volatility

秒懂歷史波動率(HV)和隱含波動率(IV)的差別

當你要從交易選擇權獲利時,最基本的常識是在高隱含波動率(高IV)的時候賣選擇權,在低IV的時候買選擇權。

但你知道市場波動率存在的意義,以及波動率如何影響期權價格嗎?

我們認為認識市場波動率是選擇權獲利的第一步,我們將深入探討什麼是市場波動率,以及歷史波動率(HV)和隱含波動率(IV)的差別。

什麼是波動率?

波動率代表數據分散程度的統計概念,所以通常用來描述一個股票價格漲跌的幅度,以數學的理論來看,波動率等於是統計數據的偏差值。

Thinkorswim分析個股的選擇權時,會看到幾個不同的市場波動率數據,其中最重要的就是歷史波動率(HV)和隱含波動率(IV)。

HV和IV有什麼不一樣?

HV是用過去股價波動的標準差計算的波動率,而IV是個向前看的預測波動指標。

如何計算歷史波動率(HV)?

如果你像我一樣已經離開高中很久了,我們來一步步的重溫高中數學並計算一個股票的波動率。

我們參考最近BABA一系列的收盤價來計算股價的波動率,使用歷史資料計算的波動率通常稱為歷史波動率(HV)。

首先用最近10個交易日的BABA收盤價計算每天價格變化的百分比。

交易日收盤價當日價格變化
10/4139.63
10/5143.142.5%
10/6144.100.7%
10/7156.008.3%
10/8161.523.5%
10/11163.951.5%
10/12163.00-0.6%
10/13167.402.7%
10/14166.78-0.4%
10/15168.000.7%

我們將這10天價格變化的標準差計算出來為2.54%。

因為每年約有252個交易日,所以我們把2.54%的標準差修正為年的標準差40.3%,就等於HV。

annual standard deviation as hv

我們可以用我們計算的HV數據對照Thinkorswim分析出來的HV數據。

baba options statistics
用Thinkorswim分析選擇權數據時會列出每個股票的波動率。

用HV Percentile的公式我們看到我們計算的HV和Thinkorswim的數據是很接近的。

hv percentile calculations

如果我們把熟悉的常態分佈圖找出來,我們知道一個隨機的數據有50%會在平均值的左邊,有50%會出現在平均值的右邊。

normal distribution and standard deviations
標準差在常態分布中定義數據位置的機率。

在平均值左右一個標準差(σ)的範圍會涵蓋68%的數據,而數據會落在+/-2σ的機率是95%。

以現在BABA價格是$158.73,HV是40%,我們有把握接下來一年內BABA收盤價有68%的機率會落在$95.24和$222.22之間。

只要過去BABA的股價波動的標準差變大,HV就會變高,表示較高的波動率。

反之如果BABA的股價標準差變小,HV就會變低,表示波動率變小。

隱含波動率(IV)如何影響選擇權價格?

選擇權價格是隱含波動率(IV)的函數,而IV是市場對股價未來波動性的看法,是用選擇權定價模型回推IV的數據。

我們都知道選擇權是一個在合約價買賣股票的權利,這個權利的價值會跟金流以及股息、利息的機會成本有關。

世界知名的Black-Scholes model是受諾貝爾經濟學獎肯定的選擇權定價模型,它以一個對數常態分佈(log-normal)來看待選擇權價格,因為價格不會小於0,而且有價格越大出現的機率越接近0的長尾效益。

log normal distribution
對數常態分布數值不會小於0,數值越大機率越接近0。

Call和Put選擇權價格的計算方式如下:

black-scholes options price
  • σ = IV
  • δ = 股息
  • S = 股價
  • K = 合約價
  • r = 無風險利率
  • T = 距離截止的時間(年)
  • N = 常態分布
  • N(d1) = 期權在價內截止時現金和股票流動的期待值
  • N(d2) = 期權在價內截止的機率

我們用AAPL股價為例計算價平$150、39天後截止的Call,並使用Thinkorswim的期權鏈來驗證我們的計算。

  • σ = 22.38%
  • S = $151.28
  • K = $150
  • r = 0.04%
  • T = 39/365 = 0.106849
  • d1 = 0.153314
  • d2 = 0.080158
  • N(d1) = 0.56
  • N(d2) = 0.53
  • C(39) = $5.05
aapl option chain bid ask IV
11/8開盤前的AAPL期權鏈。

你可能會注意,我們計算出來的Call價格$5.05是在買進價(bid)$4.90和賣出價(ask)$5.15之間。

可是到底是先有Call選擇權價格還是先有IV?

