volatility

秒懂歷史波動率(HV)和隱含波動率(IV)的差別

最近更新日期： 2025/09/29

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。

用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
AA49%16%20%9,8576,1453,712172,476742027-01-202027-01-152026-11-07
AAL57%59%5%54,40928,02726,3822,076,489822027-01-282027-01-152026-11-07
AAOI140%66%42%76,78948,73028,059463,7501102027-02-252027-01-152026-11-07
AAPL25%46%0%1,444,152687,185756,9675,627,443892027-02-042027-01-152026-11-07
ABBV31%60%1%12,8685,8836,985170,830882027-02-032027-01-152026-11-07
ABCL93%56%43%1,176992184139,48122026-11-092027-01-152026-11-07
ABNB34%22%22%44,13926,48217,657247,6221012027-02-162027-01-152026-11-07
ABSI169%84%83%1,08682725990,24852026-11-122027-01-152026-11-07
ABT29%48%0%15,0228,7436,279129,876812027-01-272027-01-152026-11-07
ABVX76%28%99%5,6564,0451,611211,511372026-12-142027-01-152026-11-07
ACAD44%19%0%1721314145,7081142027-03-012027-01-152026-11-07
ACI49%55%100%4,4299573,47262,202662027-01-122027-01-152026-11-07
ACMR124%82%45%6,3665,91545146,9141042027-02-192027-01-152026-11-07
ACN48%54%2%9,4243,9945,430105,763402026-12-172027-01-152026-11-07
ADBE43%39%34%32,05221,67810,374635,280322026-12-092027-01-152026-11-07
ADI75%98%70%6,0912,8473,244148,049172026-11-242027-01-152026-11-07
ADM23%5%89%5,7143,4862,22860,506802027-01-262027-01-152026-11-07
ADMA66%28%4%1,13192220942,7531382027-03-252027-01-152026-11-07
ADP33%51%0%1,8551,60425145,032812027-01-272027-01-152026-11-07
ADSK56%75%91%2,4341,57486053,468172026-11-242027-01-152026-11-07
AEHR121%29%34%7,5734,1763,397139,435622027-01-082027-01-152026-11-07
AEM52%63%43%6,5824,1432,43967,9151032027-02-182027-01-152026-11-07
AEO48%11%6%3,3582,44791137,445172026-11-242027-01-152026-11-07
AEP28%54%0%1,9141,56634857,6101102027-02-252027-01-152026-11-07
AES-3%2%77%69457312144,7311142027-03-012027-01-152026-11-07
AEVA132%39%86%1,00764136668,2281372027-03-242027-01-152026-11-07
AFRM74%63%35%28,01614,68813,328266,135962027-02-112027-01-152026-11-07
AG63%19%0%31,14022,9708,170622,3161102027-02-252027-01-152026-11-07
AGI44%10%12%2,8881,8651,02359,4051092027-02-242027-01-152026-11-07
AGIO166%91%58%79592057,7001102027-02-252027-01-152026-11-07
AI69%47%24%171,438169,4971,941194,537322026-12-092027-01-152026-11-07
AKAM77%81%39%31,21618,60512,611328,7391012027-02-162027-01-152026-11-07
ALAB111%75%49%39,49225,33614,156281,1131012027-02-162027-01-152026-11-07
ALB57%33%27%5,1183,3611,75799,2381022027-02-172027-01-152026-11-07
ALGN43%19%0%4543589638,446882027-02-032027-01-152026-11-07
ALK82%85%95%3,2502,27197933,496822027-01-282027-01-152026-11-07
ALNY63%85%35%1,14860953953,5641032027-02-182027-01-152026-11-07
AMAT86%88%36%45,13422,03023,104568,67552026-11-122027-01-152026-11-07
AMBA122%90%83%6,0324,0142,01874,035242026-12-012027-01-152026-11-07
AMD79%89%57%1,039,861502,164537,6973,638,166872027-02-022027-01-152026-11-07
AMGN33%69%45%7,0593,6023,457149,696942027-02-092027-01-152026-11-07
AMKR70%28%13%8,1384,3593,779151,2451002027-02-152027-01-152026-11-07
AMZN34%58%39%746,434458,412288,0224,898,118892027-02-042027-01-152026-11-07
ANET68%81%47%33,27618,16815,108228,1751002027-02-152027-01-152026-11-07
APA49%46%33%5,2962,8942,402179,1081092027-02-242027-01-152026-11-07
APH48%41%1%14,4809,6764,804249,469812027-01-272027-01-152026-11-07
APLD122%88%62%104,26675,85928,4071,010,064662027-01-122027-01-152026-11-07
APO40%28%30%4,3971,2753,122108,616962027-02-112027-01-152026-11-07
APP69%41%24%174,262118,70055,562481,2671022027-02-172027-01-152026-11-07
APPS174%98%100%2,1261,97814898,42722026-11-092027-01-152026-11-07
AR68%95%58%1,5631,11245173,4371022027-02-172027-01-152026-11-07
ARCC36%63%54%1,508861647170,727952027-02-102027-01-152026-11-07
