{"id":245,"date":"2017-04-26T13:37:52","date_gmt":"2017-04-26T13:37:52","guid":{"rendered":"http:\/\/dobretrejdy.com\/?p=245"},"modified":"2025-10-28T11:36:15","modified_gmt":"2025-10-28T09:36:15","slug":"cena-opce","status":"publish","type":"post","link":"https:\/\/dobretrejdy.com\/?p=245","title":{"rendered":"Cena opce"},"content":{"rendered":"

\u00a0 \u00a0Obchodovat opce lze tak, \u017ee na p\u0159\u00edslu\u0161n\u00fd po\u017eadovan\u00fd op\u010dn\u00ed kontrakt jednodu\u0161e kliknu do sv\u00e9 obchodn\u00ed platformy a zad\u00e1m p\u0159\u00edkaz k\u00a0jeho n\u00e1kupu. To dnes ch\u00e1pe ka\u017ed\u00fd. Kde se ale berou v\u0161echna ta \u010d\u00edsla s\u00a0cenami jednotliv\u00fdch kontrakt\u016f na jednotliv\u00fdch strikes\u00a0a v\u00a0jednotliv\u00fdch expirac\u00edch a jak jsou vlastn\u011b stanovov\u00e1na? Generuj\u00ed je burzovn\u00ed servery, kter\u00e9 pracuj\u00ed s\u00a0r\u016fzn\u00fdmi algoritmy a modely, kter\u00e9 na z\u00e1klad\u011b dostupn\u00fdch \u00fadaj\u016f vypo\u010d\u00edt\u00e1vaj\u00ed jednotliv\u00e9 ceny op\u010dn\u00edch kontrakt\u016f, kter\u00e9 jsou pak viditeln\u00e9 v\u00a0obchodn\u00edch platform\u00e1ch. Pominu nyn\u00ed vliv nab\u00eddky a popt\u00e1vky na cenu op\u010dn\u00edho kontraktu a pokus\u00edm se jednodu\u0161e uk\u00e1zat, bez n\u011bjak\u00e9ho \u201ev\u011bdeck\u00e9ho podtextu\u201c, jak jsou takov\u00e9 ceny stanoveny.<\/span><\/p>\n

\u00a0\u00a0 Z\u00e1kladem v\u00fdpo\u010dtu ceny op\u010dn\u00edho kontraktu je n\u011bjak\u00fd matematick\u00fd model<\/strong>. Model\u016f pro v\u00fdpo\u010det takov\u00e9 ceny je spousta a jejich struktura je velmi odli\u0161n\u00e1. Nebudu se zab\u00fdvat popisov\u00e1n\u00edm a odli\u0161nostmi jednotliv\u00fdch model\u016f, pokus\u00edm se objasnit v\u00fdpo\u010detn\u00ed sch\u00e9ma nejzn\u00e1m\u011bj\u0161\u00edho ze v\u0161ech model\u016f, a to Black \u2013 Scholesova modelu<\/strong>. P\u0159i prvn\u00edm pohledu na obr\u00e1zek s\u00a0matematick\u00fdm tvarem tohoto modelu to vypad\u00e1 jako nepochopiteln\u00e1 zm\u011b\u0165 znak\u016f, v\u00fdraz\u016f a matematick\u00fdch symbol\u016f. Tento chuchvalec pak stoj\u00ed alespo\u0148 za m\u00edrn\u00e9 rozpleten\u00ed, aby do\u0161lo k\u00a0n\u011bjak\u00e9mu alespo\u0148 m\u00edrn\u00e9mu pochopen\u00ed a n\u00e1sledn\u00e9mu praktick\u00e9mu vyu\u017eit\u00ed. Na internetu existuje mno\u017estv\u00ed sofistikovan\u00fdch aplikac\u00ed, kter\u00e9 V\u00e1m po zad\u00e1n\u00ed vstupn\u00edch \u00fadaj\u016f vypo\u010d\u00edtaj\u00ed teoretickou hodnotu opc\u00ed, ale je to po\u0159\u00e1d v t\u011bch aplikac\u00edch n\u011bjak zamontov\u00e1no, jak se k t\u011bmto cen\u00e1m opc\u00ed v\u00fdpo\u010dtem do\u0161lo. Pokud bych cht\u011bl takov\u00fdm aplikac\u00edm v\u011b\u0159it, mus\u00edm zjistit, jestli \u201emluv\u00ed pravdu\u201c. To nezjist\u00edm jinak ne\u017e pochopen\u00edm z\u00e1kladn\u00ed kostry v\u00fdpo\u010dtu ceny opc\u00ed, kter\u00e9 tyto aplikace prov\u00e1d\u011bj\u00ed.<\/span><\/p>\n

