r - 股票 - 计算时间序列的波动率

Question

我有一个简单的股票价格数据集，其中 Col1 代表日期，Col2 代表回报（收盘价 D/收盘价 D-1，与 Python 中的 pct_change 相同），Col3 代表 Ewma 波动率。我正在处理预测并绘制收益与 Ewma 波动率，但阅读一些文章后我意识到我需要绘制每日波动率 x Ewma 波动率，以便我可以更清楚地看到预测

所以我想看到这样的图表，但在红色中我有回报，而不是它，我需要红线是通过普通方法（简单 Vol）计算的波动率。黑色是 MTS::EWMAvol 包计算的 EwmaVol。

这是数据：

structure(list(date = structure(c(18515, 18516, 18520, 18521, 
18522, 18523, 18526, 18527, 18528, 18529, 18530, 18533, 18534, 
18535, 18536, 18537, 18540, 18541, 18542, 18543, 18544, 18547, 
18548, 18549, 18550, 18551, 18554, 18555, 18556, 18557, 18558, 
18561, 18562, 18563, 18564, 18565, 18568, 18569, 18570, 18571, 
18572, 18575, 18576, 18577, 18578, 18579, 18582, 18583, 18584, 
18585, 18586, 18589, 18590, 18591, 18592, 18593, 18596, 18597, 
18598, 18599, 18600, 18603, 18604, 18605, 18606, 18607, 18610, 
18611, 18612, 18613, 18614, 18617, 18618, 18619, 18620, 18621, 
18624, 18625, 18626, 18627, 18628, 18631, 18632, 18633, 18634, 
18635, 18638, 18639, 18640, 18641, 18642, 18645, 18646, 18647, 
18648, 18649, 18652, 18653, 18654, 18655, 18656, 18659, 18660, 
18661, 18662, 18663, 18666, 18667, 18668, 18669, 18670, 18673, 
18674, 18675, 18676, 18677, 18680, 18681, 18682, 18683, 18684, 
18687, 18688, 18689, 18690, 18691, 18694, 18695, 18696, 18697, 
18698, 18701, 18702, 18703, 18704, 18705, 18708, 18709, 18710, 
18711, 18712, 18715, 18716, 18717, 18718, 18719, 18722, 18723, 
18724, 18725, 18726, 18729, 18730, 18731, 18732, 18733, 18736, 
18737, 18738, 18739, 18740, 18743, 18744, 18745, 18746, 18747, 
18750, 18751, 18752, 18753, 18754, 18757, 18758, 18759, 18760, 
18761, 18764, 18765, 18766, 18767, 18768, 18771, 18772, 18773, 
18774, 18775, 18778, 18779, 18780, 18781, 18782, 18785, 18786, 
18787, 18788, 18789, 18792, 18793, 18794, 18795, 18796, 18799, 
18800, 18801, 18802, 18803, 18806, 18807, 18808, 18809, 18810, 
18813, 18814, 18815, 18816, 18817, 18820, 18821, 18822, 18823, 
18824, 18827, 18828, 18829, 18830, 18831, 18834, 18835, 18836, 
18837, 18838, 18841, 18842, 18843, 18844, 18845, 18848, 18849, 
18850, 18851, 18852, 18855, 18856, 18857, 18858, 18859, 18862, 
18863, 18864, 18865, 18866, 18869, 18870, 18871, 18872, 18873, 
18876, 18877, 18878, 18879, 18880, 18883, 18884), class = "Date"), 
    Retorno = c(-0.675993561014219, 0.00727122549799243, 0.0200646939724594, 
    -0.309572944244751, -0.240552943912361, -0.22033250472985, 
    -0.361838491629178, 0.425326793664922, -0.467655896347618, 
    0.184647131258419, 0.289993731622618, -0.247917340719569, 
    -0.266792070525439, 0.408121976560422, 0.432634049112388, 
    -0.526936711212769, 0.255443464814248, -0.277205195648874, 
    0.237634551321446, 0.416255267136204, 0.182381045120273, 
    0, 0.559328565933268, 0.22352526750161, 0.0344661931237814, 
    -0.0114765743015762, -0.340659866250595, 0.518121135418651, 
    0.124920612225829, 0.060477879624518, -0.132268000351469, 
    -0.419044186141948, -0.0468465628669677, -1.24962920487573, 
    0.519314480623082, -0.83241356610111, 0, 0.677072797328314, 
    0.770362872443658, 0.779540076578319, -0.128308411797546, 
    0.208939823146876, -0.313737425389519, 0.218322415089412, 
    -0.69034693281341, 0.812758658841942, 0.167317931481811, 
    -0.208730841632264, -0.387374906435024, 0.145599821661092, 
    0.107177528022895, 0.381307385634918, 0.386256536259558, 
    0.160935467100042, 0.0370218344118541, 0.241511701069377, 
    -0.33376949245172, 0.162429122410115, 0.189409487756105, 
    -0.136073192422632, 0.221928418309387, -0.294157383734931, 
    0.293123696475209, -0.308081743475511, -0.0160523988860364, 
    0.200830763685225, 0.215786923768921, 0.467113206724325, 
    0.405886001764272, 0.105544246268935, -0.128010524950925, 
    -0.195222854432975, 0.202533534363647, 0.36037155474833, 
    0.0195551377992495, 0, 0.386574054270276, -0.0520687967679869, 
    0.134723231050616, -0.0105062746232602, 0, -0.0867476700402434, 
    0.0959051831633806, -0.792631919080304, 0.714335671518634, 
    1.00993938236837, -0.129261214344111, 0.124684691358913, 
    -0.183903752322858, -0.0658608900095052, -0.160979643574251, 
    0.19290543725798, 0.251171599859635, 0.230012814573936, 0.00867119071736477, 
    -0.00849157305596641, -0.0662645178280147, -0.325684851940853, 
    -0.63526581976692, 0.987392935674623, -0.71566845639813, 
    0.823448032203283, 0.364849774654681, 0.493861329996562, 
