{"id":551,"date":"2017-06-25T07:48:27","date_gmt":"2017-06-25T05:48:27","guid":{"rendered":"http:\/\/dobretrejdy.com\/?p=551"},"modified":"2022-11-08T23:13:01","modified_gmt":"2022-11-08T21:13:01","slug":"theta","status":"publish","type":"post","link":"https:\/\/dobretrejdy.com\/?p=551","title":{"rendered":"Th\u00e9ta"},"content":{"rendered":"

\u00a0 Nev\u00edm, jestli Th\u00e9ta Kaz\u00ed Libu\u0161i, proto\u017ee nejsem vojvoda Krok, ale proto\u017ee jsem op\u010dn\u00ed obchodn\u00edk, tak v\u00edm, jak\u00a0Th\u00e9ta<\/strong> m\u016f\u017ee zkazit i velmi dobrou op\u010dn\u00ed pozici. V\u00a0p\u0159edch\u00e1zej\u00edc\u00edch \u010dl\u00e1nc\u00edch jsem ji\u017e popisoval, jak se m\u011bn\u00ed cena op\u010dn\u00edho kontraktu v\u00a0souvislost\u00ed s\u00a0pohybem podkladov\u00e9ho aktiva a jak tuto z\u00e1vislost zachycujeme pomoc\u00ed \u0159eck\u00e9ho p\u00edsmene Delta. V\u00a0n\u00e1vaznosti na pozorov\u00e1n\u00ed Delta op\u010dn\u00edho kontraktu jsem se pomoc\u00ed Gamma pokusil popsat rychlost, s\u00a0jakou se tato z\u00e1vislost zm\u011bny ceny podkladu projevuje v cen\u00e1ch opc\u00ed. Proto\u017ee se cena op\u010dn\u00edho kontraktu vypo\u010d\u00edt\u00e1v\u00e1 nap\u0159\u00edklad pomoc\u00ed Black-Scholesova oce\u0148ovac\u00edho modelu, tak mus\u00edm vyhodnotit, \u017ee krom\u011b pohybu ceny podkladov\u00e9ho aktiva m\u00e1 na cenu op\u010dn\u00edho kontraktu tak\u00e9 vliv dal\u0161\u00edch p\u011bt faktor\u016f krom\u011b Ceny podkladu<\/strong>\u00a0a t\u011bmito jsou – Hodnota strike<\/strong>, D\u00e9lka \u017eivota op\u010dn\u00edho kontraktu<\/strong>, Implied Volatilita<\/strong>, \u00darokov\u00e1 m\u00edra<\/strong> a hodnota p\u0159\u00edpadn\u011b vypl\u00e1cen\u00e9 Dividendy<\/strong>. Proto\u017ee jsem ji\u017e zm\u00ednil, \u017ee Hodnota strike, \u00darokov\u00e1 m\u00edra a hodnota Dividendy jsou \u201ezjistiteln\u00e9 konstanty\u201c, tak zb\u00fdv\u00e1 k\u00a0ur\u010den\u00ed z\u00e1vislosti ceny opce na t\u011bchto \u0161esti vstupn\u00edch hodnot\u00e1ch pouze zachytit a popsat vliv Implied Volatility a D\u00e9lky \u017eivota opce (b\u011b\u017e\u00edc\u00edho \u010dasu) a m\u011blo by b\u00fdt jasn\u011bj\u0161\u00ed, jak cel\u00e1 skl\u00e1danka vliv\u016f zm\u011bny t\u011bchto vstupn\u00edch hodnot funguje.<\/span><\/p>\n

\u00a0\u00a0 Th\u00e9ta<\/strong> popisuje a m\u011b\u0159\u00ed, jak\u00fd m\u00e1 b\u011b\u017e\u00edc\u00ed \u010das vliv na cenu op\u010dn\u00edho kontraktu<\/strong>, o tom bude dne\u0161n\u00ed \u010dl\u00e1nek. V\u00a0\u010d\u00edseln\u00e9m vyj\u00e1d\u0159en\u00ed n\u00e1m hodnota Th\u00e9ta<\/strong> sd\u011bluje, o kolik se zm\u011bn\u00ed cena op\u010dn\u00edho kontraktu za jeden den<\/strong>. Pokud m\u00e1 Long Call opce na strike 150 cenu 250 USD a hodnotu Th\u00e9ta -12, bude to jednodu\u0161e znamenat, \u017ee pokud by v\u0161echno z\u016fstalo stejn\u011b (Cena akcie, Implied Volatilita, Hodnota \u00farok\u016f, Dividendov\u00fd n\u00e1rok a Strike), tak z\u00edtra bude hodnota t\u00e9to Long Call o 12 USD ni\u017e\u0161\u00ed a bude tak st\u00e1t ji\u017e jen 238 USD.<\/span><\/p>\n

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Matematika Th\u00e9ta<\/span><\/strong><\/h1>\n

\u00a0\u00a0 Vyhodnocen\u00edm Black-Scholesova oce\u0148ovac\u00edho modelu by m\u011blo b\u00fdt mo\u017en\u00e9 zjistit matematickou z\u00e1vislost b\u011b\u017e\u00edc\u00edho \u010dasu trv\u00e1n\u00ed op\u010dn\u00edho kontraktu na jeho cenu. Vzorce jsem samoz\u0159ejm\u011b nevytvo\u0159il s\u00e1m, ale vzal je z\u00a0odborn\u00e9 literatury. Nebudu p\u00e1trat, jak to bylo vypo\u010dteno, to je toti\u017e mimo m\u00e9 schopnosti, ale budu se sna\u017eit to alespo\u0148 m\u00edrn\u011b pochopit. Vzorec pro Th\u00e9ta<\/strong> pro Call opci\u00a0<\/strong>a Put opci<\/strong> je na obr\u00e1zku<\/span><\/p>\n

