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
AAL46%23%3%79,08639,79239,2941,266,589432026-10-152026-11-202026-09-02
AAPL29%78%0%2,150,7081,465,572685,1364,075,182572026-10-292026-11-202026-09-02
ABBV23%9%8%16,46911,3965,073155,034512026-10-232026-11-202026-09-02
ABNB36%39%27%8,0033,8294,17484,905632026-11-042026-11-202026-09-02
ABT26%40%0%6,0473,6102,437123,643492026-10-212026-11-202026-09-02
ABVX58%8%99%5,8704,4731,39747,548192026-09-212026-11-202026-09-02
ACN44%45%2%3,8422,4181,42488,920292026-10-012026-11-202026-09-02
ADBE58%87%55%31,50015,02416,476396,15782026-09-102026-11-202026-09-02
ADI36%27%23%2,8631,6241,23938,936902026-12-012026-11-202026-09-02
ADM26%9%89%10,5263,2357,29143,533552026-10-272026-11-202026-09-02
AEM49%50%38%8,6125,3523,26066,468562026-10-282026-11-202026-09-02
AEO92%92%19%4,4783,2341,24449,64572026-09-092026-11-202026-09-02
AES20%16%77%1,06491914546,538572026-10-292026-11-202026-09-02
AFRM50%2%7%30,00314,99215,011145,099702026-11-112026-11-202026-09-02
AKAM56%47%0%3,9771,7952,18250,269692026-11-102026-11-202026-09-02
ALAB76%8%16%14,1888,3715,817100,335692026-11-102026-11-202026-09-02
ALLY28%19%7%1,02423379134,982492026-10-212026-11-202026-09-02
AMAT55%46%0%38,57220,46918,103300,213712026-11-122026-11-202026-09-02
AMD45%10%74%338,136170,942167,1942,078,964622026-11-032026-11-202026-09-02
AMGN35%79%49%7,5194,5942,92563,109622026-11-032026-11-202026-09-02
AMZN23%3%39%665,129414,268250,8613,833,193502026-10-222026-11-202026-09-02
ANET49%22%19%17,8849,5898,295170,251612026-11-022026-11-202026-09-02
ANF45%4%7%7,6724,2243,44835,463832026-11-242026-11-202026-09-02
APH42%28%1%6,0204,2721,74871,723562026-10-282026-11-202026-09-02
APLD73%2%4%54,02337,24816,775584,873422026-10-142026-11-202026-09-02
APO38%28%27%6,8633,4613,40291,401632026-11-042026-11-202026-09-02
APP54%11%12%21,34014,0357,305179,627702026-11-112026-11-202026-09-02
AR44%42%23%4,4143,65376151,000562026-10-282026-11-202026-09-02
ARM57%28%21%47,02025,21421,806390,888632026-11-042026-11-202026-09-02
ASML39%17%20%12,8175,0427,77560,315422026-10-142026-11-202026-09-02
ASTS65%0%0%89,06561,14527,920823,619752026-11-162026-11-202026-09-02
AVGO68%95%65%202,010124,43077,5801,725,16302026-09-022026-11-202026-09-02
AVTR62%37%12%53143967,918512026-10-232026-11-202026-09-02
AXP24%10%19%20,98814,0836,90593,783512026-10-232026-11-202026-09-02
AXTI111%4%0%19,84811,1268,722145,329572026-10-292026-11-202026-09-02
BA31%31%56%42,00927,69214,317540,547562026-10-282026-11-202026-09-02
BABA36%5%17%96,59965,69130,9081,718,208902026-12-012026-11-202026-09-02
BAC17%3%0%85,79355,38230,4111,588,393422026-10-142026-11-202026-09-02
BAX42%15%16%4,7622,7612,00136,394572026-10-292026-11-202026-09-02
BBY40%43%100%3,1892,22496546,831832026-11-242026-11-202026-09-02
BE94%8%8%92,69951,54641,153668,730572026-10-292026-11-202026-09-02
BHP40%53%18%4,0629203,14233,1791742027-02-232026-11-202026-09-02
BIDU37%2%13%16,4138,7617,652257,691832026-11-242026-11-202026-09-02
BKNG38%51%33%7,2022,5434,659106,809632026-11-042026-11-202026-09-02
BMNR70%3%12%127,35689,09438,2621,316,231792026-11-202026-11-202026-09-02
BMY24%8%84%8,8035,6813,122390,759572026-10-292026-11-202026-09-02
BP-5039%0%0%14,35111,4252,926326,587622026-11-032026-11-202026-09-02
BRK-B14%18%15%18,54110,3028,239282,2382026-11-202026-09-02