    0.429481174502912, 0.392845558392575, 0.18687659266044, -0.0496962834358631, 
    -0.351476870541759, 0.325056528852312, 0.0540948459475099, 
    0, 0, 0.298660972132666, -0.129176783491061, 0.0936264785031788, 
    -0.717102311834032, 0.0579970685670885, 0.2387869198789, 
    -0.800077283233545, -0.346606771876278, 0.652393650772446, 
    0.019543204729203, -0.186097235985271, -0.401338954104801, 
    0.770468206437961, -1.16143407489768, 0.287520645270323, 
    -0.180982644002469, 0.636164450379635, -0.167036272711984, 
    0.273933259257009, 0.0018679680615165, 0.401511529829268, 
    -1.0714528798559, 0.225507468509173, -0.0998873705026633, 
    -0.357468921258203, -0.453208884721668, 0.584325924664598, 
    0.294490804371817, -0.071870245489955, 0.227731039838296, 
    0.0272554279847483, 0.282891030886757, 0, 0.444572787367717, 
    0.107513540207911, 0.204070787509094, 0.290177231896655, 
    0.314121770459557, 0.294143400791366, 0.0423074542633505, 
    -0.111752005968369, 0.191432961182637, 0.107012720814761, 
    -0.221435538762791, -0.287455618822024, 0, -0.504458868407395, 
    0.576189122256037, 0.0513721502072407, -0.0878347180967137, 
    0.0305926251264597, 0.0409984249091759, -0.0507344439032554, 
    0.127910054528995, -0.33110581208469, 0.244321197674869, 
    -0.153002648530627, 0.550660961815173, -0.39137091346195, 
    0.00655796886117349, -1.07175015625675, 0.47234018769347, 
    0.457477961736975, 0.194987471696463, -0.192289243894243, 
    -0.100966714379365, 0.295535636777222, 0.0497612954361652, 
    0.424646083712068, -0.0235816065166123, 0.148925361065251, 
    0.0833499347084376, 0.162437322657595, 0.216822541199244, 
    -0.0266349635355871, -0.0203718557462801, 0, 0.163246069746882, 
    0.0540313182825264, -0.132667149729679, -0.0106752473427232, 
    0.0966877877911841, -0.0135235065561488, 0.286749500028446, 
    -0.123925251554195, -0.0750149494882748, -0.00131099907860658, 
    0.0788369651503004, 0.310420308737175, 0.0738549668615309, 
    -0.0388124917441666, 0.156992583882095, -0.158341400377075, 
    0.138832514569506, 0.0484161074075555, 0.0644817162954546, 
    -0.075831329755838, 0.594706467883038, 0.0582157771824145, 
    -0.224095914091399, 0.433246293201151, -0.340500528636388, 
    0.0408415756500143, 0.45961172993559, 0.136168616599819, 
    0.0264246421863121, -0.0041223988663561, -0.273325208808114, 
    -0.429764244359346, 0.318952765660581, 0.152571137442228, 
    0.378021240701817, -0.0502434439840156, -0.284587147638002, 
    -0.549313963668678, 0.024940657477001, 0.106379612006064, 
    -0.666213312763818, 0.101187879104207, 0.212900264239358, 
    -0.319050618049279, 0.151814926005171, 0.165719848192862, 
    0.111396078192044, -0.192914594549868, -0.0785555116791173, 
    -0.0633138947667031, -0.100685336741663, -0.70572669007387, 
    -0.636169672803793, -0.0256706550272056, 0.568449636874711, 
    0.431844471002692, -0.0884432149109783, 0.507974104651909, 
    0.253656436799725, -0.551492331609423, 0.473346006073304, 
    -0.230628440542497, -0.36475396210053, 0.0553706780422077, 
    -0.458282184750842, 0.127876503287846, 0.329153343062354, 
    0, -0.640854284349025, 0.314530520275267, -0.547495384943616, 
    0.532252306040703, 0), EwmaVol = c(0.401545880470543, 
    0.37957402999614, 0.357002237552554, 0.336710024448518, 0.318760036517056, 
    0.316732889747995, 0.306462909109581, 0.288335641955465, 
    0.285974951159514, 0.27897153978688, 0.26226816859379, 0.285059883553795, 
    0.272374799205532, 0.268378720050093, 0.262349047774286, 
    0.258978405250914, 0.253148786729867, 0.238963348264941, 
    0.225541112253008, 0.234992747615912, 0.222414110918961, 
    0.209069264263823, 0.206230071488549, 0.20121898142488, 0.189404201517459, 
    0.179625218204264, 0.169480509616124, 0.174732838517365, 
    0.164762013463212, 0.156538802813315, 0.153370969102807, 
    0.145432704491324, 0.14287274912088, 0.21547817272594, 0.214028935828116, 
    0.234147750804581, 0.220098885756306, 0.21209598867207, 0.242287370393438, 
    0.261087909529102, 0.248230680408422, 0.243595317635679, 
    0.230164613514584, 0.217002608357163, 0.22967146650814, 0.248916351205143, 
    0.239617766167996, 0.225423319002878, 0.218347622569303, 
    0.206598225427181, 0.196302279540574, 0.185030606442786, 
    0.188266218750961, 0.181245068143354, 0.17041364058184, 0.161095631643361, 