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\u00a0\u00a0 Vzorce vypadaj\u00ed opravdu na prvn\u00ed pohled hrozn\u011b. Na obr\u00e1zku jsem u vzorce Th\u00e9ta Call opce vyzna\u010dil n\u011bkolik z\u00e1kladn\u00edch oblast\u00ed, kter\u00e9 n\u00e1m cel\u00fd proces pochopen\u00ed pro mo\u017en\u00e9 dal\u0161\u00ed zpracov\u00e1n\u00ed m\u016f\u017ee velmi zjednodu\u0161it.<\/span><\/p>\n

\u00a0 \u00a0V\u00a0prvn\u00ed \u010derven\u00e9m obd\u00e9ln\u00edku<\/span> je hodnota 1\/T<\/strong>, kde T je po\u010det dn\u016f v\u00a0kalend\u00e1\u0159n\u00edm roce<\/strong>, tedy 365<\/strong>. Touto hodnotou se d\u011bl\u00ed nejv\u00fdznamn\u011bj\u0161\u00ed \u010d\u00e1st vzorce v\u00fdpo\u010dtu. To je pro pochopen\u00ed Th\u00e9ta pro tuto chv\u00edli to nejpodstatn\u011bj\u0161\u00ed zji\u0161t\u011bn\u00ed<\/strong>. Vypl\u00fdv\u00e1 z\u00a0n\u011bj, \u017ee Th\u00e9ta se m\u011bn\u00ed ka\u017ed\u00fd kalend\u00e1\u0159n\u00ed den<\/strong>., a toto je t\u0159eba opravdu registrovat, proto\u017ee to nen\u00ed na prvn\u00ed pohled patrn\u00e9. Je to ale pochopiteln\u00e9, \u010das b\u011b\u017e\u00ed po\u0159\u00e1d i kdy\u017e se s\u00a0opcemi neobchoduje, tedy nap\u0159\u00edklad o v\u00edkendech, \u010das nelze nijak zastavit nebo jej po\u0161\u0165ouchnout rychleji vp\u0159ed. Pokud v\u00a0p\u00e1tek skon\u010d\u00ed obchodov\u00e1n\u00ed na n\u011bjak\u00e9 cen\u011b s\u00a0n\u011bjakou Delta a Gamma, tak tyto \u00fadaje nebudou v\u00a0ned\u011bli odpoledne jin\u00e9, proto\u017ee se o v\u00edkendu s\u00a0podkladov\u00fdm aktivem neobchoduje. Toto se v\u0161ak net\u00fdk\u00e1 Th\u00e9ta, proto\u017ee \u010das plyne i o v\u00edkendu. V\u00a0uveden\u00e9m p\u0159\u00edkladu s Long Call opc\u00ed na strike 150 a cenou podkladu v\u00a0p\u00e1tek na Close ve v\u00fd\u0161i 250 USD a hodnotu Th\u00e9ta -12, tak budu muset konstatovat, \u017ee za sobotu a ned\u011bli hodnota opce ztrat\u00ed 2 x -12 USD, tedy cel\u00fdch -24 USD. Pokud by akcie otev\u0159ela v\u00a0pond\u011bl\u00ed na Open a pokud by v\u0161echno z\u016fstalo stejn\u011b (Cena akcie, Implied Volatilita, Hodnota \u00farok\u016f, Dividendov\u00fd n\u00e1rok a Strike), tak by m\u00e1 Long Call 150 st\u00e1la ji\u017e jen 250 USD \u2013 24 USD = 226 USD.<\/span><\/p>\n

\u00a0 V\u00a0zelen\u00e9m krou\u017eku<\/span> um\u00edst\u011bn\u00e9m v \u010ditateli zlomku je exponenci\u00e1ln\u00ed funkce, jej\u00edm\u017e exponentem je sou\u010din hodnoty Dividendy a D\u00e9lka \u017eivota opce (-q*t). Proto\u017ee jsem v\u00a0\u010dl\u00e1nc\u00edch v\u00fdpo\u010dtu ceny opc\u00ed a v\u00a0\u010dl\u00e1nc\u00edch o Dividend\u00e1ch uv\u00e1d\u011bl, \u017ee hodnota Dividendy vstupuje do Black-Scholesova vzorce ve sv\u00e9m anualizovan\u00e9m tvaru<\/strong>, m\u016f\u017eeme se na hodnotu exponentu exponenci\u00e1ln\u00ed funkce d\u00edvat, jako by byl t\u00e9m\u011b\u0159 nulov\u00fd a cokoliv t\u00e9m\u011b\u0159 na nultou je t\u00e9m\u011b\u0159 jedna, tato \u010d\u00e1st zlomku tedy nem\u00e1 na hodnotu Th\u00e9ta praktick\u00fd vliv a m\u016f\u017eeme ji z\u00a0v\u00fdpo\u010dtu vylou\u010dit. \u00a0<\/span><\/p>\n

\u00a0V\u00a0dal\u0161\u00edm \u010derven\u00e9m obd\u00e9ln\u00edku<\/span> jsem ozna\u010dil oblast, kter\u00e1 p\u0159edstavuje Distribu\u010dn\u00ed funkci norm\u00e1ln\u00edho rozd\u011blen\u00ed<\/strong> pro hodnotu d1<\/strong>. Tuto hodnotu jsem ji\u017e zji\u0161\u0165oval a ukazoval jej\u00ed matematick\u00fd tvar v\u00a0\u010dl\u00e1nku Cena opc\u00ed<\/strong><\/a>,<\/span> tam jsem tak\u00e9 vyu\u017e\u00edval jej\u00ed hodnotu p\u0159i ur\u010dov\u00e1n\u00ed ceny opce.\u00a0 Jej\u00ed v\u00fdpo\u010det nen\u00ed slo\u017eit\u00fd a Excel si s\u00a0n\u00ed um\u00ed poradit a nav\u00edc je vyu\u017e\u00edv\u00e1na i u jin\u00fdch ji\u017e ilustrovan\u00fdch v\u00fdpo\u010dt\u016f, tak\u017ee ji m\u00e1m ji\u017e ve sv\u00e9m uk\u00e1zkov\u00e9m Excelu ji\u017e \u201ep\u0159edpo\u010d\u00edtanou\u201c.<\/span><\/p>\n

