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
AA47%8%17%65,55547,34518,210212,158952027-01-202026-12-182026-10-17
AAL55%54%5%70,19027,88342,3071,437,86552026-10-222026-12-182026-10-17
AAOI106%26%16%71,18239,31731,865308,224192026-11-052026-12-182026-10-17
AAPL25%46%0%2,099,9311,092,7111,007,2204,384,889162026-11-022026-12-182026-10-17
ABBV34%81%9%10,1955,7494,446176,468132026-10-302026-12-182026-10-17
ABCL4,8743,5211,35387,987232026-11-092026-12-182026-10-17
ABNB40%56%33%12,7736,1506,623109,546192026-11-052026-12-182026-10-17
ABT37%92%1%10,2576,9353,322116,58942026-10-212026-12-182026-10-17
ABVX71%21%99%13,5943,8119,78366,099582026-12-142026-12-182026-10-17
ACI47%55%100%6,1565,40475265,757872027-01-122026-12-182026-10-17
ACN38%21%1%17,2519,4467,805151,927612026-12-172026-12-182026-10-17
ADBE45%56%37%36,61920,24216,377393,533532026-12-092026-12-182026-10-17
ADI49%65%44%15,1007,6037,49747,036452026-12-012026-12-182026-10-17
ADM4,5273,82869949,417172026-11-032026-12-182026-10-17
AEHR216%98%77%11,0875,4835,60468,716832027-01-082026-12-182026-10-17
AEM45%27%27%5,4903,2082,28251,413112026-10-282026-12-182026-10-17
AEO43%2%4%4,7653,6811,08463,899382026-11-242026-12-182026-10-17
AEP1,23388634727,544112026-10-282026-12-182026-10-17
AES5485044450,762122026-10-292026-12-182026-10-17
AEVA2,8352,51432136,617182026-11-042026-12-182026-10-17
AFRM79%75%41%17,2658,6628,603132,467192026-11-052026-12-182026-10-17
AG46%0%4%58,04442,56715,477851,905192026-11-052026-12-182026-10-17
AGI6,6303,6432,98735,496112026-10-282026-12-182026-10-17
AI56%15%13%206,841199,7627,079247,423532026-12-092026-12-182026-10-17
AKAM69%74%34%28,80116,76812,033175,379192026-11-052026-12-182026-10-17
ALAB94%52%33%24,40314,7859,618120,955172026-11-032026-12-182026-10-17
ALB57%28%26%10,9827,1923,79092,469182026-11-042026-12-182026-10-17
ALK4,3961,7412,65541,85632026-10-202026-12-182026-10-17
ALLY27,17027,05811231,85132026-10-202026-12-182026-10-17
AMAT52%27%14%51,92124,92926,992359,795262026-11-122026-12-182026-10-17
AMBA71%31%68%9,2986,0783,22041,238452026-12-012026-12-182026-10-17
AMD56%40%31%812,437445,696366,7412,438,832172026-11-032026-12-182026-10-17
AMGN29%43%32%7,6155,2412,37460,941172026-11-032026-12-182026-10-17
AMKR78%49%17%5,5403,0592,48173,55192026-10-262026-12-182026-10-17
AMT3,6022,63496827,070102026-10-272026-12-182026-10-17
AMZN36%71%39%835,570481,617353,9534,401,664122026-10-292026-12-182026-10-17
ANET57%55%31%28,52914,03014,499242,921172026-11-032026-12-182026-10-17
APA54%64%44%12,33210,3721,960106,426182026-11-042026-12-182026-10-17
APH23,5566,07017,486214,757112026-10-282026-12-182026-10-17
APLD111%59%50%156,88683,55573,331834,477872027-01-122026-12-182026-10-17
APO48%62%45%10,4054,2416,164153,183172026-11-032026-12-182026-10-17
APP74%55%33%40,55015,82624,724231,894182026-11-042026-12-182026-10-17
AR64%92%52%8,3126,6891,62337,393112026-10-282026-12-182026-10-17
ARCC3,5502,59695465,853102026-10-272026-12-182026-10-17
ARM77%65%42%58,51629,77328,743540,523182026-11-042026-12-182026-10-17
AS64%64%99%3,7073,450257105,587312026-11-172026-12-182026-10-17
ASML46%38%31%30,77913,43317,34685,5161022027-01-272026-12-182026-10-17
ASST97%31%91%27,69118,4559,236693,469272026-11-132026-12-182026-10-17
