 0.2363 | 0.2408 | 0.2463 | 0.2466 | | 2.6000 | 0.2252 | 0.2324 | 0.2365 | 0.2517 | 0.2526 | ![](https://box.kancloud.cn/2016-07-30_579cbdb925a60.png) ## 4. 組合計算在本節中，我們假設客戶已經擁有了自己的期權頭寸，希望利用量化實驗室的功能進行風險監控。我們假設有以下的期權頭寸： | 期權代碼 | 數量 | 行權價（￥） | 到期時間 | | --- | --- | | 10000004 | -7000 | 2.35 | 2015-03-25 | | 10000011 | 2000 | 2.20 | 2015-04-22 | | 10000027 | 5000 | 2.25 | 2015-06-24 | | 10000047 | 3000 | 2.45 | 2015-09-23 | 然后我們構造 `OptionBook`: ```py optionIDs = ['10000011', '10000027', '10000004', '10000047'] amounts = [2000, 5000, -7000, 3000] optBook = OptionBook(optionIDs, amounts) print u'期權頭寸：' optBook.description() 期權頭寸： ``` | | dataDate | dataTime | optionId | instrumentID | contractType | strikePrice | expDate | lastPrice | amount | | --- | --- | | 0 | 2015-03-13 | 13:24:58 | 10000004 | 510050C1503M02350 | CO | 2.3500 | March 25th, 2015 | 0.1229 | -7000 | | 1 | 2015-03-13 | 13:24:32 | 10000011 | 510050C1504M02200 | CO | 2.2000 | April 22nd, 2015 | 0.2778 | 2000 | | 2 | 2015-03-13 | 13:24:52 | 10000027 | 510050P1506M02250 | PO | 2.2500 | June 24th, 2015 | 0.0450 | 5000 | | 3 | 2015-03-13 | 13:24:52 | 10000047 | 510050C1509M02450 | CO | 2.4500 | September 23rd, 2015 | 0.1889 | 3000 | ### 4.1 使用Black插值模型計算組合風險 ```py optBook.riskReport(volInterpolatorVariance) ``` | | optionId | vol | price | delta | gamma | rho | theta | vega | | --- | --- | | 0 | 10000004 | 0.2060 | -860.3000 | -6370.8417 | -12316.8687 | -488.8540 | 1592.3418 | -508.3851 | | 1 | 10000011 | 0.2634 | 555.6000 | 1828.2807 | 1456.7054 | 433.8000 | -307.9681 | 256.2961 | | 2 | 10000027 | 0.2484 | 220.5000 | -1103.5286 | 4552.0335 | -831.0864 | -856.2742 | 1945.3136 | | 3 | 10000047 | 0.2509 | 566.7000 | 1659.5347 | 2626.2983 | 1876.5865 | -503.9843 | 2135.1356 | | portfolio | NaN | nan | 482.5000 | -3986.5549 | -3681.8315 | 990.4461 | -75.8848 | 3828.3602 | ### 4.2 使用SABR模型組合風險 ```py optBook.riskReport(volInterpolatorSABR) ``` | | optionId | vol | price | delta | gamma | rho | theta | vega | | --- | --- | | 0 | 10000004 | 0.2157 | -865.4365 | -6301.5462 | -12703.7735 | -483.0602 | 1800.8937 | -549.0791 | | 1 | 10000011 | 0.2523 | 552.8686 | 1845.2432 | 1405.9255 | 438.6890 | -272.7679 | 236.9632 | | 2 | 10000027 | 0.2347 | 194.1368 | -1048.6009 | 4677.9921 | -785.3771 | -785.2668 | 1888.5079 | | 3 | 10000047 | 0.2511 | 566.9933 | 1659.5667 | 2624.8517 | 1876.4726 | -504.2584 | 2135.1279 | | portfolio | NaN | nan | 448.5622 | -3845.3372 | -3995.0043 | 1046.7243 | 238.6007 | 3711.5199 | ### 4.3 使用SVI模型組合風險 ```py optBook.riskReport(volInterpolatorSVI) ``` | | optionId | vol | price | delta | gamma | rho | theta | vega | | --- | --- | | 0 | 10000004 | 0.2126 | -863.7639 | -6323.4081 | -12591.1718 | -484.8898 | 1734.2876 | -536.4362 | | 1 | 10000011 | 0.2634 | 555.6000 | 1828.2807 | 1456.7054 | 433.8000 | -307.9681 | 256.2961 | | 2 | 10000027 | 0.2355 | 195.6318 | -1051.9049 | 4670.9045 | -788.1010 | -789.3710 | 1892.0017 | | 3 | 10000047 | 0.2495 | 563.6855 | 1659.2077 | 2641.2567 | 1877.7596 | -501.1669 | 2135.2142 | | portfolio | NaN | nan | 451.1534 | -3887.8246 | -3822.3052 | 1038.5689 | 135.7815 | 3747.0758 | ## 5 比較不同模型的擬合市場數據的能力這里我們比較不同的模型，對于市場數據的擬合能力。這里我們可以觀察到單論你和能力 `BlackVarianceSurface > SviCalibratedVolSruface > SABRCalibratedVolSruface `。這里我們并不想下這樣的結論：這些模型的優劣也有相同的排序。另一個我們可以觀察到的現象，對于近月合約（流動性最好），波動率微笑是最規則的。在這個期限上，三種模型的擬合都很到位。隨著期限的上升，流動性的下降，買賣價差也隨之擴大。這時候波動率微笑變得愈發不規則，這個時候一個完美擬合至市場的模型是否必要，是一個很大的問題：如果市場報價并不理性，一個優秀的模型應該可以指出這種不合理點，而不是簡單的接受市場的非理性。 ```py from matplotlib import pylab strikes = sorted(analyticResult['strikePrice'].unique()) expiries = [Date(2015,3,25),Date(2015,4,25),Date(2015,6,25),Date(2015,9,25)] maturity = [(date - EvaluationDate())/ 365.0 for date in expiries] volSurfaces = [volInterpolatorSABR, volInterpolatorSVI] def plotModelFitting(index, volSurfaces, legends = ['Market Quote', 'SABR', 'SVI']): # Using Black variance surface to extrace the rar wolatility data = volInterpolatorVariance.volatility(strikes, maturity[index], True) pylab.plot(strikes, data, 'r+-.', markersize = 8) for s in volSurfaces: data = s.volatility(strikes, maturity[index], True) pylab.plot(strikes, data) pylab.xlabel('Strike') pylab.ylabel('Volatility') pylab.legend(legends, loc = 'best', fontsize = 12) pylab.title(u'行權結算日: ' + str(expiries[index]), fontproperties = font, fontsize = 20) pylab.grid(True) pylab.subplots(2,2, figsize = (16,14)) for i in range(1,5): pylab.subplot('22' + str(i)) plotModelFitting(i-1, volSurfaces) ``` ![](https://box.kancloud.cn/2016-07-30_579cbdb959f20.png)