\u00a0 Pro oblast ozna\u010denou zelenou elipsou<\/span> plat\u00ed stejn\u00e1 interpretace jako pro oblast ozna\u010denou zelen\u00fdm krou\u017ekem, do hodnoty Th\u00e9ta vstupuj\u00ed anualizovan\u00e9 Dividendy, tak\u017ee zanedbateln\u00e1 hodnota, kterou nemus\u00edme do sv\u00e9ho v\u00fdpo\u010dtu zahrnovat.<\/span><\/p>\n

\u00a0 Pokud bych tedy cel\u00fd vzorec takto \u201eosekal\u201c a po\u010de\u0161til, tak si mohu jeho matematick\u00fd tvar v\u00a0\u010de\u0161tin\u011b<\/strong> vyobrazit tak, jak je vid\u011bt na n\u00ed\u017ee uveden\u00e9m obr\u00e1zku.<\/span><\/p>\n

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\u00a0 Podle takov\u00e9ho vzorce by pak nem\u011bl b\u00fdt probl\u00e9m si Theta vypo\u010d\u00edtat nap\u0159\u00edklad v\u00a0Excelu, proto\u017ee obsahuje pouze jednoduch\u00e9 matematick\u00e9 operace se vstupn\u00edmi hodnotami a vyu\u017e\u00edv\u00e1 funkce, kter\u00e9 ji\u017e byly pou\u017eity v\u00a0p\u0159edchoz\u00edch v\u00fdpo\u010dtech ceny opc\u00ed nebo \u0159eck\u00fdch p\u00edsmen. V\u00a0takov\u00e9m excelovsk\u00e9m se\u0161itu jsem vytvo\u0159il dv\u011b funkce pro v\u00fdpo\u010det Th\u00e9ta Call a Th\u00e9ta Put opc\u00ed a je mo\u017en\u00e9 je spou\u0161t\u011bt kdekoliv tomto se\u0161itu po zad\u00e1n\u00ed funkce \u201e=ThetaCall<\/strong>\u201c nebo \u201e=ThetaPut<\/strong>\u201c se zad\u00e1n\u00edm argument\u016f podle n\u00ed\u017ee uveden\u00e9ho obr\u00e1zku.<\/span><\/p>\n

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\u00a0 \u00a0Tento jednoduch\u00fd se\u0161it v\u00a0Excelu je ke\u00a0st\u00e1\u017een\u00ed zde<\/a><\/strong><\/span> a tak\u00e9 si m\u016f\u017eete na z\u00e1lo\u017ece V\u00fdvoj\u00e1\u0159 zobrazit ve VBA jednoduch\u00fd k\u00f3d vzorce k v\u00fdpo\u010dtu, tento si m\u016f\u017eete voln\u011b kop\u00edrovat nap\u0159\u00edklad do vlastn\u00edch tabulek. P\u0159i otev\u00edr\u00e1n\u00ed sta\u017een\u00e9ho se\u0161itu mus\u00edte na v\u00fdzvu programu „povolit makra“.\u00a0<\/span><\/p>\n

\u00a0Mo\u017en\u00e1 to cel\u00e9 vypad\u00e1 zbyte\u010dn\u00e9, takto pitvat a zab\u00fdvat se slo\u017eit\u00fdmi matemetick\u00fdmi vzorci, kdy\u017e v ka\u017ed\u00e9 slu\u0161n\u00e9 obchodn\u00ed platform\u011b jsou ji\u017e \u0159eck\u00e1 p\u00edsmena zobrazena. V\u017edy, kdy\u017e jsem otev\u0159el n\u011bjakou publikaci o opc\u00edch, tak jsem nar\u00e1\u017eel na podobn\u00e9 slo\u017eit\u00e9 vzorce a kladl jsem si ot\u00e1zku, jestli to nen\u00ed zbyte\u010dn\u00e9 to do t\u011bchto publikac\u00ed d\u00e1vat, kdo to vlastn\u011b \u010dte nebo rozum\u00ed tomu v\u016fbec n\u011bkdo? P\u0159i bedliv\u011bj\u0161\u00edm pohledu na takov\u00e9 chuchvalce znak\u016f a v\u00fdraz\u016f a jejich p\u0159evod na \u010desk\u00e9 v\u00fdrazy jsem pak ale zji\u0161\u0165oval, \u017ee to zase tak slo\u017eit\u00e9 nen\u00ed, \u017ee se to tak vlastn\u011b jenom slo\u017eit\u011b tv\u00e1\u0159\u00ed. Proto se sna\u017e\u00edm takov\u00e9 zjednodu\u0161ov\u00e1n\u00ed uk\u00e1zat ve sv\u00fdch \u010dl\u00e1nc\u00edch, snad to nevad\u00ed…<\/span><\/p>\n

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Logika Th\u00e9ta<\/span><\/strong><\/h1>\n

