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
AA53%24%27%12,1769,6452,531133,904232026-10-152026-11-202026-09-22
AAL59%68%5%141,750111,21230,5381,230,307232026-10-152026-11-202026-09-22
AAOI92%10%8%66,44050,10916,331187,092442026-11-052026-11-202026-09-22
AAP67%53%26%4,2862,7521,53428,105572026-11-182026-11-202026-09-22
AAPL23%31%0%1,462,803993,959468,8443,925,816372026-10-292026-11-202026-09-22
ABBV23%8%8%15,17010,7554,415155,195312026-10-232026-11-202026-09-22
ABCL76%7%32%3,5682,84572378,169492026-11-102026-11-202026-09-22
ABNB32%16%20%7,9424,7533,18966,914432026-11-042026-11-202026-09-22
ABT25%29%0%7,3845,3772,00796,363292026-10-212026-11-202026-09-22
ABVX86%46%99%11,7067,2954,41172,901832026-12-142026-11-202026-09-22
ACI42%49%100%2,5061,66883852,980282026-10-202026-11-202026-09-22
ACN59%88%3%17,43410,7086,726114,90592026-10-012026-11-202026-09-22
ADBE39%35%28%26,81016,54910,261334,897782026-12-092026-11-202026-09-22
ADI64%94%68%3,5662,2631,30355,047702026-12-012026-11-202026-09-22
ADM33%36%90%2,9261,5501,37634,179352026-10-272026-11-202026-09-22
AEHR110%14%29%12,0697,1804,88946,105142026-10-062026-11-202026-09-22
AEM39%14%20%3,7202,3791,34143,661362026-10-282026-11-202026-09-22
AEO37%0%1%9,6987,7371,96176,332632026-11-242026-11-202026-09-22
AES12%3%77%1,1571,04211539,696372026-10-292026-11-202026-09-22
AFRM58%14%17%17,63211,3046,328103,385502026-11-112026-11-202026-09-22
AG55%1%6%21,46113,2908,171456,805502026-11-112026-11-202026-09-22
AGI53%44%14%3,6982,1141,58464,729362026-10-282026-11-202026-09-22
AI56%13%13%13,82011,7982,022197,601782026-12-092026-11-202026-09-22
AKAM91%90%51%11,9176,7945,12395,470492026-11-102026-11-202026-09-22
ALAB107%68%44%40,68828,24812,440110,214492026-11-102026-11-202026-09-22
ALB50%7%12%6,0663,9012,16543,464432026-11-042026-11-202026-09-22
ALK45%13%43%4,4733,3331,14040,853232026-10-152026-11-202026-09-22
ALLY27%14%0%1,10586124442,471282026-10-202026-11-202026-09-22
AMAT52%33%14%55,68335,16620,517297,447512026-11-122026-11-202026-09-22
AMBA91%63%74%5,3724,0081,36435,483702026-12-012026-11-202026-09-22
AMD58%47%35%1,313,851798,269515,5822,440,725422026-11-032026-11-202026-09-22
AMGN29%42%31%10,0906,4853,60551,495422026-11-032026-11-202026-09-22
AMKR77%48%24%9,9407,7592,18173,117412026-11-022026-11-202026-09-22
AMZN31%39%39%1,095,015855,715239,3003,774,588372026-10-292026-11-202026-09-22
ANET53%37%25%32,78423,6489,136164,165412026-11-022026-11-202026-09-22
APA45%29%26%7,2193,5463,673106,789432026-11-042026-11-202026-09-22
APH49%49%1%14,58910,5214,068154,095362026-10-282026-11-202026-09-22
APLD86%8%21%97,12267,78129,341601,348222026-10-142026-11-202026-09-22
APO36%18%23%4,7633,6371,12677,089432026-11-042026-11-202026-09-22
APP62%32%21%61,09540,92220,173206,207502026-11-112026-11-202026-09-22
APPS102%48%52%8,2447,1941,05035,932502026-11-112026-11-202026-09-22
AR84%99%82%7,0393,9723,06739,883362026-10-282026-11-202026-09-22
ARCC14%5%29%4,8312,6762,15571,276352026-10-272026-11-202026-09-22
ARM85%69%51%187,755136,01651,739530,486432026-11-042026-11-202026-09-22