ASTS85%15%23%167,28488,81378,4711,051,287302026-11-162026-12-182026-10-17
ASX24,8723,54921,323121,506122026-10-292026-12-182026-10-17
AVAV67%19%24%5,1543,4271,72728,894522026-12-082026-12-182026-10-17
AVGO37%12%13%514,913298,870216,0432,158,571542026-12-102026-12-182026-10-17
AVTR8538391495,925112026-10-282026-12-182026-10-17
AXON76%75%34%6,0602,5403,52028,665242026-11-102026-12-182026-10-17
AXP33%69%60%24,41419,0955,319161,62562026-10-232026-12-182026-10-17
AXTI125%21%0%22,26412,03310,231169,570122026-10-292026-12-182026-10-17
AZN6,0464,2471,79982,505132026-10-302026-12-182026-10-17
B36%2%99%18,56412,0016,563406,496232026-11-092026-12-182026-10-17
BA43%95%84%102,27773,05429,223756,416102026-10-272026-12-182026-10-17
BABA39%19%27%135,03983,61251,4271,385,495452026-12-012026-12-182026-10-17
BAC27%57%0%175,89794,60981,2882,102,509902027-01-152026-12-182026-10-17
BBWI57%24%0%7,9253,8694,05632,674322026-11-182026-12-182026-10-17
BBY46%69%100%3,9332,3021,63141,621382026-11-242026-12-182026-10-17
BE102%25%23%172,56577,00195,564748,62352026-10-222026-12-182026-10-17
BEKE114%95%51%2,7482,170578143,227242026-11-102026-12-182026-10-17
BHP4,1671,3162,85172,7631292027-02-232026-12-182026-10-17
BIDU40%13%19%34,30220,20914,093225,599382026-11-242026-12-182026-10-17
BILI2,0079701,03794,200262026-11-122026-12-182026-10-17
BIRK5,0262,6922,33436,435612026-12-172026-12-182026-10-17
BKNG41%51%37%13,1617,6185,543190,114172026-11-032026-12-182026-10-17
BMNR77%21%20%211,21390,239120,9741,487,523342026-11-202026-12-182026-10-17
BMY38%84%90%16,0589,4996,559471,662122026-10-292026-12-182026-10-17
BN9,8733,0406,83367,675262026-11-122026-12-182026-10-17
BP58%99%14%34,24627,1977,049303,780132026-10-302026-12-182026-10-17
BRK-B15%38%20%51,55326,05525,498365,4002026-12-182026-10-17
BROS67%72%0%8,4846,1522,33260,765182026-11-042026-12-182026-10-17
BSP11,4113,1348,27754,993262026-11-122026-12-182026-10-17
BSX53%92%55%20,20910,15410,055563,669112026-10-282026-12-182026-10-17
BTI6,7445,6951,04939,6241172027-02-112026-12-182026-10-17
BX55%94%61%42,58110,13232,449262,84552026-10-222026-12-182026-10-17
BXMT41511230328,287122026-10-292026-12-182026-10-17
C29%27%3%85,16134,78250,379725,329892027-01-142026-12-182026-10-17
CAG34%30%45%4,9673,5181,449121,330762027-01-012026-12-182026-10-17
CARR52%81%54%3,2171,6681,54947,082122026-10-292026-12-182026-10-17
CART39%13%9%7,4237,15227143,887192026-11-052026-12-182026-10-17
CAT50%88%56%20,7479,55411,193130,549122026-10-292026-12-182026-10-17
CAVA76%82%44%15,27510,5164,75999,613182026-11-042026-12-182026-10-17
CBRS88%35%25%112,88428,55084,334301,115462026-12-022026-12-182026-10-17
CCI4,7214,09862344,65342026-10-212026-12-182026-10-17
CCJ49%16%13%13,4976,1687,329329,910132026-10-302026-12-182026-10-17
CCL36%5%0%44,47124,61319,858705,640622026-12-182026-12-182026-10-17
CCXI3,8461,4732,37377,1612026-12-182026-10-17
CDE49%0%4%17,16411,0776,087308,892182026-11-042026-12-182026-10-17
CEG48%31%3%9,4533,8285,625139,445232026-11-092026-12-182026-10-17
CELH60%45%24%14,93810,0744,864320,048192026-11-052026-12-182026-10-17
CF47%44%29%3,2431,5951,64842,254182026-11-042026-12-182026-10-17
CG57221036242,057192026-11-052026-12-182026-10-17
CHKP3,4191,9541,46549,631162026-11-022026-12-182026-10-17