ARM77%63%42%74,06829,81044,258943,621882027-02-032027-01-152026-11-07
ARWR66%44%1%65642223441,86952026-11-122027-01-152026-11-07
AS71%78%0%3,0862,87920779,591102026-11-172027-01-152026-11-07
ASML57%73%45%28,79412,51016,284208,134812027-01-272027-01-152026-11-07
ASST97%30%91%28,07315,74212,3311,089,52462026-11-132027-01-152026-11-07
ASTS135%97%76%173,238115,12258,1161,252,85722026-11-092027-01-152026-11-07
ASX66%37%88%8,7644,2694,495115,555962027-02-112027-01-152026-11-07
AU65%65%35%1,7811,46531643,5501042027-02-192027-01-152026-11-07
AUPH34%6%100%209208133,9491172027-03-042027-01-152026-11-07
AVAV74%43%31%5,1752,9922,18375,097312026-12-082027-01-152026-11-07
AVGO58%84%48%463,984237,019226,9652,520,046332026-12-102027-01-152026-11-07
AXGN98%62%100%33221137,8241082027-02-232027-01-152026-11-07
AXON66%57%26%12,2637,1535,11080,3811152027-03-022027-01-152026-11-07
AXP31%58%52%19,25413,9205,334117,670762027-01-222027-01-152026-11-07
AXTI125%21%0%20,69615,1975,499260,4661032027-02-182027-01-152026-11-07
AZN36%73%94%1,07943564458,026962027-02-112027-01-152026-11-07
B53%76%99%24,01516,0307,985431,83422026-11-092027-01-152026-11-07
BA33%44%60%100,14941,50658,643758,741812027-01-272027-01-152026-11-07
BABA51%83%58%134,87294,22240,6501,378,549242026-12-012027-01-152026-11-07
BAC28%63%0%151,917105,03846,8791,794,838692027-01-152027-01-152026-11-07
BBIO43%8%11%2281458341,0001102027-02-252027-01-152026-11-07
BE108%37%27%181,986106,16775,819814,761962027-02-112027-01-152026-11-07
BEKE78%70%48%1,24569555066,19692026-11-162027-01-152026-11-07
BHF93%77%98%7,7466,5891,15772,02342026-11-112027-01-152026-11-07
BHP32%15%15%3,0621,2751,787103,1941002027-02-152027-01-152026-11-07
BIDU56%73%50%34,37525,9698,406401,25092026-11-162027-01-152026-11-07
BIIB37%33%18%1,05766938861,8821022027-02-172027-01-152026-11-07
BILI58%39%86%1,5161,297219235,977172026-11-242027-01-152026-11-07
BKNG47%72%47%8,8814,8903,991648,3691102027-02-252027-01-152026-11-07
BKR67%84%98%3,5801,5612,01984,469812027-01-272027-01-152026-11-07
BL162%95%100%55521733839,7751012027-02-162027-01-152026-11-07
BMNR84%47%30%154,14178,22375,9181,491,591132026-11-202027-01-152026-11-07
BMRN47%42%92%62382443,9181092027-02-242027-01-152026-11-07
BMY37%82%90%27,9756,12221,853464,444892027-02-042027-01-152026-11-07
BNTX59%87%43%62136225954,7471152027-03-022027-01-152026-11-07
BP40%90%14%18,70714,6554,052280,182942027-02-092027-01-152026-11-07
BRK-B25%99%61%44,90124,75420,147356,5082027-01-152026-11-07
BROS53%38%0%14,8268,3096,51774,4281092027-02-242027-01-152026-11-07
BRZE38%8%99%1,111958153123,610312026-12-082027-01-152026-11-07
BSP118%68%22%2,3381792,15970,91352026-11-122027-01-152026-11-07
BSX46%78%44%15,9938,9717,022474,871882027-02-032027-01-152026-11-07
BTI48%59%2%1,8971,35054741,377962027-02-112027-01-152026-11-07
BTU80%86%56%7,3284,1873,14142,819892027-02-042027-01-152026-11-07
BX41%39%35%74,7587,01667,742220,177822027-01-282027-01-152026-11-07
C36%71%3%61,45620,64040,816619,131682027-01-142027-01-152026-11-07
CAG38%48%45%4,1081,3542,75494,004552027-01-012027-01-152026-11-07
CAMT562%99%69%3,9268333,09349,687952027-02-102027-01-152026-11-07
CAR75%55%11%6,0615,63642563,4331002027-02-152027-01-152026-11-07
CARR48%70%48%1,59893965933,824942027-02-092027-01-152026-11-07
CART22%0%0%1,3771,164213168,4461022027-02-172027-01-152026-11-07
CAT47%78%48%34,04717,87316,174148,821892027-02-042027-01-152026-11-07
CAVA68%65%34%5,8103,1812,62978,1221152027-03-022027-01-152026-11-07
CBRL64%33%72%98922576446,110202026-11-272027-01-152026-11-07
CBRS128%80%66%41,93620,67221,264367,47852026-11-122027-01-152026-11-07
CCI36%57%29%5,7144235,29137,777812027-01-272027-01-152026-11-07
CCJ60%58%28%192,827159,78633,041335,846972027-02-122027-01-152026-11-07