AS49%24%25%15,2451,63113,61492,404632026-11-242026-11-202026-09-22
ASML46%38%31%16,7948,0998,69553,352222026-10-142026-11-202026-09-22
ASST83%7%91%109,99295,15314,8391,345,854522026-11-132026-11-202026-09-22
ASTS69%2%5%105,21575,94729,268744,742552026-11-162026-11-202026-09-22
ASX54%16%88%7,4536,3781,07578,248302026-10-222026-11-202026-09-22
AVAV67%19%24%4,5492,9271,62230,059772026-12-082026-11-202026-09-22
AVGO39%12%16%503,372388,722114,6501,708,720792026-12-102026-11-202026-09-22
AVTR69%50%14%10799850,826312026-10-232026-11-202026-09-22
AXP24%15%21%8,9004,6364,26478,727312026-10-232026-11-202026-09-22
AXTI110%6%0%48,20132,49315,708144,661372026-10-292026-11-202026-09-22
AZN33%65%94%7,2703,4593,81151,996382026-10-302026-11-202026-09-22
B44%20%99%21,45415,3016,153346,294372026-10-292026-11-202026-09-22
BA31%34%57%71,14553,41417,731546,947362026-10-282026-11-202026-09-22
BABA51%80%59%157,668124,34333,3251,492,480702026-12-012026-11-202026-09-22
BAC20%10%0%95,38661,76533,6211,398,238222026-10-142026-11-202026-09-22
BAX36%4%6%1,7171,55616128,293372026-10-292026-11-202026-09-22
BBWI67%57%0%3,8742,5691,30531,378572026-11-182026-11-202026-09-22
BBY39%35%100%3,0951,4471,64828,586632026-11-242026-11-202026-09-22
BE83%3%4%123,27968,92554,354594,595372026-10-292026-11-202026-09-22
BEKE61%53%47%1,6491,27237728,241492026-11-102026-11-202026-09-22
BHF92%73%22%34012022040,078502026-11-112026-11-202026-09-22
BHP34%31%17%2,3731,1031,27031,3721542027-02-232026-11-202026-09-22
BHVN98%31%10%1,3361,2686837,988562026-11-172026-11-202026-09-22
BIDU49%29%35%30,52923,5436,986264,340632026-11-242026-11-202026-09-22
BILI60%42%86%5,4885,15533392,166512026-11-122026-11-202026-09-22
BIRK64%52%94%4,6954,38730842,490862026-12-172026-11-202026-09-22
BKNG45%73%44%71,93165,3076,624162,806432026-11-042026-11-202026-09-22
BKR50%63%98%3,4403,10233830,404362026-10-282026-11-202026-09-22
BMNR82%29%27%232,026152,25479,7721,444,593592026-11-202026-11-202026-09-22
BMY27%28%86%24,55011,49113,059441,946372026-10-292026-11-202026-09-22
BNY31%47%1%7,1523,4023,75028,815232026-10-152026-11-202026-09-22
BP41%94%14%16,15612,4153,741265,481422026-11-032026-11-202026-09-22
BRK-B14%22%16%34,96123,66311,298275,0282026-11-202026-09-22
BROS50%25%17%12,7449,3823,36255,852502026-11-112026-11-202026-09-22
BRUN164%46%32%1,10291019247,485712026-12-022026-11-202026-09-22
BSX39%58%32%38,87031,3837,487682,304362026-10-282026-11-202026-09-22
BTDR100%10%0%25,07218,8476,225240,017552026-11-162026-11-202026-09-22
BTU62%31%27%1,9821,26272031,014372026-10-292026-11-202026-09-22
BX38%37%93%10,7235,8754,848192,741232026-10-152026-11-202026-09-22
BYND85%40%98%5,9614,1181,843217,921502026-11-112026-11-202026-09-22
C33%53%3%30,94120,54610,395483,981212026-10-132026-11-202026-09-22
CAG39%53%45%10,0068,6341,372109,65782026-09-302026-11-202026-09-22
CARR34%19%22%1,9481,40554353,675302026-10-222026-11-202026-09-22
CART43%23%12%5,6785,00767143,938562026-11-172026-11-202026-09-22
CAT39%48%33%17,8988,7079,191110,010432026-11-042026-11-202026-09-22