\u00a0\u00a0 Z Black-Scholesova vzorce<\/strong> pro v\u00fdpo\u010det teoretick\u00e9 hodnoty opc\u00ed<\/strong> vypl\u00fdv\u00e1, \u017ee ke stanoven\u00ed ceny opce pot\u0159ebujeme m\u00edt ur\u010dit\u00e9 vstupn\u00ed veli\u010diny<\/strong>, bez jejich\u017e znalosti takovou cenu nem\u016f\u017eeme spo\u010d\u00edtat, t\u011bmito hodnotami jsou:<\/span><\/p>\n

1<\/strong>\/ Cena podkladov\u00e9ho aktiva – <\/strong>cena za kterou se moment\u00e1ln\u011b obchoduje<\/span><\/p>\n

2<\/strong>\/ Strike<\/strong> \u2013 na kter\u00e9m strike chceme cenu vypo\u010d\u00edtat<\/span><\/p>\n

3<\/strong>\/ \u010cas trv\u00e1n\u00ed op\u010dn\u00edho kontraktu<\/strong> \u2013 doba \u017eivota opce<\/span><\/p>\n

4<\/strong>\/ Volatilita<\/strong><\/span><\/p>\n

5<\/strong>\/ Dividendy<\/strong> \u2013 pokud se za \u017eivota sledovan\u00e9 opce vypl\u00e1cej\u00ed<\/span><\/p>\n

6<\/strong>\/ \u00darokov\u00e1 m\u00edra<\/strong> – existuj\u00edc\u00ed za \u017eivota opce<\/span><\/p>\n

\u00a0\u00a0 Z obr\u00e1zku vyjad\u0159uj\u00edc\u00ed Black-Scholes\u016fv vzorec vypl\u00fdv\u00e1, \u017ee vlastn\u011b cel\u00e1 podstata v\u00fdpo\u010dtu teoretick\u00e9 ceny opce je jen o jednoduch\u00e9m pochopen\u00ed jednotliv\u00fdch v\u00fdznam\u016f vzorce.<\/span><\/p>\n

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\u00a0 Prvn\u00ed dva \u0159\u00e1dky<\/strong> – vzorce \u2013 pak vyjad\u0159uj\u00ed jednotliv\u00e9 postupy pro v\u00fdpo\u010det ceny Call opce<\/strong> a Put opce<\/strong>, na dal\u0161\u00edch dvou \u0159\u00e1dc\u00edch<\/strong> je v\u00fdpo\u010det jak\u00e9si hodnoty d1 a d2<\/strong>, kter\u00e9 jsou pou\u017eity ve vzorci v prvn\u00edch dvou \u0159\u00e1dc\u00edch. Nebudu uv\u00e1d\u011bt, co jednotliv\u00e9 v\u00fdrazy znamenaj\u00ed, proto\u017ee vzorce se v r\u016fzn\u00fdch pramenech v tomto ozna\u010dov\u00e1n\u00ed v\u00fdraz\u016f li\u0161\u00ed, ale zkus\u00edm si vzorec p\u0159ev\u00e9st na v\u00fd\u0161e uveden\u00e9 veli\u010diny \u201ev \u010de\u0161tin\u011b\u201c. Pokud tedy dosad\u00edm za jednotliv\u00e9 symboly \u010desk\u00e1 slova<\/strong>, tak je mo\u017en\u00e9 vzorce l\u00e9pe \u201erozkl\u00ed\u010dovat\u201c a tak\u00e9 mo\u017en\u00e1 pochopit.<\/span><\/p>\n

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\u00a0\u00a0\u00a0 Na prvn\u00ed pohled je z\u0159ejm\u00e9, \u017ee se jedn\u00e1 vlastn\u011b o slo\u017eeninu tvo\u0159enou v\u017edy z rozd\u00edlu dvou velmi podobn\u00fdch hodnot<\/strong>. K lep\u0161\u00edmu grafick\u00e9mu pochopen\u00ed tohoto rozd\u00edlu hodnot v \u201epo\u010de\u0161t\u011bl\u00e9m vzorci\u201c ozna\u010d\u00edm tyto jednotliv\u00e9 \u010d\u00e1sti slo\u017eit\u00e9ho vzorce.<\/span><\/p>\n