CCL48%42%0%20,63411,3999,235700,075412026-12-182027-01-152026-11-07
CDE50%1%4%50,68533,00617,679321,2911092027-02-242027-01-152026-11-07
CDNS52%53%0%2,4085321,87689,0111082027-02-232027-01-152026-11-07
CEG55%66%5%17,3266,20711,119238,59422026-11-092027-01-152026-11-07
CELH56%33%20%29,36423,0716,293611,3051172027-03-042027-01-152026-11-07
CENX74%33%99%2,3527591,59365,6341102027-02-252027-01-152026-11-07
CF51%52%33%3,0751,8401,23534,1631022027-02-172027-01-152026-11-07
CG49%34%1%2,871962,775114,193962027-02-112027-01-152026-11-07
CGON224%97%76%14,1159,4774,63860,02752026-11-122027-01-152026-11-07
CHKP52%69%34%42419522973,018892027-02-042027-01-152026-11-07
CHRW52%80%56%61441750,403882027-02-032027-01-152026-11-07
CHTR81%83%5%23,13117,7185,413235,184832027-01-292027-01-152026-11-07
CHWY66%81%49%6,3383,8322,506150,903262026-12-032027-01-152026-11-07
CHYM57%18%100%5,8793,5532,326106,2411162027-03-032027-01-152026-11-07
CIEN98%71%40%12,1465,6676,47941,677332026-12-102027-01-152026-11-07
CLF113%98%1%39,30725,07914,228537,3561002027-02-152027-01-152026-11-07
CLMT80%79%29%24,51821,8452,673206,9561112027-02-262027-01-152026-11-07
CLS96%86%61%17,32811,8355,493100,047812027-01-272027-01-152026-11-07
CLX26%13%0%3,9342,5821,35269,202892027-02-042027-01-152026-11-07
CMCSA32%24%3%46,17012,07134,0991,250,763822027-01-282027-01-152026-11-07
CME29%49%0%2,8601,6001,26058,290952027-02-102027-01-152026-11-07
CMG34%14%2%25,36817,2398,129591,942942027-02-092027-01-152026-11-07
CNC43%17%0%19,0374,90614,13198,825942027-02-092027-01-152026-11-07
CNQ42%78%34%2,6032,30529833,9641172027-03-042027-01-152026-11-07
COF36%53%0%7,8344,0393,79574,498802027-01-262027-01-152026-11-07
COHR99%63%51%40,56624,67015,896244,850952027-02-102027-01-152026-11-07
COIN64%30%32%214,503148,83065,6731,108,4231032027-02-182027-01-152026-11-07
COMP87%61%0%3,2642,628636131,4151152027-03-022027-01-152026-11-07
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O16%17%77%2,8771,98289598,0221082027-02-232027-01-152026-11-07
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PYPL35%36%51%52,67644,2478,429879,580942027-02-092027-01-152026-11-07
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RIO22%6%99%3,7412,7401,00147,0851092027-02-242027-01-152026-11-07
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ROIV78%79%14%1,2721,1997335,73422026-11-092027-01-152026-11-07
RTX36%82%100%8,7414,9583,783140,510802027-01-262027-01-152026-11-07
S76%80%44%12,55912,011548109,758312026-12-082027-01-152026-11-07
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SCHW30%54%100%11,4696,4475,022222,630732027-01-192027-01-152026-11-07
SE96%97%87%9,8345,5194,31588,18332026-11-102027-01-152026-11-07
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XP70%65%16%5,2912,7352,556373,236172026-11-242027-01-152026-11-07
XPEV70%84%39%20,18219,0591,123222,26592026-11-162027-01-152026-11-07
XRT38%87%100%2,3739051,46827,7052027-01-152026-11-07
XYZ43%21%18%72,73767,3725,365296,6861102027-02-252027-01-152026-11-07
YPF54%62%85%4,6282,8671,76151,1161172027-03-042027-01-152026-11-07
Z47%17%99%1,58992066938,0101012027-02-162027-01-152026-11-07
ZETA113%97%65%19,35714,8154,542217,36722026-11-092027-01-152026-11-07
ZIM51%37%32%79646832843,136112026-11-182027-01-152026-11-07
ZM53%70%40%7,8325,8341,998122,481162026-11-232027-01-152026-11-07
ZS103%96%100%11,9797,4934,486100,852242026-12-012027-01-152026-11-07
ZTS19%2%100%3,7732,4451,32897,3831012027-02-162027-01-152026-11-07

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

  2. Nick

    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. Tony

      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
看我們的交易成效
擊敗標普500指數450%的完整交易策略
看我們的交易成效