CAVA60%44%24%6,9704,5432,42783,456492026-11-102026-11-202026-09-22
CBRS76%14%10%24,13716,4957,642151,697712026-12-022026-11-202026-09-22
CCI31%34%30%1,16590925627,584292026-10-212026-11-202026-09-22
CCJ52%23%17%20,26915,6254,644245,292382026-10-302026-11-202026-09-22
CCL48%45%0%55,73041,27314,457641,99872026-09-292026-11-202026-09-22
CCXI147%85%64%8,8887,7821,10651,1952026-11-202026-09-22
CDE70%19%12%13,4829,1404,342289,571502026-11-112026-11-202026-09-22
CEG44%11%2%13,4029,3114,091109,981482026-11-092026-11-202026-09-22
CELH61%47%25%19,71713,4336,284420,570442026-11-052026-11-202026-09-22
CF70%94%60%4,7331,2053,52830,089432026-11-042026-11-202026-09-22
CG43%20%1%7,2815,7051,57641,432492026-11-102026-11-202026-09-22
CHTR136%99%10%6,0312,6683,36362,987382026-10-302026-11-202026-09-22
CHWY58%61%39%9,3337,4351,898114,309722026-12-032026-11-202026-09-22
CHYM32%2%99%1,40770869936,377502026-11-112026-11-202026-09-22
CIEN76%30%100%7,6654,2823,38345,985792026-12-102026-11-202026-09-22
CIFR95%8%12%176,81083,71693,0941,212,399502026-11-112026-11-202026-09-22
CLF73%60%0%29,98817,69712,291404,299342026-10-262026-11-202026-09-22
CLMT54%19%16%3,1772,20996839,932452026-11-062026-11-202026-09-22
CLS67%11%17%7,6483,9923,65662,160342026-10-262026-11-202026-09-22
CLSK81%12%21%69,78053,75416,026573,712852026-12-162026-11-202026-09-22
CLX32%29%0%7,1264,5252,60157,367432026-11-042026-11-202026-09-22
CMCSA27%6%3%55,33314,31541,018509,678302026-10-222026-11-202026-09-22
CMG41%61%3%40,78014,98125,799443,119362026-10-282026-11-202026-09-22
CMPS79%32%44%4,3973,1961,20148,809372026-10-292026-11-202026-09-22
CNC50%39%0%3,3482,1011,24745,776352026-10-272026-11-202026-09-22
CNQ34%38%81%13,89812,4421,45636,648372026-10-292026-11-202026-09-22
CODI145%87%85%276106170109,367712026-12-022026-11-202026-09-22
COF28%10%24%4,0192,8281,19154,121302026-10-222026-11-202026-09-22
COHR81%34%38%27,62314,19413,429157,236502026-11-112026-11-202026-09-22
COIN70%49%40%190,236129,85260,384746,628372026-10-292026-11-202026-09-22
COMP74%37%0%1,4931,38810536,557502026-11-112026-11-202026-09-22
COP34%54%0%17,86711,6746,193159,992372026-10-292026-11-202026-09-22
COPX49%38%49%6,5712,5833,988162,0642026-11-202026-09-22
CORZ66%1%7%86,23757,05129,186808,944502026-11-112026-11-202026-09-22
COST29%88%54%42,98826,73316,255166,60722026-09-242026-11-202026-09-22
CPB46%86%100%9,5425,1654,37797,732782026-12-092026-11-202026-09-22
CPNG53%49%100%6,2154,4651,750191,707492026-11-102026-11-202026-09-22
CPRI75%39%13%1,48686362333,493442026-11-052026-11-202026-09-22
CPRT27%13%0%3,3391,2492,09053,198572026-11-182026-11-202026-09-22
CRCL79%22%27%83,05256,63426,418548,805572026-11-182026-11-202026-09-22
CRDO70%2%4%50,78533,00317,782209,004712026-12-022026-11-202026-09-22
CRGY68%24%100%3,3312,91641533,471482026-11-092026-11-202026-09-22
CRK70%52%27%3,5553,03052542,622422026-11-032026-11-202026-09-22
CRM38%28%28%50,09531,30718,788422,612772026-12-082026-11-202026-09-22
CRSP71%55%36%5,6314,5911,04040,143432026-11-042026-11-202026-09-22
CRWD53%54%36%101,82059,21742,603496,142702026-12-012026-11-202026-09-22