\u00a0\u00a0 Hodnota Th\u00e9ta jednotliv\u00fdch opc\u00ed na jednotliv\u00fdch strikes maj\u00ed velmi podobnou logiku, jako m\u00e1 hodnota Gamma z\u00a0p\u0159edchoz\u00edho \u010dl\u00e1nku, co\u017e bude m\u00edt sv\u00e9 d\u016fsledky popisovan\u00e9 d\u00e1le. Proto\u017ee nejv\u00edce pr\u00e9mia je obsa\u017eeno v\u00a0cen\u011b opc\u00ed na ATM strike, tedy na strikes, kter\u00e9 jsou nejbl\u00ed\u017ee obchodovan\u00e9 cen\u011b podkladov\u00e9ho aktiva, bude tak\u00e9 hodnota Th\u00e9ta<\/strong> na t\u011bchto ATM strikes nejvy\u0161\u0161\u00ed<\/strong>. Na strike, kter\u00e9 jsou vzd\u00e1len\u011bj\u0161\u00ed od t\u011bchto ATM strike hodnota Th\u00e9ta kles\u00e1, a to v\u00a0obou sm\u011brech, tedy kles\u00e1 u opc\u00ed se strike<\/strong>, kter\u00e9 jsou v\u00edce \u201emimo pen\u00edze\u201c<\/strong> a tak\u00e9 stejn\u011b kles\u00e1<\/strong>, jak se opce v\u00edce \u201epono\u0159uj\u00ed do pen\u011bz“<\/strong>, tedy \u010d\u00edm v\u00edce OTM nebo ITM, t\u00edm je hodnota Th\u00e9ta ni\u017e\u0161\u00ed.<\/span><\/p>\n

\u00a0\u00a0 Stejn\u011b to plat\u00ed tak\u00e9 pro jednotliv\u00e9 expirace. U opc\u00ed, kter\u00e9 maj\u00ed stejn\u00fd strike, ale jinou expirac\u00ed plat\u00ed, \u017ee \u010d\u00edm v\u00edce m\u00e1 opce svou expiraci vzd\u00e1len\u011bj\u0161\u00ed<\/strong>, t\u00edm je hodnota Th\u00e9ta ni\u017e\u0161\u00ed<\/strong>. \u010casov\u00e1 hodnota \u2013 pr\u00e9mium \u2013 u velmi vzd\u00e1len\u00fdch opc\u00ed tak na plynut\u00ed \u010dasu nereaguje tak citliv\u011b, jako cena opc\u00ed s\u00a0bli\u017e\u0161\u00edmi expiracemi. Opce s\u00a0nejbli\u017e\u0161\u00ed expirac\u00ed pak maj\u00ed hodnotu Th\u00e9ta nejvy\u0161\u0161\u00ed, zjednodu\u0161en\u011b \u0159e\u010deno, jak se kr\u00e1t\u00ed opci \u010das jej\u00edho \u017eivota, t\u00edm zb\u011bsileji m\u00e1 Th\u00e9ta schopnost p\u016fsobit na sni\u017eov\u00e1n\u00ed a rozpad jej\u00ed ceny. \u00a0Na obr\u00e1zku m\u016f\u017eete vid\u011bt jednotliv\u00e9 hodnoty Th\u00e9ta pro jednotliv\u00e9 expirace a jednotliv\u00e9 strike.<\/span><\/p>\n

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\u00a0 Z\u00e1kladn\u00ed logika pro sledov\u00e1n\u00ed celkov\u00e9 expozice m\u00e9ho op\u010dn\u00edho portfolia v\u016f\u010di plynouc\u00edmu \u010dasu pak bude vych\u00e1zet z\u00a0celkov\u00e9 hodnoty Th\u00e9ta m\u00fdch op\u010dn\u00edch pozic. K\u00a0takov\u00e9mu p\u0159\u00edstupu pak budu muset opat\u0159it hodnotu Th\u00e9ta pat\u0159i\u010dn\u00fdm matematick\u00fdm znam\u00e9nkem.<\/span><\/p>\n

Th\u00e9ta Long opc\u00ed je z\u00e1porn\u00e1, Th\u00e9ta Short opc\u00ed je kladn\u00e1<\/span><\/strong><\/h2>\n

\u00a0 Pokud budu dr\u017eitel Long Call<\/strong> opce nebo Long Put<\/strong> opce, bude \u010das pracovat v\u00a0m\u016fj neprosp\u011bch<\/strong>, pokud se nebudou pat\u0159i\u010dn\u011b pohybovat ostatn\u00ed cenotvorn\u00e9 prvky hodnoty m\u00fdch Long opc\u00ed, tedy nebude dostate\u010dn\u00fd pohyb na podkladov\u00e9m aktivu nebo bude klesat nebo stagnovat Implied Volatilita. Pokud by tyto prvky byl nem\u011bnn\u00e9, tak o hodnotu Th\u00e9ta bude cena opce ka\u017edodenn\u011b ne\u00faprosn\u011b ni\u017e\u0161\u00ed. O hodnotu Th\u00e9ta (z\u00e1pornou)<\/strong> by se tak ka\u017edodenn\u011b zv\u00fd\u0161ila m\u00e1 ztr\u00e1ta<\/strong> na takov\u00e9m Long op\u010dn\u00edm kontraktu, o tuto hodnotu Th\u00e9ta m\u00e9n\u011b bych byl schopen na trhu takovou opci prodat a ztr\u00e1tov\u011b vystoupit z\u00a0pozice.<\/span><\/p>\n