事實上在股票市場的莊家(Market Maker)會蒐集所有交易平台,例如德美利證劵、第一證劵、盈透證劵、Robinhood等的交易訂單,再根據Put和Call的供需訂定出價平的期權價格。

在訂定出價平的期權價格後,就可以用Black-Scholes模型推算出隱含波動率,從AAPL的例子來看,針對不同的IV數據,可以反覆推算出不同的Call價格。

IVCall價格
10%2.67
30%6.56
50%10.47
70%14.37
90%18.27

我們看到以$5.05的Call價值,IV應該在10%-30%之間。

IV interpolation
用10%和30%的IV以及Call價格推算出正確的IV是22.30%。

我們再用$5.05推算出現在正確的IV為22.30%,也就是市場對股價未來波動的預測。

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SymbolIVIV PercIV RankTotal Options VolumeCall Options VolumePut Options VolumeOpen InterestDays To/Since EarningsEarnings Date
AA65%70%46%15,0919,4065,685112,551922026-07-222026-06-182026-04-21
AAL66%85%3%171,64989,02882,6211,885,52622026-04-232026-06-182026-04-21
AAOI164%94%61%36,47215,55020,92287,916162026-05-072026-06-182026-04-21
AAPL31%76%2%1,408,1201,019,503388,6173,592,09992026-04-302026-06-182026-04-21
ABBV37%90%9%11,8068,0073,799151,80382026-04-292026-06-182026-04-21
ABNB48%82%42%8,9565,7433,21394,763162026-05-072026-06-182026-04-21
ABT25%56%0%18,60212,2886,31497,380862026-07-162026-06-182026-04-21
ABVX103%65%41%6,7604,9681,79230,498342026-05-252026-06-182026-04-21
ACN50%86%58%7,6323,5924,04043,019582026-06-182026-06-182026-04-21
ADBE46%80%38%48,11136,04612,065253,330512026-06-112026-06-182026-04-21
ADI41%66%46%14,43010,2624,16831,331362026-05-272026-06-182026-04-21
ADM39%75%98%1,22894828025,358142026-05-052026-06-182026-04-21
ADMA77%60%40%1,09954455542,329222026-05-132026-06-182026-04-21
AEHR144%66%94%13,6539,4654,18836,615912026-07-212026-06-182026-04-21
AEM50%78%53%5,5612,4093,15242,74792026-04-302026-06-182026-04-21
AEO57%21%17%9,1434,2974,84636,332362026-05-272026-06-182026-04-21
AES17%2%100%4,4984,00349575,76792026-04-302026-06-182026-04-21
AFRM95%87%52%21,94615,0726,874174,315162026-05-072026-06-182026-04-21
AG90%63%57%50,02938,48911,540525,578212026-05-122026-06-182026-04-21
AGI49%54%0%3,6493,08156826,46282026-04-292026-06-182026-04-21
AGIO79%33%3%2,6971,6321,06535,69282026-04-292026-06-182026-04-21
AGNC35%56%19%23,88912,27211,617329,365972026-07-272026-06-182026-04-21
AKAM68%86%0%6,2074,9001,30750,384162026-05-072026-06-182026-04-21
ALAB103%85%54%12,2047,7184,48685,237142026-05-052026-06-182026-04-21
ALB62%50%37%8,1712,1436,02867,641152026-05-062026-06-182026-04-21
ALK67%80%3%9,4124,4244,98845,103862026-07-162026-06-182026-04-21
AMAT60%89%0%20,07810,2179,861154,297232026-05-142026-06-182026-04-21
AMD56%61%87%462,669283,877178,7922,204,472142026-05-052026-06-182026-04-21
AMGN38%92%43%8,9073,6235,28435,99992026-04-302026-06-182026-04-21
AMKR81%80%34%7,8722,8515,02149,38462026-04-272026-06-182026-04-21
AMPX107%36%97%43,33538,7144,621187,478162026-05-072026-06-182026-04-21
AMZN43%85%0%667,579399,794267,7854,170,98282026-04-292026-06-182026-04-21