BRUN148%16%16%3,1752,72844737,267912026-12-022026-11-202026-09-02
BSX45%82%43%122,100115,9506,150506,982562026-10-282026-11-202026-09-02
BTU57%14%19%6,2932,0674,22672,230572026-10-292026-11-202026-09-02
BX44%57%94%30,5129,50121,011233,214432026-10-152026-11-202026-09-02
BYND120%77%100%5,2323,7821,450202,665702026-11-112026-11-202026-09-02
C27%17%3%31,85416,68615,168492,136412026-10-132026-11-202026-09-02
CAPR147%89%32%8,7795,4273,352113,038762026-11-172026-11-202026-09-02
CART48%33%16%1,4931,01348037,972762026-11-172026-11-202026-09-02
CAT37%39%30%36,65016,31920,331172,944632026-11-042026-11-202026-09-02
CBRS73%3%5%38,55725,75412,803200,353912026-12-022026-11-202026-09-02
CCL42%25%0%67,08732,34234,745742,092152026-09-172026-11-202026-09-02
CCXI168%90%77%2,2991,36193850,1432026-11-202026-09-02
CDE67%11%15%16,5739,9376,636349,740702026-11-112026-11-202026-09-02
CDNS48%44%29%3,9411,2502,69137,522542026-10-262026-11-202026-09-02
CEG45%17%2%8,7065,9122,794107,020682026-11-092026-11-202026-09-02
CF52%58%34%9,2675,3343,93341,876632026-11-042026-11-202026-09-02
CHTR61%67%31%5,8814,3611,52087,628582026-10-302026-11-202026-09-02
CHWY70%85%54%4,9423,1201,822108,62972026-09-092026-11-202026-09-02
CHYM61%16%100%1,48089158943,416702026-11-112026-11-202026-09-02
CIFR99%9%16%100,36176,34924,0121,186,168702026-11-112026-11-202026-09-02
CLF75%67%0%15,08812,7272,361361,411542026-10-262026-11-202026-09-02
CLMT72%71%18%5,1293,9611,16842,364652026-11-062026-11-202026-09-02
CLS71%24%24%11,6377,2244,41365,856542026-10-262026-11-202026-09-02
CLSK98%50%43%39,25032,7606,490577,9401052026-12-162026-11-202026-09-02
CLYM233%83%2%2,2783271,95134,298702026-11-112026-11-202026-09-02
CMPS78%26%44%1,6211,43019176,249572026-10-292026-11-202026-09-02
CNC42%10%0%5,1042,6972,40760,407552026-10-272026-11-202026-09-02
CODI65%14%14%134134041,045912026-12-022026-11-202026-09-02
COHR72%20%33%16,6358,0388,597168,640702026-11-112026-11-202026-09-02
COIN62%29%29%120,35471,15249,202735,060572026-10-292026-11-202026-09-02
COP42%92%1%13,3305,8087,522143,666572026-10-292026-11-202026-09-02
COPX56%61%49%12,4499,5792,870175,4842026-11-202026-09-02
CORZ82%27%0%31,96826,7555,213915,627702026-11-112026-11-202026-09-02
COST23%46%33%25,63312,29013,343158,380222026-09-242026-11-202026-09-02
CPB52%95%100%12,0944,2277,867100,10012026-09-032026-11-202026-09-02
CPNG42%30%100%4,7373,2621,475283,254692026-11-102026-11-202026-09-02
CPRI95%69%48%72044028045,900642026-11-052026-11-202026-09-02
CPRT35%21%0%1,54854999967,15272026-09-092026-11-202026-09-02
CRCL80%24%28%61,21240,73420,478568,756772026-11-182026-11-202026-09-02
CRDO118%82%53%58,48431,60426,880134,216912026-12-022026-11-202026-09-02
CRK103%93%53%26,42024,9021,51873,453622026-11-032026-11-202026-09-02
CRM41%34%96%102,47342,30560,168701,220972026-12-082026-11-202026-09-02
CRWD65%85%54%120,66665,84454,822690,484902026-12-012026-11-202026-09-02
CRWV67%0%2%145,85560,50385,3521,775,111752026-11-162026-11-202026-09-02
CSCO28%36%97%41,71222,88518,827594,120772026-11-182026-11-202026-09-02
CSIQ83%13%7%2,7211,85486780,620712026-11-122026-11-202026-09-02
CSX27%35%95%30,23926,9593,280104,623432026-10-152026-11-202026-09-02
CVNA60%28%19%27,02911,98015,049419,502572026-10-292026-11-202026-09-02
CVS31%41%52%14,12510,0564,069153,551632026-11-042026-11-202026-09-02