\u00a0\u00a0 Vypisovatel Short Call<\/strong> nebo Short Put<\/strong> opc\u00ed to maj\u00ed s\u00a0hodnotou Th\u00e9ta p\u0159esn\u011b naopak. \u010cas pracuje pro vypisovatele<\/strong>. Pokud ostatn\u00ed cenotvorn\u00e9 prvky jako je Pohyb podkladu a Implied Volatilita budou nev\u00fdrazn\u00e9, bude hodnota Th\u00e9ta ka\u017ed\u00fd den ub\u00edrat na cen\u011b vypsan\u00fdch opc\u00ed, a to je p\u0159esn\u011b to, co si vypisovatel p\u0159eje. Pokud by se podklad nepohyboval a Implied Volatilita byla nem\u011bnn\u00e1 nebo se sni\u017eovala, tak o hodnotu Th\u00e9ta (kladnou)<\/strong> by Short opce pro vypisovatele ka\u017ed\u00fd den ztratila na sv\u00e9 hodnot\u011b, co\u017e by prezentovalo hodnotu zisku<\/strong> na tomto op\u010dn\u00edm kontraktu, o tuto hodnotu Th\u00e9ta m\u00e9n\u011b bych byl schopen na trhu takovou opci koupit zp\u011bt a vystoupit ziskov\u011b z\u00a0pozice. O kladnou hodnotu Th\u00e9ta tak roste m\u016fj profit.<\/span><\/p>\n

\u00a0\u00a0 U slo\u017eit\u011bj\u0161\u00edch op\u010dn\u00edch pozic pak mohu pomoc\u00ed celkov\u00e9 hodnoty Th\u00e9ta zji\u0161\u0165ovat, nakolik je takov\u00e9 slo\u017eit\u011bj\u0161\u00ed portfolio vystaveno riziku plynouc\u00edho z\u00a0b\u011bhu \u010dasu m\u00fdch dr\u017een\u00fdch op\u010dn\u00edch pozic. Na n\u00ed\u017ee uveden\u00e9m obr\u00e1zku je vid\u011bt jednoduch\u00e1 Delta-Neutral<\/strong> op\u010dn\u00ed pozice 3 x ATM Long Straddle<\/strong> na akcii AAPL s\u00a0expirac\u00ed za jeden m\u011bs\u00edc. Ob\u011b Long opce Call i Put jsou na strike 146, Delta-Neutralitu jsem vytvo\u0159il po\u0159\u00edzen\u00edm 23 Short akci\u00ed AAPL.<\/strong><\/span><\/p>\n

\"\"<\/p>\n

\u00a0 Tato Delta-Neutral op\u010dn\u00ed pozice, tak jak je vid\u011bt na obr\u00e1zku m\u00e1 Delta<\/strong> na hodnot\u011b 0<\/strong>, jej\u00ed celkov\u00e1 Gamma je 36<\/strong> a celkov\u00e1 hodnota Th\u00e9ta je -30<\/strong>. Co to znamen\u00e1? Kladn\u00e1 Gamma znamen\u00e1, \u017ee op\u010dn\u00ed pozici bude velmi sv\u011bd\u010dit pohyb v\u00a0jak\u00e9mkoliv sm\u011bru, proto\u017ee je kladn\u00e1. \u010c\u00edm v\u011bt\u0161\u00ed pohyb t\u00edm l\u00e9pe, to vypl\u00fdv\u00e1 z\u00a0popisovan\u00e9ho stavu Gamma v\u00a0minul\u00e9m \u010dl\u00e1nku<\/strong><\/a><\/span>. Hodnota Th\u00e9ta je z\u00e1porn\u00e1 a je na hodnot\u011b -30. Neznamen\u00e1 to nic jin\u00e9ho, \u017ee pokud se akcie AAPL nepohne ani o cent a nevzroste Implied Volatilita, tak z\u00edtra bude hodnota<\/strong> m\u00fdch 3 x Long Straddle o -30 USD ni\u017e\u0161\u00ed<\/strong>, a to by bylo nep\u0159\u00edjemn\u00e9.<\/span><\/p>\n

\u00a0\u00a0 Jak tedy \u010delit ztr\u00e1t\u011b hodnoty takov\u00e9ho portfolia p\u016fsoben\u00edm t\u00e9to z\u00e1porn\u00e9 Th\u00e9ta? Proveden\u00edm jej\u00ed neutralizace<\/strong>. Proto\u017ee jsem popisoval, \u017ee hodnota Th\u00e9ta je vy\u0161\u0161\u00ed<\/strong> u opc\u00ed s bli\u017e\u0161\u00ed expiraci<\/strong>, ale \u017ee je ni\u017e\u0161\u00ed na strikes<\/strong>, kter\u00e9 jsou vzd\u00e1len\u011bj\u0161\u00ed od ATM strikes<\/strong>, budu k\u00a0neutralizaci hledat po\u0159\u00edzen\u00ed takov\u00e9ho n\u00e1stroje, kter\u00fd mi takovou neutralizaci zajist\u00ed. Na obr\u00e1zku jsou vid\u011bt dal\u0161\u00ed po\u0159\u00edzen\u00e9 pozice a nov\u00e9 hodnoty Th\u00e9ta.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0 \u00a0Zapomn\u011bl jsem uv\u00e9st samoz\u0159ejmou v\u011bc, kterou je, \u017ee po\u0159\u00edzen\u00ed podkladov\u00e9ho aktiva nem\u00e1 na hodnotu Th\u00e9ta \u017e\u00e1dn\u00fd vliv. Podkladov\u00e9 akcie \u017e\u00e1dnou \u010dasovou slo\u017eku ve sv\u00e9 cen\u011b obsa\u017eenou nemaj\u00ed, mus\u00edm tedy hledat pro neutralizaci \u00a0Th\u00e9ta pouze op\u010dn\u00ed pozice, tyto mohu do sv\u00e9ho portfolia p\u0159id\u00e1vat nebo je ze sv\u00e9ho portfolia odeb\u00edrat. Pro \u00fapravu pozice 3 x Long Straddle s\u00a0negativn\u00ed Th\u00e9ta jsem tak hledal adekv\u00e1tn\u00ed op\u010dn\u00ed pozice, kter\u00fdmi bych dodal do portfolia tolik Th\u00e9ta, aby byla celkov\u011b t\u00e9m\u011b\u0159 nula. Vybral jsem si 3x Short Call<\/strong> na vy\u0161\u0161\u00edm strike<\/strong> s\u00a0bli\u017e\u0161\u00ed expirac\u00ed<\/strong> a 3x Short Put<\/strong> na ni\u017e\u0161\u00edm strike<\/strong> s\u00a0bli\u017e\u0161\u00ed expirac\u00ed<\/strong>. V\u00fdb\u011br bli\u017e\u0161\u00ed expirace jsem provedl proto, \u017ee Th\u00e9ta opc\u00ed v\u00a0bli\u017e\u0161\u00edch expirac\u00edch je vy\u0161\u0161\u00ed ne\u017e ve vzd\u00e1len\u011bj\u0161\u00ed, kde ji\u017e m\u00e1m p\u016fvodn\u00ed Long opce, opce se vzd\u00e1len\u011bj\u0161\u00edm strike od ATM jsem volil proto, \u017ee maj\u00ed Th\u00e9ta ni\u017e\u0161\u00ed ne\u017e opce s ATM strike, tak\u017ee by tato obchodn\u00ed operace mohla zajistit p\u0159i stejn\u00e9m mno\u017estv\u00ed nov\u00fdch kontrakt\u016f dod\u00e1n\u00ed stejn\u00e9ho mno\u017estv\u00ed Th\u00e9ta. Prodal jsem vlastn\u011b 3 x Short Strangle<\/strong> na bli\u017e\u0161\u00edch strike<\/strong>. Pokud se pod\u00edv\u00e1m na nov\u00e9 hodnoty Gamma a Th\u00e9ta tak zji\u0161\u0165uji velmi kuri\u00f3zn\u00ed v\u011bc. Celkov\u00e1 hodnota Gamma<\/strong> je -1<\/strong> a celkov\u00e1 hodnota Th\u00e9ta<\/strong> je tak\u00e9 -1<\/strong>.<\/span><\/p>\n