ANET59%72%38%26,11518,1997,916160,512142026-05-052026-06-182026-04-21
APA49%48%0%14,72112,5572,164106,000152026-05-062026-06-182026-04-21
APG41%56%36%1401093130,60592026-04-302026-06-182026-04-21
APH57%83%57%5,4442,6582,78656,02982026-04-292026-06-182026-04-21
APLD112%47%38%108,56173,87134,690573,7191212026-08-202026-06-182026-04-21
APO66%96%72%8,2475,0633,184145,482152026-05-062026-06-182026-04-21
APP86%82%32%51,82440,37311,451135,046152026-05-062026-06-182026-04-21
AR53%76%36%3,4502,48596539,47882026-04-292026-06-182026-04-21
ARCC32%53%0%7,8562,3875,469101,73372026-04-282026-06-182026-04-21
ARES57%73%46%5,1982,7202,47840,205102026-05-012026-06-182026-04-21
ARM88%97%81%151,938122,59729,341449,585152026-05-062026-06-182026-04-21
ASML57%90%63%16,3305,63710,69355,352852026-07-152026-06-182026-04-21
ASST132%67%92%16,07912,2503,8291,590,824432026-06-032026-06-182026-04-21
ASTS107%62%48%333,073227,798105,275735,094272026-05-182026-06-182026-04-21
ASX49%12%88%2,9072,28462331,08822026-04-232026-06-182026-04-21
AVGO41%31%17%226,307106,784119,5231,300,120442026-06-042026-06-182026-04-21
AVTX445%97%87%2,2213991,82269,20892026-04-302026-06-182026-04-21
AXP36%80%58%11,3676,0315,33695,59322026-04-232026-06-182026-04-21
AXTI222%85%0%20,99212,6838,309148,34592026-04-302026-06-182026-04-21
B46%57%47%15,7627,1928,570328,548202026-05-112026-06-182026-04-21
BA50%99%73%69,62537,73031,895590,99912026-04-222026-06-182026-04-21
BABA46%60%46%77,71354,69523,0181,149,140232026-05-142026-06-182026-04-21
BAC24%29%100%106,21752,67453,5431,574,160842026-07-142026-06-182026-04-21
BAX58%81%48%2,7391,3651,37440,89992026-04-302026-06-182026-04-21
BBY37%28%100%6,3503,6912,65939,798362026-05-272026-06-182026-04-21
BCS50%80%91%2,5101,1381,37238,63172026-04-282026-06-182026-04-21
BE122%75%1%66,49740,30226,195363,42372026-04-282026-06-182026-04-21
BIDU67%97%0%13,3709,2414,129129,913282026-05-192026-06-182026-04-21
BILI56%32%32%4,4821,9902,49226,590362026-05-272026-06-182026-04-21
BILL87%71%51%6,6054,4632,14227,93792026-04-302026-06-182026-04-21
BKNG51%92%64%15,9649,6456,319101,69272026-04-282026-06-182026-04-21
BMNR97%42%17%188,133124,37263,7611,227,932992026-07-292026-06-182026-04-21
BMY38%83%58%18,0859,0039,082285,60692026-04-302026-06-182026-04-21
BP40%91%10%9,6106,8002,810214,44072026-04-282026-06-182026-04-21
BRK-B17%66%35%44,33732,57911,758379,0052026-06-182026-04-21
BROS69%74%99%5,8442,9352,90932,553152026-05-062026-06-182026-04-21
BSX57%98%83%17,84110,8197,022159,00912026-04-222026-06-182026-04-21
BTDR212%99%3%8,2357,253982397,686272026-05-182026-06-182026-04-21
BTU65%46%31%9,3174,9504,36727,564142026-05-052026-06-182026-04-21