CRWV76%8%11%324,332239,42984,9031,911,506552026-11-162026-11-202026-09-22
CSCO33%58%97%43,29132,02911,262494,801572026-11-182026-11-202026-09-22
CSGP67%49%100%2,0151,28273343,163352026-10-272026-11-202026-09-22
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CXW44%18%26%1,6061,14745934,056482026-11-092026-11-202026-09-22
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D27%46%28%2,6102,28132933,751382026-10-302026-11-202026-09-22
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DAX29%37%45%00002026-11-202026-09-22
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GAP38%11%9%6,7265,3141,41298,692582026-11-192026-11-202026-09-22
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GE32%31%26%11,5267,7183,808126,813282026-10-202026-11-202026-09-22
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GIS48%75%1%9,7675,6854,082152,80012026-09-232026-11-202026-09-22
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GM31%24%99%15,76810,0305,738116,795282026-10-202026-11-202026-09-22
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GRAL88%25%29%7,9995,1112,88847,931572026-11-182026-11-202026-09-22
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GS31%35%33%28,25415,79712,457159,955212026-10-132026-11-202026-09-22
GTLB51%6%8%3,7392,79094965,258762026-12-072026-11-202026-09-22
HAL35%18%32%13,68511,4222,263238,224282026-10-202026-11-202026-09-22
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HL55%2%5%15,35210,0535,299294,619502026-11-112026-11-202026-09-22
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HOOD66%46%34%307,776190,538117,2381,454,682432026-11-042026-11-202026-09-22
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HYMC78%1%2%2,1611,31684529,394422026-11-032026-11-202026-09-22
IBKR44%50%39%17,09510,3196,77641,735282026-10-202026-11-202026-09-22
IBM35%41%45%44,11933,67510,444365,226292026-10-212026-11-202026-09-22
IEF8%81%100%154,471115,00339,468610,4122026-11-202026-09-22
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INTU45%35%32%9,6014,7294,87269,979702026-12-012026-11-202026-09-22
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IOT69%53%29%18,23112,1686,06362,721652026-11-262026-11-202026-09-22
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KEY27%17%97%4,9404,30463643,813282026-10-202026-11-202026-09-22
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KSA3123332026-11-202026-09-22
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MMM3,3742,53783739,075352026-10-272026-11-202026-09-22
MO22%36%90%12,6498,8273,822161,005372026-10-292026-11-202026-09-22
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MS35%64%100%13,7038,5975,106144,596222026-10-142026-11-202026-09-22
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NET79%81%43%39,30326,86412,43985,079372026-10-292026-11-202026-09-22
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ZS55%27%100%24,11116,5977,514121,329702026-12-012026-11-202026-09-22
ZTS40%42%100%5,9423,6882,254106,016502026-11-112026-11-202026-09-22

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