CHTR75%80%5%9,4705,6613,80963,160202026-11-062026-12-182026-10-17
CHWY39%7%15%10,7797,2963,483164,590472026-12-032026-12-182026-10-17
CI30%18%2%5,9335,22970426,514192026-11-052026-12-182026-10-17
CIEN88%50%34%12,5605,9756,58547,146542026-12-102026-12-182026-10-17
CL29%73%100%3,9923,51447835,427132026-10-302026-12-182026-10-17
CLF97%98%0%109,37163,60445,767627,64122026-10-192026-12-182026-10-17
CLMT5,4894,1301,35954,116202026-11-062026-12-182026-10-17
CLS105%95%74%10,0584,8615,19781,32692026-10-262026-12-182026-10-17
CLX6,3523,6322,72067,379162026-11-022026-12-182026-10-17
CMCSA46%82%3%33,73221,26212,470538,00652026-10-222026-12-182026-10-17
CMG43%63%3%65,80423,50442,300685,546112026-10-282026-12-182026-10-17
CMPS2,0121,36065283,523122026-10-292026-12-182026-10-17
CNC58%69%0%4,3213,2861,03546,042102026-10-272026-12-182026-10-17
CNH106367036,708242026-11-102026-12-182026-10-17
CNQ38%59%28%5,9615,09187079,327192026-11-052026-12-182026-10-17
COF42%77%59%9,5096,2033,30676,71232026-10-202026-12-182026-10-17
COHR80%31%28%52,64118,52634,115210,323182026-11-042026-12-182026-10-17
COIN76%75%48%260,069153,224106,845696,232122026-10-292026-12-182026-10-17
COP31%24%0%28,62022,8745,746175,077192026-11-052026-12-182026-10-17
COPX42%17%1%10,4097,3893,020207,5592026-12-182026-10-17
CORZ73%11%15%175,79567,553108,242791,159192026-11-052026-12-182026-10-17
COST18%6%17%52,29628,44723,849190,293542026-12-102026-12-182026-10-17
CPB35%37%100%4,7363,0691,66765,955532026-12-092026-12-182026-10-17
CPNG60%67%51%7,1855,7391,446226,588242026-11-102026-12-182026-10-17
CPRI2,2522,07018258,775192026-11-052026-12-182026-10-17
CPRT2,3411,55678549,286322026-11-182026-12-182026-10-17
CRCL82%35%31%108,49864,62743,871582,654182026-11-042026-12-182026-10-17
CRDO80%12%14%29,86419,48610,378202,519462026-12-022026-12-182026-10-17
CRGY16,69416,47621840,605162026-11-022026-12-182026-10-17
CRK9,8089,23357541,684182026-11-042026-12-182026-10-17
CRM45%52%37%55,93331,89024,043450,197522026-12-082026-12-182026-10-17
CRSP58%12%16%7,1001,6905,41031,612182026-11-042026-12-182026-10-17
CRWD56%61%40%159,13476,90482,230738,908452026-12-012026-12-182026-10-17
CRWV100%71%36%1,239,723611,703628,0203,454,462302026-11-162026-12-182026-10-17
CSCO38%73%97%59,43521,36238,073591,530322026-11-182026-12-182026-10-17
CSX35%75%96%4,2463,0261,22056,88942026-10-212026-12-182026-10-17
CVE2,9032,37452942,859182026-11-042026-12-182026-10-17
CVNA84%79%41%57,11921,77735,342517,839112026-10-282026-12-182026-10-17
CVS37%72%62%16,4829,6466,836162,010182026-11-042026-12-182026-10-17
CVX363%100%100%68,79055,00813,782430,269132026-10-302026-12-182026-10-17
D1,9151,13977629,013132026-10-302026-12-182026-10-17
DAL41%32%100%33,04014,35718,683320,325832027-01-082026-12-182026-10-17
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FANG3,0052,66234327,119162026-11-022026-12-182026-10-17
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FIG68%21%100%35,74519,09016,655251,176182026-11-042026-12-182026-10-17
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FLG20,45513,3707,08572,32462026-10-232026-12-182026-10-17
FLR43826217634,348202026-11-062026-12-182026-10-17
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FPS8,3435,0573,28690,253462026-12-022026-12-182026-10-17