BW125%38%100%4,8663,7911,07532,480162026-05-072026-06-182026-04-21
BX47%80%96%13,6657,1376,528190,77522026-04-232026-06-182026-04-21
C36%77%55%41,24321,33219,911700,116842026-07-142026-06-182026-04-21
CAG38%70%45%12,4547,5724,882111,614792026-07-092026-06-182026-04-21
CAR243%100%100%89,92622,82667,100136,514132026-05-042026-06-182026-04-21
CARR43%66%0%1,5971,42117637,79592026-04-302026-06-182026-04-21
CART62%78%29%14,16811,6402,52826,972152026-05-062026-06-182026-04-21
CAT45%90%74%23,5409,58913,951112,40692026-04-302026-06-182026-04-21
CAVA67%75%34%7,1425,0392,10360,459422026-06-022026-06-182026-04-21
CC70%26%100%46,10844,5731,53524,443142026-05-052026-06-182026-04-21
CCJ66%82%1%11,6726,9564,716208,063142026-05-052026-06-182026-04-21
CCL62%89%14%48,65030,36918,281679,848702026-06-302026-06-182026-04-21
CDE76%23%6%18,78612,9035,883308,801152026-05-062026-06-182026-04-21
CDNS99%100%100%7,7626,2401,52243,48262026-04-272026-06-182026-04-21
CEG53%52%37%12,6873,9528,73595,262202026-05-112026-06-182026-04-21
CELH75%83%46%41,06427,76713,297335,847212026-05-122026-06-182026-04-21
CF54%84%42%14,35011,4572,89357,900152026-05-062026-06-182026-04-21
CG57%71%0%4,1671833,98465,883162026-05-072026-06-182026-04-21
CGON114%64%47%2302082224,955162026-05-072026-06-182026-04-21
CHTR98%98%78%5,5512,3563,19541,41532026-04-242026-06-182026-04-21
CHWY55%70%40%28,10423,9264,178133,460432026-06-032026-06-182026-04-21
CHYM89%45%22%1,08378929441,737152026-05-062026-06-182026-04-21
CI39%74%1%2,5281,3581,17028,48492026-04-302026-06-182026-04-21
CIFR138%89%55%159,804117,44742,357869,775212026-05-122026-06-182026-04-21
CL30%87%100%2,4801,2401,24038,153102026-05-012026-06-182026-04-21
CLS90%85%50%15,5739,2016,37241,02262026-04-272026-06-182026-04-21
CLSK112%80%23%38,36729,3728,995525,421162026-05-072026-06-182026-04-21
CLX38%68%100%4,7083,2501,45826,20992026-04-302026-06-182026-04-21
CMCSA51%95%2%16,0609,1396,921274,72922026-04-232026-06-182026-04-21
CMG55%91%52%25,3299,20716,122438,85882026-04-292026-06-182026-04-21
CNC63%82%1%10,0467,9342,112138,61372026-04-282026-06-182026-04-21
CNH64%16%10%1988011837,89492026-04-302026-06-182026-04-21
CNQ37%71%99%5,2724,57369952,113162026-05-072026-06-182026-04-21
CODI103%65%28%3,1622,99017281,210152026-05-062026-06-182026-04-21
COF57%99%77%9,6873,9225,765126,01102026-04-212026-06-182026-04-21
COHR102%87%64%18,1584,94913,20967,306222026-05-132026-06-182026-04-21
COIN80%92%54%221,808182,19239,616700,963162026-05-072026-06-182026-04-21
COP37%80%41%29,43421,9267,508174,50692026-04-302026-06-182026-04-21
COPX68%88%97%3,2211,9111,31055,4462026-06-182026-04-21
CORZ79%31%1%77,93262,21315,7191,091,762222026-05-132026-06-182026-04-21