Neutralizace Th\u00e9ta sm\u011b\u0159uje k Neutralizaci Gamma<\/span><\/strong><\/h2>\n

\u00a0\u00a0 Z\u00a0minul\u00e9ho \u010dl\u00e1nku o Gamma<\/a><\/strong><\/span>\u00a0vyplynulo, \u017ee hodnoty Gamma<\/strong> pro Long opce jsou kladn\u00e9<\/strong> a pro Short opce<\/strong> jsou z\u00e1porn\u00e9<\/strong>. U hodnoty Th\u00e9ta<\/strong> je tomu p\u0159esn\u011b\u00a0naopak<\/strong>. Pokud tedy neutralizuji hodnotu Th\u00e9ta, tak tak\u00e9 sm\u011b\u0159uji k neutralizaci hodnoty Gamma. Co to cel\u00e9 znamen\u00e1? Odejmul jsem pozici risk vypl\u00fdvaj\u00edc\u00ed s\u00a0pohybu podkladu a tak\u00e9 z\u00a0p\u016fsoben\u00ed b\u011bhu \u010dasu<\/strong><\/span>. Proto\u017ee je m\u00e1 pozice jednodu\u0161e \u010diteln\u00e1, tak v\u00edm, \u017ee m\u00e1m OTM Short Strangle na bli\u017e\u0161\u00edm strike a ATM Long Straddle na vzd\u00e1len\u011bj\u0161\u00edm strike. Pokud se cena pohne n\u011bkter\u00fdm sm\u011brem, tak sice Short op\u010dn\u00ed pozice nov\u00e9ho Short Strangle p\u016fjdou proti mn\u011b, ale vzd\u00e1len\u011bj\u0161\u00ed Long opce p\u016fvodn\u00edho Long Straddle budou pracovat v\u00a0m\u016fj prosp\u011bch, tento prosp\u011bch z\u00a0Long Straddle bude d\u00edky sv\u00e9mu strike v\u017edy vy\u0161\u0161\u00ed ne\u017e ztr\u00e1ta ze Short Strangle. Pokud bych si p\u0159edstavil pohyb cel\u00e9 pozice v \u010dase a sledoval, s jakou dynamikou se bude vyv\u00edjet Th\u00e9ta m\u00e9 pozice, tak bych mohl zjistit, \u017ee pokud by se podklad velmi nepohyboval a z\u016fst\u00e1val by na stejn\u00e9 \u00farovni, tak by se Th\u00e9ta zvy\u0161ovala sm\u011brem k expiraci prvn\u00ed \u010d\u00e1sti pozice (Short Strangle). Po expiraci tohoto Short Strangle bude op\u011bt z\u00e1porn\u00e1, proto\u017ee mi z\u016fstanou pouze vzd\u00e1len\u011bj\u0161\u00ed Long opce p\u016fvodn\u00edho Long Straddle. Mohu pak prov\u00e9st dal\u0161\u00ed podobnou neutralizaci po\u0159\u00edzen\u00edm Short Strangle nad\/pod m\u00fdmi Long opcemi. T\u00edm dod\u00e1m do pozice pot\u0159ebnou d\u00e1vku Th\u00e9ta, ale hlavn\u011b dal\u0161\u00ed pr\u00e9mium, kter\u00e9 by m\u011blo financovat p\u016fvodn\u00ed n\u00e1klady na po\u0159\u00edzen\u00ed Long Straddle. Pokud by tyto „neutraliza\u010dn\u00ed“ Short opce byly ve stejn\u00e9 expiraci jako jsou opce Long Straddle, vytvo\u0159il bych tak na ka\u017ed\u00e9 stran\u011b Call i Put vlastn\u011b Vertik\u00e1ln\u00ed Spready (Bull Call Spread<\/a><\/strong><\/span> a Bear Put Spread) a pokud by sou\u010det hodnoty pr\u00e9mi\u00ed z\u00edskan\u00fdch v\u0161emi minul\u00fdmi i sou\u010dasn\u00fdmi Short opcemi byl vy\u0161\u0161\u00ed ne\u017e jsou po\u0159izovac\u00ed n\u00e1klady na p\u016fvodn\u00ed Long Straddle, byl bych jist\u00fd v\u00edt\u011bz…<\/span><\/p>\n