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\u00a0 \u00a0Pokud si tyto slo\u017eeniny takto p\u0159evedu do \u010de\u0161tiny, tak je zjevn\u00e9, \u017ee cena opce Call<\/strong>\u00a0je tvo\u0159ena Cenou podkladu<\/strong>\u00a0upravenou o \u201en\u011bjakou hodnotu\u201c (\u010d\u00e1st A) od kter\u00e9 je ode\u010d\u00edt\u00e1na hodnota Strike opce\u00a0<\/strong>upraven\u00e1 o \u201en\u011bjakou hodnotu\u201c (\u010d\u00e1st B). U v\u00fdpo\u010dtu ceny opce Put<\/strong>\u00a0je situace obr\u00e1cen\u00e1, kdy se ode\u010d\u00edt\u00e1 od hodnoty Strike\u00a0<\/strong>upravenou o \u201en\u011bjakou hodnotu\u201c (\u010d\u00e1st B\u201c) hodnota Ceny podkladu<\/strong>\u00a0upravenou o \u201en\u011bjakou hodnotu\u201c\u00a0 (\u010d\u00e1st A\u201c).<\/span><\/p>\n

\u00a0\u00a0 Tento v\u00fdpo\u010det pak respektuje z\u00e1kladn\u00ed logiku, kdy cena op\u010dn\u00edho kontraktu<\/strong> se odv\u00edj\u00ed od jeho vnit\u0159n\u00ed hodnoty<\/strong> \u2013 hodnoty, kterou je opce \u201ev pen\u011bz\u00edch\u201c. Pokud tedy cena Call opce<\/strong> je v\u00a0\u00fapln\u00e9m zjednodu\u0161en\u00ed vypo\u010dtena jako Cena podkladu m\u00ednus Strike<\/strong> a k\u00a0tomu je p\u0159id\u00e1no \u201eje\u0161t\u011b n\u011bco dal\u0161\u00edho\u201c, tak p\u0159i cen\u011b akcie 145 USD bude m\u00edt Call opce se strike 135<\/strong> (tedy 10 bodu \u201ev\u00a0pen\u011bz\u00edch\u201c) cenu 145 USD (cena akcie) -135 USD (strike) = 10 USD<\/strong> a \u201eje\u0161t\u011b n\u011bco dal\u0161\u00edho<\/strong>\u201c, cena takov\u00e9 opce na tomto strike 135 tak bude minim\u00e1ln\u011b t\u011bchto 10 USD. Hodnotu \u201eje\u0161t\u011b n\u011bco dal\u0161\u00edho<\/strong>\u201c bych pak mohl jednodu\u0161e pojmenovat jako op\u010dn\u00ed pr\u00e9mium<\/strong>. Pokud by naopak byla hodnota strike \u201emimo pen\u00edze\u201c, tedy nad sou\u010dasnou obchodovanou cenou, nap\u0159\u00edklad bych cht\u011bl vypo\u010d\u00edtat hodnotu Call opce se strike 150<\/strong>, potom by t\u00edmto rozd\u00edlem byla hodnota \u201e\u017e\u00e1dn\u00e1 vnit\u0159n\u00ed hodnota\u201c<\/strong>, konkr\u00e9tn\u011b cena 145 USD (cena akcie) -150 USD (strike) = -5 USD a \u201eje\u0161t\u011b n\u011bco dal\u0161\u00edho\u201c<\/strong>. Proto\u017ee vnit\u0159n\u00ed hodnota opce nem\u016f\u017ee b\u00fdt z\u00e1porn\u00e1 ale nejm\u00e9n\u011b nula, byla by v\u00fdsledkem tohoto v\u00fdpo\u010dtu pr\u00e1v\u011b hodnota ozna\u010dovan\u00e1 jako \u201eje\u0161t\u011b n\u011bco dal\u0161\u00edho\u201c \u2013 tedy \u010dist\u00e9 pr\u00e9mium. Ve \u00fapln\u00e9m a nejjednodu\u0161\u0161\u00edm shrnut\u00ed by tedy takov\u00e1 matematick\u00e1 interpretace BS modelu mohla zn\u00edt, \u017ee opce \u201eITM – v\u00a0pen\u011bz\u00edch\u201c<\/strong> m\u00e1 cenu \u201evnit\u0159n\u00ed hodnoty + pr\u00e9mium\u201c<\/strong> a opce \u201eOTM – mimo pen\u00edze\u201c<\/strong> m\u00e1 pak hodnotu \u201epouze pr\u00e9mium\u201c<\/strong>.\u00a0<\/span><\/p>\n

\u00a0\u00a0\u00a0 Smyslem tohoto vzorce z takov\u00e9 \u201e\u010desk\u00e9 pta\u010d\u00ed perspektivy\u201c je, \u017ee opce Call i Put na stejn\u00e9m strike by m\u011bly m\u00edt sob\u011b navz\u00e1jem odpov\u00eddaj\u00edc\u00ed hodnoty<\/strong> podle tohoto strike v z\u00e1vislosti na cen\u011b podkladu. Pokud se pod\u00edv\u00e1m na vzorec z pohledu hodnot, kter\u00e9 zn\u00e1me a kter\u00e9 si m\u016f\u017eeme do vzorce jednodu\u0161e dosadit (Cena Podkladu, Strike, \u017divot opce, Volatilita, \u00daroky a Dividenda), potom n\u00e1m zb\u00fdvaj\u00ed pouze dva v\u00fdrazy, kter\u00e9 je pot\u0159eba rozkl\u00ed\u010dovat, a kter\u00e9 jsou v obd\u00e9ln\u00edku A a B ozna\u010deny \u0161ipkami:<\/span><\/p>\n