COST21%38%27%26,96212,84614,116111,317992026-07-292026-06-182026-04-21
CPB43%88%100%22,9788,25814,72097,280502026-06-102026-06-182026-04-21
CPNG55%79%100%9,0397,0172,022225,906212026-05-122026-06-182026-04-21
CPRI51%16%35%2,4011,73666581,075432026-06-032026-06-182026-04-21
CRCL99%78%27%70,04746,48623,561444,488202026-05-112026-06-182026-04-21
CRDO103%78%0%31,86419,24012,624127,078432026-06-032026-06-182026-04-21
CRGY79%6%8%2,3662,17918728,910132026-05-042026-06-182026-04-21
CRM46%75%96%84,04351,03533,008602,185432026-06-032026-06-182026-04-21
CRML117%0%0%33,76824,9168,852214,8501342026-09-022026-06-182026-04-21
CRWD52%76%45%30,08716,78313,304180,947492026-06-092026-06-182026-04-21
CRWV97%54%27%207,406121,89885,5081,438,470162026-05-072026-06-182026-04-21
CSCO29%66%97%70,43054,58715,843468,253292026-05-202026-06-182026-04-21
CSX51%95%15%6,2795,29298770,70612026-04-222026-06-182026-04-21
CTRA40%66%99%1,5191,08543444,39592026-04-302026-06-182026-04-21
CVE33%17%56%1,3921,28410835,40992026-04-302026-06-182026-04-21
CVNA91%85%48%38,78916,89521,894197,03482026-04-292026-06-182026-04-21
CVS36%70%99%22,31916,2876,032190,596152026-05-062026-06-182026-04-21
CVX34%90%0%49,88133,48216,399427,090102026-05-012026-06-182026-04-21
CWAN27%12%64%5531054362,525152026-05-062026-06-182026-04-21
CYTK173%96%98%2,6181,2651,35359,00892026-04-302026-06-182026-04-21
CZR59%59%0%24,53213,79010,742127,65372026-04-282026-06-182026-04-21
D27%41%28%3,7403,23650443,569102026-05-012026-06-182026-04-21
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XME42%62%25%55724231521,8112026-06-182026-04-21
XOM33%81%0%82,06359,29922,764872,009102026-05-012026-06-182026-04-21
XOP38%74%42%13,1064,5478,559205,4072026-06-182026-04-21
XP62%62%7%96774522272,371142026-05-052026-06-182026-04-21
XPER2201452026-06-182026-04-21
XPEV55%29%60%12,9479,2433,704169,453362026-05-272026-06-182026-04-21
XRT41%94%100%2,7931,0691,72431,9982026-06-182026-04-21
XYZ60%77%36%27,46021,1016,359292,445162026-05-072026-06-182026-04-21
YPF40%13%15%3,0742,65142333,114172026-05-082026-06-182026-04-21
Z61%65%99%2,6121,92269028,566152026-05-062026-06-182026-04-21
ZETA104%88%41%15,3657,5207,845189,66492026-04-302026-06-182026-04-21
ZIM43%12%13%7,8573,6194,23868,580342026-05-252026-06-182026-04-21
ZM54%85%54%23,02615,6487,378179,216342026-05-252026-06-182026-04-21
ZS61%77%100%8,4224,9793,44370,280372026-05-282026-06-182026-04-21

開箱斜槓投資達人擊敗標普500指數450%的完整交易策略

在〈秒懂歷史波動率(HV)和隱含波動率(IV)的差別〉中有 5 則留言

  1. 剛才發現選擇權分析器真的可以快速找到高IV的股票清單
    這樣我就可以找到更多的Iron Condor交易機會了
    謝謝

    1. HV和IV雖然都是分析波動的數據
      一個是過去的標準差
      一個是預估的未來標準差

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擊敗標普500指數450%的完整交易策略
擊敗標普500指數450%的完整交易策略