CVX32%79%100%48,48232,09416,388427,535512026-10-232026-11-202026-09-02
CXW43%17%25%80643237434,743682026-11-092026-11-202026-09-02
CYTK48%12%96%7977326536,155572026-10-292026-11-202026-09-02
CZR23%10%100%7,2657,13013585,342622026-11-032026-11-202026-09-02
DAL36%9%100%54,81444,56410,250285,988362026-10-082026-11-202026-09-02
DASH46%31%19%8,5063,5684,93871,325632026-11-042026-11-202026-09-02
DDOG69%69%38%11,6495,9075,742100,622642026-11-052026-11-202026-09-02
DELL104%99%87%276,253136,137140,116409,899902026-12-012026-11-202026-09-02
DG42%57%33%5,5563,7751,78142,697922026-12-032026-11-202026-09-02
DIA12%19%16%52,74423,91428,830207,3162026-11-202026-09-02
DIS26%35%99%20,65710,14010,517416,009712026-11-122026-11-202026-09-02
DKNG50%27%0%22,64918,5724,077623,378582026-10-302026-11-202026-09-02
DKS39%21%11%8,8575,6243,233135,171832026-11-242026-11-202026-09-02
DLO21%1%0%3062238386,585772026-11-182026-11-202026-09-02
DLTR40%28%23%5,1732,9292,24443,545832026-11-242026-11-202026-09-02
DOW36%3%44%8,0795,5602,519300,601502026-10-222026-11-202026-09-02
DUOL63%19%12%8,1564,9883,16842,900702026-11-112026-11-202026-09-02
DVN44%75%99%13,0206,2706,750355,198692026-11-102026-11-202026-09-02
DXJ30%64%100%17070100312026-11-202026-09-02
EBAY30%14%10%2,5241,2451,27930,956632026-11-042026-11-202026-09-02
EEM20%28%0%226,51366,866159,6472,710,7722026-11-202026-09-02
EFA18%54%26%65,7779,83355,944355,6472026-11-202026-09-02
ELF54%10%12%5,4033,4701,93335,323702026-11-112026-11-202026-09-02
ENPH67%27%24%20,78712,7108,077263,988552026-10-272026-11-202026-09-02
ERO42%4%82%2,1521,72342983,341692026-11-102026-11-202026-09-02
EWJ26%50%32%1,7781,08169710,5152026-11-202026-09-02
EWS28%39%0%55052026-11-202026-09-02
EWY46%33%28%71,96350,22921,734744,7252026-11-202026-09-02
EWZ35%75%21%440,066417,20322,8634,755,2692026-11-202026-09-02
EXK137%50%96%1,9851,690295115,956692026-11-102026-11-202026-09-02
F30%19%0%52,93335,00217,9311,214,675562026-10-282026-11-202026-09-02
FAST27%24%61%2,4963422,15434,300422026-10-142026-11-202026-09-02
FCX48%39%51%53,86041,06412,796722,424432026-10-152026-11-202026-09-02
FHN32%24%0%51,80151,74655161,694492026-10-212026-11-202026-09-02
FIGR111%64%42%5,2843,6831,60173,185712026-11-122026-11-202026-09-02
FLG48%58%0%2,6601,80086093,833512026-10-232026-11-202026-09-02
FLNC79%1%3%4,2002,8641,336103,357892026-11-302026-11-202026-09-02
FLY92%4%13%3,7032,4081,29574,901772026-11-182026-11-202026-09-02
FPS71%11%10%4,7444,35339137,080132026-09-152026-11-202026-09-02
FRO65%78%0%4,8133,2641,54979,165892026-11-302026-11-202026-09-02
FSLR47%7%12%34,97310,99223,981366,236572026-10-292026-11-202026-09-02
FSM97%21%24%1,3901,12126941,351702026-11-112026-11-202026-09-02
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XLP17%65%35%14,4488,9575,491361,1442026-11-202026-09-02
XLV16%23%38%14,4406,3668,074169,8042026-11-202026-09-02
XME26%0%11%11,42011,15826244,4352026-11-202026-09-02
XOM27%36%0%43,88629,21814,668743,355512026-10-232026-11-202026-09-02
XOP47%97%66%8,9915,5573,434171,5932026-11-202026-09-02
XP61%47%13%2,8962,230666149,847832026-11-242026-11-202026-09-02
XYZ37%4%10%28,74019,0269,714279,785642026-11-052026-11-202026-09-02
ZM49%57%35%9,1626,0103,152140,363822026-11-232026-11-202026-09-02
ZS117%100%100%14,1827,0997,083104,79412026-09-032026-11-202026-09-02

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