    0.160389804076746, 0.156316917381599, 0.14852488563309, 0.142019675657794, 
    0.133567051476024, 0.125838895726541, 0.11969455573153, 0.119360323208544, 
    0.11750261880258, 0.112148663686316, 0.108243847740347, 0.115163834443589, 
    0.116212022405643, 0.109409013330819, 0.104496900700937, 
    0.10935285581462, 0.105502302791016, 0.101242444242857, 0.09516847810389, 
    0.0894583694176566, 0.0866069786756536, 0.0817380126900134, 
    0.0773367431654428, 0.0726971569867781, 0.0683353275675715, 
    0.0697812759496627, 0.067691476973121, 0.129966833467446, 
    0.126803399533392, 0.171461998066648, 0.171739783002973, 
    0.197564652471901, 0.189022309519642, 0.179950836609547, 
    0.170183058064679, 0.164266188880656, 0.155101252531341, 
    0.148693223428185, 0.14012494879068, 0.133740625026294, 0.125716772617523, 
    0.119105020311106, 0.117086850187538, 0.145347969102275, 
    0.152463434186314, 0.158687203287356, 0.152449871680205, 
    0.166738452722435, 0.158612506047059, 0.160075907173878, 
    0.151254857380356, 0.142343596709454, 0.142934873378322, 
    0.142665594947683, 0.134145123063853, 0.126096415680022, 
    0.118530630739221, 0.112499802745561, 0.110940338230715, 
    0.104545755177033, 0.135780351022354, 0.133312910743497, 
    0.125726130222031, 0.153200898521969, 0.159065047312098, 
    0.155282128215572, 0.146884947547679, 0.138117117632574, 
    0.130622632663405, 0.152186093616364, 0.253518876239024, 
    0.238323024716563, 0.227569746334944, 0.248057416617638, 
    0.234104106541416, 0.221001436475852, 0.208519869481825, 
    0.209685706242652, 0.239728740398097, 0.234167233383272, 
    0.224220956969507, 0.216318345630569, 0.223196193500169, 
    0.224922152734894, 0.212452796555951, 0.200672435018375, 
    0.197518356826799, 0.188183960822706, 0.177785419155766, 
    0.16711829400642, 0.169717068257208, 0.166026638555189, 0.156957479697871, 
    0.153622766010829, 0.14469286668481, 0.138471748094382, 0.131579951121295, 
    0.124018474660646, 0.120182498675561, 0.113234218642543, 
    0.107149115926987, 0.101721766522229, 0.095618460530895, 
    0.0999442416592745, 0.101574073875603, 0.0957296378477016, 
    0.093118066436934, 0.0914320009168463, 0.0871185787307817, 
    0.0823469513367038, 0.0811192489506884, 0.0825047887866796, 
    0.0860049643565581, 0.0808493443261423, 0.0961929240668569, 
    0.0911638648549433, 0.0857640508042613, 0.104905012906323, 
    0.114721311495374, 0.109831409732472, 0.104612358275864, 
    0.0993594406351853, 0.0946255646854852, 0.0895721816070949, 
    0.0845410520311026, 0.0838606211253721, 0.0789729132909391, 
    0.0747186193653219, 0.0705734402792115, 0.0688594831676326, 
    0.0657400666843101, 0.0634447557051325, 0.0633681690044842, 
    0.0595660788642152, 0.0603886782791013, 0.0587833071039431, 
    0.057511124086288, 0.0543325953300019, 0.0512261329106077, 
    0.0491856952988916, 0.0510463463396217, 0.0487190552131411, 
    0.047891041488347, 0.0467019683194386, 0.0466241053525344, 
    0.0456515495748067, 0.0431468387328283, 0.041317889619408, 
    0.0452423873993231, 0.0486383165176941, 0.0479392218342959, 
    0.0454006830162697, 0.0435713468777161, 0.0419873301594818, 
    0.0536531567181674, 0.0506716342092926, 0.0562970018467919, 
    0.0684016291611351, 0.0674546466335945, 0.0634076483792872, 
    0.067163694596286, 0.0640197920338736, 0.061921707762386, 
    0.0589219002148625, 0.0567269880819515, 0.0678661716944311, 
    0.0660541475889322, 0.062251261441256, 0.0624556318584788, 
    0.0635712086121672, 0.0630732335813346, 0.0691297797235716, 
    0.0653096157302932, 0.0636744930080208, 0.0944386419928364, 
    0.0915130579751466, 0.0863295417576338, 0.0867829530305672, 
    0.0839894020970701, 0.0791825005794653, 0.0766098726649444, 
    0.0753903595328056, 0.0733451437270916, 0.0693926680771279, 
    0.0664728433228, 0.0956887810320563, 0.0954558159033218, 
    0.0922581275391543, 0.09091195032168, 0.0929899977659706, 
    0.091341181932747, 0.131126103751573, 0.129655613187944, 
    0.148447176829185, 0.153225134955549, 0.153634505982304, 
    0.160933771494317, 0.151965634321099, 0.167395816107282, 
    0.160837085230127, 0.167419121889831, 0.157373974576441, 
    0.217309648664878, 0.211280213400328, 0.212032193587911, 
    0.22982849323927, 0.216038783644914)), class = "data.frame", row.names = c(NA, 
-263L))