\u00a0 \u00a0e \u2013 neboli Exponenci\u00e1ln\u00ed funkce<\/strong>\u00a0(\u010derven\u00e9 \u0161ipky), jej\u00edm\u017e exponentem je v jednom p\u0159\u00edpad\u011b sou\u010din -Dividenda a \u017divot Opce (ve vzorci A) a v druh\u00e9m (ve vzorci B) je exponentem sou\u010din -\u00daroky a \u017divot Opce. Z t\u00e9to exponenci\u00e1ln\u00ed funkce n\u00e1m bude sta\u010dit za zaznamen\u00e1n\u00ed<\/strong>, \u017ee pokud nebude<\/strong> za \u017divota Opce vypl\u00e1cena Dividenda<\/strong>, potom bude hodnota Dividenda = 0, cel\u00fd exponent bude nula a cokoliv na \u201enultou\u201c je v\u017edycky jedna, tak\u017ee hodnota t\u00e9to exponenci\u00e1ln\u00ed funkce bude tak\u00e9 jedna<\/strong> a nebude m\u00edt na po\u010d\u00edtanou cenu opce \u017e\u00e1dn\u00fd vliv<\/strong>. To sam\u00e9 plat\u00ed u druh\u00e9 exponenci\u00e1ln\u00ed funkce, kdy na vliv ceny opce maj\u00ed vliv \u00daroky nebo doba \u017divota Opce, pokud bude hodnota \u00darok\u016f nula nebo hodnota<\/strong> \u017divota opce nula<\/strong> (opce je \u00fapln\u011b t\u011bsn\u011b p\u0159ed expirac\u00ed), tak obdobn\u011b bude koeficient nula a cel\u00e1 druh\u00e1 exponenci\u00e1ln\u00ed funkce bude (op\u011bt cokoliv na \u201enultou\u201c je jedna) m\u00edt hodnotu jedna a nebude m\u00edt pak na cenu po\u010d\u00edtan\u00e9 opce \u017e\u00e1dn\u00fd vliv<\/strong>. Hodnotu exponenci\u00e1ln\u00ed funkce n\u00e1m hrav\u011b vypo\u010d\u00edt\u00e1 Excel (funkce EXP), tak\u017ee si nemus\u00edme s t\u00edmto v\u00fdpo\u010dtem l\u00e1mat hlavu.<\/span><\/p>\n

\u00a0 \u00a0N\u00a0\u2013 neboli Distribu\u010dn\u00ed funkce Norm\u00e1ln\u00edho rozd\u011blen\u00ed <\/strong>(zelen\u00e9 \u0161ipky), kter\u00e1 m\u00e1 ve vzorci pro v\u00fdpo\u010det opc\u00ed argumenty Djedna a Ddva. Jejich v\u00fdpo\u010det p\u0159eveden\u00fd do \u010de\u0161tiny je vid\u011bt na screenu v\u00fd\u0161e. Tyto argumenty jsou jednodu\u0161e spo\u010d\u00edtateln\u00e9 v Excelu, proto\u017ee obsahuj\u00ed pouze n\u00e1mi zn\u00e1m\u00e9 hodnoty (Cena Podkladu, Strike, \u017divot opce, Volatilita, \u00daroky a Dividenda), zbytek v\u00fdpo\u010dtu tvo\u0159\u00ed jednoduch\u00e9 matematick\u00e9 operace. Tak\u00e9 hodnotu distribu\u010dn\u00ed funkce n\u00e1m spo\u010d\u00edt\u00e1 Excel (funkce NORMSDIST), tak\u017ee nemus\u00edme m\u00edt obavu, \u017ee toto bude pro nematematika n\u011bjak\u00fd nep\u0159ekonateln\u00fd probl\u00e9m.<\/span><\/p>\n

\u00a0\u00a0\u00a0 Cel\u00fd v\u00fdpo\u010det teoretick\u00e9 hodnoty opce Call nebo Put bychom potom podle tohoto modelu mohli zjednodu\u0161it tak, \u017ee nejd\u0159\u00edve vypo\u010d\u00edt\u00e1me<\/strong> hodnoty Djedna<\/strong> a Ddva<\/strong>, jako argumenty distribu\u010dn\u00ed funkce, kter\u00e1 se n\u00e1m v Black-Scholesov\u011b modelu objevuje a tyto potom dosadit do samotn\u00e9ho vzorce<\/strong>\u00a0pro v\u00fdpo\u010det jednotliv\u00fdch cen pro Call i Put.<\/span><\/p>\n