\u00a0\u00a0\u00a0 Jedin\u00fd<\/strong> risk, <\/strong>kter\u00fd mi z\u016fstal<\/strong>, a kter\u00fd jsem pozici neodejmul, je risk<\/strong> vypl\u00fdvaj\u00edc\u00ed z\u00a0Implied Volatility<\/strong>, jako posledn\u00edmu cenotvorn\u00e9mu prvku, kter\u00fd jsem zat\u00edm nezafixoval (o n\u011bm n\u011bkdy p\u0159\u00ed\u0161t\u011b).<\/span><\/p>\n

\n

\u00a0\u00a0 P\u0159id\u00e1v\u00e1n\u00edm (ub\u00edr\u00e1n\u00edm) op\u010dn\u00edch pozic Long nebo Short na obou stran\u00e1ch Long i Put pak mohu nejen podle celkov\u00fdch sou\u010dt\u016f hodnot \u0159eck\u00fdch p\u00edsmen Delta a Gamma, ale tak\u00e9 Th\u00e9ta, sni\u017eovat expozici portfolia vliv\u016fm tr\u017en\u00edho prost\u0159ed\u00ed, kter\u00fdmi jsou v\u00a0p\u0159\u00edpad\u011b op\u010dn\u00edho obchodov\u00e1n\u00ed pohyb podkladu sou\u010dasn\u011b s\u00a0b\u011bhem \u010dasu :c)<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0 Nev\u00edm, jestli Th\u00e9ta Kaz\u00ed Libu\u0161i, proto\u017ee nejsem vojvoda Krok, ale proto\u017ee jsem op\u010dn\u00ed obchodn\u00edk, tak v\u00edm, jak\u00a0Th\u00e9ta m\u016f\u017ee zkazit i velmi dobrou op\u010dn\u00ed pozici. V\u00a0p\u0159edch\u00e1zej\u00edc\u00edch \u010dl\u00e1nc\u00edch jsem ji\u017e popisoval, jak se m\u011bn\u00ed cena op\u010dn\u00edho kontraktu v\u00a0souvislost\u00ed s\u00a0pohybem podkladov\u00e9ho aktiva a jak tuto z\u00e1vislost zachycujeme pomoc\u00ed \u0159eck\u00e9ho p\u00edsmene Delta. V\u00a0n\u00e1vaznosti Continue Reading<\/i><\/a><\/p>\n","protected":false},"author":1,"featured_media":564,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[2],"tags":[26,32,31,27,33],"class_list":["post-551","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-opcni-zaklady","tag-delta","tag-gamma","tag-short-strangle","tag-straddle","tag-theta"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/s8zd8A-theta","jetpack-related-posts":[{"id":3202,"url":"https:\/\/dobretrejdy.com\/?p=3202","url_meta":{"origin":551,"position":0},"title":"Delta Neutral – VI.","author":"dobretrejdy :c)","date":"4.5.2019","format":false,"excerpt":"\u00a0 \u00a0Je pond\u011bl\u00ed 25.3.2019 a j\u00e1 sleduji t\u0159et\u00ed d\u00edl \u010dtvrt\u00e9 s\u00e9rie kultovn\u00edho seri\u00e1lu Billions. Taylor rozepisuje na tabuli matematickou \u00favahu, kter\u00e1 demonstruje spletitost, slo\u017eitost a sofistikovanost vyd\u011bl\u00e1v\u00e1n\u00ed pen\u011bz na finan\u010dn\u00edch trz\u00edch. Snaha je pravd\u011bpodobn\u011b uk\u00e1zat, \u017ee pokud to nem\u00e1te v\u00a0hlav\u011b matematicky v\u00a0po\u0159\u00e1dku, nem\u00e1te \u0161anci se takov\u00fdm investorsk\u00fdm veli\u010din\u00e1m rovnat. \u00a0\u00a0\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed kombinace\u201c","block_context":{"text":"Op\u010dn\u00ed kombinace","link":"https:\/\/dobretrejdy.com\/?cat=4"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/05\/mean.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/05\/mean.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/05\/mean.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/05\/mean.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":574,"url":"https:\/\/dobretrejdy.com\/?p=574","url_meta":{"origin":551,"position":1},"title":"Vega","author":"dobretrejdy :c)","date":"2.7.2017","format":false,"excerpt":"\u00a0\u201e\u2026 p\u0159esto\u017ee se v\u017eilo, \u017ee popis faktor\u016f p\u016fsob\u00edc\u00edch na tvorbu op\u010dn\u00ed ceny jsme zvykl\u00ed ozna\u010dovat \u0159eck\u00fdmi p\u00edsmeny Delta, Gamma, Th\u00e9ta, Rho, Vega, tak mus\u00edm podotknout, \u017ee Vega nen\u00ed p\u00edsmenem \u0159eck\u00e9 abecedy\u2026\u201c, v\u00a0tomto smyslu v\u011bt\u0161inou b\u00fdvaj\u00ed uv\u00e1d\u011bny \u010dl\u00e1nky o \"Vega\" zab\u00fdvaj\u00edc\u00ed se vlivem zm\u011bny Implied Volatility na cenu op\u010dn\u00edho kontraktu, z\u0159ejm\u011b\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed z\u00e1klady\u201c","block_context":{"text":"Op\u010dn\u00ed z\u00e1klady","link":"https:\/\/dobretrejdy.com\/?cat=2"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/07\/30.06.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/07\/30.06.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/07\/30.06.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/07\/30.06.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":3346,"url":"https:\/\/dobretrejdy.com\/?p=3346","url_meta":{"origin":551,"position":2},"title":"Delta Neutral – VIII.","author":"dobretrejdy :c)","date":"8.6.2019","format":false,"excerpt":"\u00a0 \u00a0Obchodov\u00e1n\u00ed s\u00a0vyu\u017eit\u00edm prvk\u016f Delta Neutrality nen\u00ed, po s\u00e9rii \u010dl\u00e1nk\u016f popisuj\u00edc\u00ed tuto techniku, pravd\u011bpodobn\u011b v\u016fbec k\u00a0zahozen\u00ed a mohlo by m\u00edt slu\u0161n\u00fd obchodn\u00ed potenci\u00e1l. K\u00a0jeho vyu\u017eit\u00ed je ale zapot\u0159eb\u00ed pochopit hlub\u0161\u00ed vztahy mezi jednotliv\u00fdmi obchodn\u00edmi prvky a odhalit tak dal\u0161\u00ed souvislosti, kter\u00e9 mohou vytvo\u0159it vyu\u017eiteln\u00e9 obchodn\u00ed sch\u00e9ma. Prozat\u00edm jsem se dotkl\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed kombinace\u201c","block_context":{"text":"Op\u010dn\u00ed kombinace","link":"https:\/\/dobretrejdy.com\/?cat=4"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/06\/main.