FRO4,2222,4401,782112,500442026-11-302026-12-182026-10-17
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FXE6774092687,2162026-12-182026-10-17
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GIS8,8482,4296,419158,585672026-12-232026-12-182026-10-17
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GRPN6,7885,92086852,545192026-11-052026-12-182026-10-17
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GTLB51%7%8%8,8007,5151,28588,693512026-12-072026-12-182026-10-17
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HAL48%92%74%12,6519,8632,788229,61532026-10-202026-12-182026-10-17
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IP64%87%29%2,6261,82080627,797112026-10-282026-12-182026-10-17
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KEY7,5377,00053732,53432026-10-202026-12-182026-10-17
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KNX6145783668,77442026-10-212026-12-182026-10-17
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LBRT1,43873370549,05742026-10-212026-12-182026-10-17
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LOW28%27%28%15,5829,1506,43283,465322026-11-182026-12-182026-10-17
LQD20%98%95%138,72318,254120,4691,349,1582026-12-182026-10-17
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LW1,8876311,25640,677762027-01-012026-12-182026-10-17
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MAT10,9227,3703,552133,015192026-11-052026-12-182026-10-17
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MET3,6302,2881,34245,801182026-11-042026-12-182026-10-17
META56%94%64%900,049497,560402,4892,805,04842026-10-212026-12-182026-10-17
MGM19,1387,26311,87589,041112026-10-282026-12-182026-10-17
MGNI1,9441,82412033,354182026-11-042026-12-182026-10-17
MIR72353019351,634102026-10-272026-12-182026-10-17
MKC3,5822,59898432,4501032027-01-282026-12-182026-10-17
MMED5,2481,7503,49834,029742026-12-302026-12-182026-10-17
MMM40%89%63%7,2103,9123,29865,10032026-10-202026-12-182026-10-17
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MP69%27%33%23,6219,75213,869312,458192026-11-052026-12-182026-10-17
MPC6,6383,8832,75545,180172026-11-032026-12-182026-10-17
MPLX1,52897655246,436172026-11-032026-12-182026-10-17
MRK38%92%63%19,94612,7647,182292,928122026-10-292026-12-182026-10-17
MRNA117%99%100%245,987131,163114,824626,017202026-11-062026-12-182026-10-17
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MS34%56%91%47,71220,98426,728254,653892027-01-142026-12-182026-10-17
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MXL2,1429551,18739,83052026-10-222026-12-182026-10-17
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NET73%71%38%27,14012,08615,054106,557192026-11-052026-12-182026-10-17
NFLX63%98%74%375,613221,448154,1653,376,56732026-10-202026-12-182026-10-17
NKE39%56%0%152,82795,63357,1941,916,106612026-12-172026-12-182026-10-17
NLY32%74%64%6,5862,7363,850136,56532026-10-202026-12-182026-10-17
NOW66%82%46%163,52795,59767,930894,786112026-10-282026-12-182026-10-17
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ZTS5,1483,9151,233108,130192026-11-052026-12-182026-10-17

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

留言功能已關閉。

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