No a k \u010demu je to cel\u00e9 vlastn\u011b dobr\u00e9 a jak znalosti a pochopen\u00ed tohoto vzorce vyu\u017e\u00edt pro vlastn\u00ed obchodov\u00e1n\u00ed?<\/span><\/p>\n

\u00a0 \u00a0V\u0161e by mohlo prakticky vyplynout z p\u0159eveden\u00ed cel\u00e9ho vzorce do Excelu<\/strong>, kter\u00fd by se mohl st\u00e1t z\u00e1kladem pro jednoduch\u00e9 op\u010dn\u00ed v\u00fdpo\u010dty. Proto\u017ee by bylo dosti kostrbat\u00e9 a nepraktick\u00e9 jednotliv\u00e9 \u010d\u00e1sti v\u00fdpo\u010dtu op\u010dn\u00ed ceny zad\u00e1vat do Excelu pomoc\u00ed logick\u00fdch funkc\u00ed, ud\u011blal jsem to tak, \u017ee jsem v Excelu vytvo\u0159il pro jednotliv\u00e9 ceny opc\u00ed Call a Put samostatn\u00e9 funkce<\/strong>. P\u0159esn\u011b podle postupu s p\u0159ede\u0161l\u00e9ho v\u00fdpo\u010dtu jsem nejd\u0159\u00edve \u201eExcelu \u0159ekl\u201c, jak m\u00e1 vypo\u010d\u00edtat hodnoty Djedna a Ddva, jako argumenty distribu\u010dn\u00ed funkce, abych potom tyto vypo\u010d\u00edtan\u00e9 argumenty vlo\u017eil do funkce, kter\u00e1 p\u0159\u00edmo vypo\u010dte cenu Call nebo Put na zadan\u00e9m strike podle p\u0159\u00edslu\u0161n\u00fdch parametr\u016f. V Excelu, kter\u00fd je p\u0159ilo\u017een k tomuto p\u0159\u00edsp\u011bvku jsou vytvo\u0159eny speci\u00e1ln\u00ed funkce CallCena a PutCena<\/strong>, tak\u00e9 m\u016f\u017eete tyto funkce vid\u011bt, jak jsou ve VBA naprogramov\u00e1ny a tyto si m\u016f\u017eete nap\u0159\u00edklad zkop\u00edrovat do Va\u0161eho excelu a potom s t\u011bmito funkcemi b\u011b\u017en\u011b pracovat (jednodu\u0161e si zkop\u00edrujete cel\u00fd viditeln\u00fd text k\u00f3du). Pro ty, kte\u0159\u00ed nev\u00ed, jak se k funkc\u00edm ve VBA dostat – kliknete na kartu \u201eV\u00fdvoj\u00e1\u0159\u201c, potom na \u201eVisual Basic\u201c a uveden\u00fd script m\u016f\u017eete ze sekce Module cel\u00fd kop\u00edrovat a p\u0159en\u00e1\u0161et do Va\u0161eho Excelu, kde si va\u0161eho \u201eV\u00fdvoj\u00e1\u0159e\u201c a okno \u201eVisual Basic\u201c stejn\u00fdm zp\u016fsobem otev\u0159ete. Zdatn\u011bj\u0161\u00ed znalci excelu uvid\u00ed, \u017ee fukce jsou ve VBA vytvo\u0159eny \u201eotrock\u00fdm\u201c p\u0159episem uveden\u00fdch vzorc\u016f Black-Scholesova modelu do VBA, t\u00e9m\u011b\u0159 nic sv\u011btoborn\u00e9ho. (p\u0159i otev\u00edr\u00e1n\u00ed excelovsk\u00e9ho se\u0161itu mus\u00edte na v\u00fdzvu programu \u201epovolit makra\u201c)<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 Pokud si takov\u00fd sv\u016fj Excel se zkop\u00edrovan\u00fdm k\u00f3dem otev\u0159ete nebo vyu\u017eijete p\u0159ilo\u017een\u00fd, tak m\u016f\u017eete p\u0159\u00edmo v bu\u0148ce zad\u00e1vat v\u00fdpo\u010det ceny Call a Put opc\u00ed, tyto funkce CallCena a PutCena maj\u00ed v\u017edy \u0161est argument\u016f, kter\u00e9 mus\u00edte do funkce dosadit, t\u011bmito argumenty jsou CenaPodkladu, Strike, ZivotOpce, Uroky, Volatilita, Dividenda<\/strong>, tedy ty zn\u00e1m\u00e9 argumenty, kter\u00e9 cenu opce tvo\u0159\u00ed. Po spr\u00e1vn\u00e9m zad\u00e1n\u00ed v\u0161ech argument\u016f se n\u00e1m v bu\u0148ce s funkc\u00ed objev\u00ed cena p\u0159\u00edslu\u0161n\u00e9 opce. V p\u0159ilo\u017een\u00e9m Excelu jsou jednotliv\u00e9 argumenty uvedeny v lev\u00e9 \u010d\u00e1sti v bled\u011b mod\u0159e ozna\u010den\u00fdch bu\u0148k\u00e1ch tabulky.<\/span><\/p>\n