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/06\/main.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/06\/main.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/06\/main.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":2911,"url":"https:\/\/dobretrejdy.com\/?p=2911","url_meta":{"origin":551,"position":3},"title":"Delta Neutral – II.","author":"dobretrejdy :c)","date":"3.3.2019","format":false,"excerpt":"\u00a0 \u00a0Pro\u010d se v\u016fbec zab\u00fdvat ot\u00e1zkou Delta Neutrality, co mi p\u0159in\u00e1\u0161\u00ed a k\u00a0\u010demu vlastn\u011b v\u016fbec je, by mohl b\u00fdt z\u00e1kladn\u00ed dotaz po p\u0159e\u010dten\u00ed minul\u00e9ho \u010dl\u00e1nku. Jako op\u010dn\u00ed obchodn\u00edk, vybaven z\u00e1kladn\u00edmi znalostmi o tvorb\u011b ceny op\u010dn\u00edho kontraktu v\u00edm, \u017ee cena opce je vypo\u010d\u00edt\u00e1v\u00e1na matematick\u00fdmi modely, do kter\u00fdch vstupuj\u00ed jednotliv\u00e9 cenotvorn\u00e9 komponenty,\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed kombinace\u201c","block_context":{"text":"Op\u010dn\u00ed kombinace","link":"https:\/\/dobretrejdy.com\/?cat=4"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/03\/Delta-pozitive-1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/03\/Delta-pozitive-1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/03\/Delta-pozitive-1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/03\/Delta-pozitive-1.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":522,"url":"https:\/\/dobretrejdy.com\/?p=522","url_meta":{"origin":551,"position":4},"title":"Gamma","author":"dobretrejdy :c)","date":"19.6.2017","format":false,"excerpt":"\u00a0 \u00a0 K\u00a0dokonalej\u0161\u00edmu pochopen\u00ed z\u00e1vislosti ceny opce na pohybu podkladov\u00e9ho aktiva vyj\u00e1d\u0159en\u00e9ho \u0159eck\u00fdm p\u00edsmenem Delta, jak jsem jej popisoval v\u00a0\u010dl\u00e1nku Delta je zapot\u0159eb\u00ed hlub\u0161\u00edho ponoru do problematiky \u0159eck\u00fdch p\u00edsmen, kdy\u017e t\u00edm nejbli\u017e\u0161\u00edm p\u00edsmenem k\u00a0popisovan\u00e9 Delta je \u0159eck\u00e9 p\u00edsmeno Gamma. Tak jako Rumburak byl \u010darod\u011bj druh\u00e9 kategorie, tak tak\u00e9 na Gamma\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed z\u00e1klady\u201c","block_context":{"text":"Op\u010dn\u00ed z\u00e1klady","link":"https:\/\/dobretrejdy.com\/?cat=2"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/06\/180750308.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/06\/180750308.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/06\/180750308.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/06\/180750308.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":308,"url":"https:\/\/dobretrejdy.com\/?p=308","url_meta":{"origin":551,"position":5},"title":"Delta","author":"dobretrejdy :c)","date":"4.5.2017","format":false,"excerpt":"\u00a0 \u00a0Delta je rozd\u00edl. Delta Praha \u2013 Brno je 200 (kilometr\u016f), o tom ale \u010dl\u00e1nek nebude. Bude to o Delta op\u010dn\u00edch kontrakt\u016f. Porozum\u011bn\u00ed Delta je jednou ze z\u00e1kladn\u00edch dovednost\u00ed, kterou by m\u011bl disponovat ka\u017ed\u00fd op\u010dn\u00ed trader. Toto jednoduch\u00e9 \u0159eck\u00e9 p\u00edsmeno ozna\u010duje m\u00edru z\u00e1vislosti ceny opce na pohybu podkladov\u00e9ho aktiva. Vyjdu\u2026","rel":"","context":"V \u201eOp\u010dn\u00ed z\u00e1klady\u201c","block_context":{"text":"Op\u010dn\u00ed z\u00e1klady","link":"https:\/\/dobretrejdy.com\/?cat=2"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/05\/Delta.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/05\/Delta.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/05\/Delta.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/05\/Delta.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]}],"jetpack_featured_media_url":"https:\/\/dobretrejdy.com\/wp-content\/uploads\/2017\/06\/theta.jpg","_links":{"self":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=551"}],"version-history":[{"count":14,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/551\/revisions"}],"predecessor-version":[{"id":1413,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/551\/revisions\/1413"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/media\/564"}],"wp:attachment":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}