现在，我需要有一列包含资产的每日波动率。

在 R 中最简单的方法是什么？

标签： rtime-seriesstockstandard-deviationvolatility

Answer 1

波动率是给定时期内回报的（通常是年化的）标准差。波动率的确切定义取决于一些惯例（百分比回报与对数回报、天数惯例），这在很大程度上取决于您的上下文。

当我们谈论波动性时，我们不太清楚我们在谈论什么

根据您的数据，可以使用zoo函数计算一些波动率指标rollapply。请注意这里的示例不符合大多数约定（您通常会乘以sqrt(daycount/horizon)年化）

library(zoo)
library(ggplot2)
#Define a horizon for volatility calculation, e.g. 20 days
horizon = 20

#Note: volatility is not annualized!
data['vols'] = c(rep(NA, horizon-1), rollapply(as.vector(data$Retorno), horizon, FUN = function(x) sd(x)))

#Alternatively, calculate some measure of day-to-day change in return that is not a volatility
data['not_a_vol'] = abs(data$Retorno - lag(data$Retorno))

然后，您可以将结果绘制为：

ggplot() + 
  geom_bar(aes(x=data$date, y=data$Retorno), stat = 'Identity') + 
  geom_line(aes(x = data$date, y= data$vols, color = 'red'), lwd=1.5)

您的分析似乎朝着波动率分析的方向发展，因此您可能会发现 GARCH 模型或波动率指数移动平均线很有趣。