\u00a0\u00a0 Aby byly jednotliv\u00e9 argumenty funkce CallCena a PutCena zad\u00e1ny spr\u00e1vn\u011b pro Va\u0161e dal\u0161\u00ed v\u00fdpo\u010dty, tak mus\u00edte v\u011bd\u011bt, \u017ee:<\/span><\/p>\n

1\/<\/strong> Cena podkladov\u00e9ho aktiva<\/strong>\u00a0\u2013 zad\u00e1v\u00e1 se jako klasick\u00e9 \u010d\u00edslo<\/span><\/p>\n

2\/ Strike<\/strong>\u00a0\u2013 na kter\u00e9m strike chceme cenu vypo\u010d\u00edtat \u2013 zad\u00e1v\u00e1 se jako klasick\u00e9 \u010d\u00edslo<\/span><\/p>\n

3\/ \u017divot opce<\/strong>\u00a0\u2013 zad\u00e1v\u00e1 se jako klasick\u00e9 \u010d\u00edslo, kter\u00e9 je rozd\u00edlem data po\u0159\u00edzen\u00ed opce a data zbaven\u00ed se opce, v\u0161e\u00a0p\u0159epo\u010dteno na ro\u010dn\u00ed b\u00e1z<\/strong>i, tak\u017ee tento v\u00fdsledn\u00fd rozd\u00edl d\u011bl\u00edme \u010d\u00edslem 365<\/span><\/p>\n

4\/ Volatilita<\/strong>\u00a0\u2013 zad\u00e1v\u00e1 se v %<\/span><\/p>\n

5\/ Dividendy<\/strong>\u00a0\u2013 zad\u00e1v\u00e1 se v % v\u00fdplatn\u00edm pom\u011bru k cen\u011b<\/strong> podkladov\u00e9ho aktiva a v jej\u00ed anualizovan\u00e9m tvaru<\/strong> \u2013 nap\u0159. XYZ vypl\u00e1c\u00ed 4 x ro\u010dn\u011b 0,50 USD dividendu, tedy celkem 2 USD\/rok.\u00a0 Cena XYZ je 50 USD, v\u00fdsledkem je 2\/50 = 0,04 = 4%<\/span><\/p>\n

6\/ \u00darokov\u00e1 m\u00edra\u00a0<\/strong>za \u017eivota opce \u2013 jak\u00e1 je aktu\u00e1ln\u00ed \u00farokov\u00e1 m\u00edra US st\u00e1tn\u00edch dluhopis\u016f v obdob\u00ed do expirace op\u010dn\u00edho kontraktu<\/span><\/p>\n

\u00a0\u00a0\u00a0 Pokud takto dosad\u00edte tyto hodnoty do fukce CallCena a PutCena, objev\u00ed se V\u00e1m ve v\u00fdsledku ceny opc\u00ed<\/strong>. Pod\u00edvejte se do uk\u00e1zkov\u00e9ho Excelu, jak jsou tam tyto hodnoty zad\u00e1ny a uvid\u00edte, \u017ee pr\u00e1ce s takovou tabulkou je velmi jednoduch\u00e1. Po zad\u00e1n\u00ed hodnot do modr\u00fdch bun\u011bk nejen\u017ee uvid\u00edte cenu Call a Put opce na zadan\u00e9m strike, ale tak\u00e9 se v\u00e1m vygeneruje jednoduch\u00fd op\u010dn\u00ed \u0159et\u011bzec s p\u011bti strikes na ka\u017edou stranu od ATM hodnoty<\/strong>, sestaven\u00fd pr\u00e1v\u011b z t\u011bchto naprogramovan\u00fdch funkc\u00ed (v tabulce je tak\u00e9 vid\u011bt bu\u0148ku \u201eKrok Strike\u201c pro vypln\u011bn\u00ed nap\u0159\u00edklad hodnotou 2.5, kdyby strikes v op\u010dn\u00edm \u0159et\u011bzci byly od sebe takto vzd\u00e1len\u00e9).<\/span>\u00a0<\/span><\/p>\n

\"\"\u00a0 \u00a0Abychom si mohli potvrdit a ov\u011b\u0159it, \u017ee funkce v Excelu pracuj\u00ed spr\u00e1vn\u011b, p\u0159ipojuji screen se zadanou cenou a parametry ve srovn\u00e1n\u00ed s aplikac\u00ed, kterou si m\u016f\u017eete st\u00e1hnout nap\u0159\u00edklad ze str\u00e1nek Interactive Brokers<\/a><\/strong><\/span>. Do tabulky jsou zad\u00e1ny sou\u010dasn\u00e9 ceny akcie AAPL<\/strong> obchoduj\u00edc\u00ed se za 142,27 USD<\/strong>, kter\u00e1 nap\u0159\u00edklad za dobu \u017eivota opce vypl\u00e1c\u00ed \u010dtvrtletn\u00ed dividendu ve v\u00fd\u0161i 0,57 USD\/akcii<\/strong> (potom do \u0159\u00e1dku Dividenda uvedeme \u00fadaj podle v\u00fdpo\u010dtu: 0,57 x 4 = 2,28 USD\/rok, cena akcie je 142,47 USD, potom 2,28 USD\/142,47 USD = 1.60%).\u00a0 Doba \u017eivota<\/strong>\u00a0opce je 25 dn\u016f<\/strong> tak, aby zahrnovala tak\u00e9 tuto vypl\u00e1cenou dividendu. Hodnota Implied Volatility<\/strong> byla vypln\u011bna hodnotou 22,69%<\/strong> a \u00faroky<\/strong> byly stanoveny ve v\u00fd\u0161i 1,75% p.a.<\/strong> Ceny jsou t\u00e9m\u011b\u0159 identick\u00e9, jak ve vytvo\u0159en\u00e9m Excelu tak v aplikaci z IB, rozd\u00edly jsou zp\u016fsobeny pravd\u011bpodobn\u011b zaokrouhlov\u00e1n\u00edm. Porovn\u00e1val jsem ceny Call i Put opc\u00ed se strike 142.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 P\u0159esto\u017ee jsem uvedl, \u017ee se nebudu zab\u00fdvat jin\u00fdmi modely ne\u017e Black-Scholesov\u00fdm modelem, uvedu srovn\u00e1n\u00ed v\u00fdpo\u010dtu ceny opc\u00ed podle jin\u00e9ho zn\u00e1m\u00e9ho op\u010dn\u00edho oce\u0148ovac\u00edho modelu \u2013 Binomick\u00e9ho modelu,<\/strong> jeho\u017e kalkulaci m\u016f\u017eete vyu\u017e\u00edt v\u00a0aplikaci na str\u00e1nk\u00e1ch Livevol<\/a><\/strong><\/span>. Pokud zad\u00e1m stejn\u00e9 parametry a provedu takov\u00fd v\u00fdpo\u010det ceny opc\u00ed na strike 142<\/strong>, uvid\u00edm v\u00fdpo\u010det ceny, kter\u00fd se li\u0161\u00ed od BS modelu o cca +\/-\u00a00,20 USD u ka\u017ed\u00e9 s\u00a0opc\u00ed<\/strong>. Proto\u017ee nev\u00edm, jak byla aplikace binomick\u00e9ho modelu tvo\u0159ena (ani se o ni nebudu pokou\u0161et) tak je zde v\u00fdznamn\u00fd rozd\u00edl. Jak bych si ji m\u011bl vysv\u011btlit nebo kter\u00e9mu modelu v\u00edce v\u011b\u0159it?<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0\u00a0 Nebudu se pou\u0161t\u011bt do kritiky jednotliv\u00fdch model\u016f a slo\u017eit\u011b matematicky dokazovat, kde nap\u0159\u00edklad ud\u011blali auto\u0159i BS modelu chybu, proto\u017ee takov\u00fdch fundovan\u00fdch diskuz\u00ed je k\u00a0dispozici velk\u00e9 mno\u017estv\u00ed a p\u0159ebrodit se p\u0159es n\u011b p\u0159edstavuje b\u00fdt vybaven matematick\u00fdmi dovednostmi nach\u00e1zej\u00edc\u00edmi se za alespo\u0148 m\u00fdm horizontem pozn\u00e1n\u00ed. V\u00a0jedn\u00e9 funkcionalit\u011b ale BS model nen\u00ed \u00fapln\u011b p\u0159esn\u00fd, pokud je matematicky vyj\u00e1d\u0159en jako na v\u00fd\u0161e uveden\u00fdch obr\u00e1zc\u00edch a dosti siln\u011b se rozch\u00e1z\u00ed s\u00a0obchodn\u00ed realitou. Pokud do jeho v\u00fdpo\u010dtu zahrnu v\u00fdplatu dividendy zp\u016fsobem, jak\u00fdm jsem ji popsal, tedy v\u00a0jej\u00edm anualizovan\u00e9m tvaru, tak to znamen\u00e1, \u017ee cena opce osahuje takovou vypl\u00e1cenou dividendu, a to tak, jako kdyby ka\u017ed\u00fd den vypl\u00e1cela dividendu ve v\u00fd\u0161i vypo\u010dtenou na tento jeden den. Takto to ale ve skute\u010dnosti nen\u00ed, proto\u017ee v\u00fd\u0161e dividendy, pokud se vypl\u00e1c\u00ed za dobu \u017eivota opce, se zcela prom\u00edt\u00e1 do hodnoty Put opce, aby bezprost\u0159edn\u011b po jej\u00ed v\u00fdplat\u011b na Ex-Dividend Day se v\u00a0hodnot\u011b t\u00e9to Put opce t\u00e9m\u011b\u0159 neodr\u00e1\u017eela. Tuto skute\u010dnost ve sv\u00e9m v\u00fdpo\u010dtu tak l\u00e9pe moment\u00e1ln\u011b zachycuje v\u00fdpo\u010det podle binomick\u00e9ho modelu podle obr\u00e1zku v\u00fd\u0161e. Nev\u00edm ale, jestli je to \u201edokonalost\u00ed\u201c binomick\u00e9ho modelu nebo n\u011bjak\u00e1 jin\u00e1 p\u0159\u00ed\u010dina.<\/span><\/p>\n

\u00a0 Pokud jsou k\u00a0v\u00fdpo\u010dtu ceny opce<\/strong> podle takov\u00e9ho BS modelu nutn\u00e9 m\u00edt k\u00a0dispozici \u00fadaje o Cen\u011b Podkladu, Strike, D\u00e9lce \u017eivota opce, Implied Volatilit\u011b, \u00daroku a Dividend\u011b<\/strong>, pak m\u016f\u017eeme, pokud zn\u00e1me<\/strong> pr\u00e1v\u011b po\u010d\u00edtanou cenu opce<\/strong> nap\u0159\u00edklad z\u00a0op\u010dn\u00ed obchodn\u00ed platformy, vypo\u010d\u00edtat ka\u017edou jednotlivou d\u00edl\u010d\u00ed hodnotu tvo\u0159\u00edc\u00ed takov\u00fd v\u00fdpo\u010det<\/strong><\/span>. Z\u00a0praktick\u00e9ho hlediska je toti\u017e na prvn\u00ed pohled jasn\u00e9, \u017ee na cenu opce m\u00e1 nejv\u011bt\u0161\u00ed vliv hodnota Implied Volatility<\/strong>, kter\u00e1 je pak v\u00a0takov\u00e9m v\u00fdpo\u010dtu \u201enejv\u011bt\u0161\u00edm hr\u00e1\u010dem<\/strong>\u201c. Pokud bychom toti\u017e nap\u0159\u00edklad zji\u0161\u0165ovali cenu opc\u00ed<\/strong> na stejn\u00fd strike<\/strong> u akci\u00ed, kter\u00e9 se obchoduj\u00ed za stejnou cenu<\/strong>, maj\u00ed stejnou dobu do expirace<\/strong> za stejn\u00fdch \u00farokov\u00fdch podm\u00ednek<\/strong> a nap\u0159\u00edklad nevypl\u00e1cej\u00ed dividendu<\/strong>, pak by m\u011bly tyto opce m\u00edt stejnou hodnotu<\/strong><\/span> \u2013 pokud by ov\u0161em m\u011bly stejnou hodnotu Implied Volatility<\/strong>. Z\u00a0t\u00e9to jednoduch\u00e9 \u00favahy pak vypl\u00fdv\u00e1, \u017ee Implied Volatilita je t\u00edm nejv\u011bt\u0161\u00edm hybatelem ceny op\u010dn\u00edch kontrakt\u016f, jej\u00ed v\u00fd\u0161e se do ceny okam\u017eit\u011b a velmi razantn\u011b prom\u00edt\u00e1 a tvo\u0159\u00ed jej\u00ed cenu.<\/strong> Pokud bych cht\u011bl tuto skute\u010dnost demonstrovat na n\u011bjak\u00e9 obchodn\u00ed realit\u011b, tak na n\u00ed\u017ee uveden\u00e9m obr\u00e1zku je vid\u011bt moment\u00e1ln\u00ed cena Call opc\u00ed na strike 100<\/strong> akciov\u00e9ho titulu Time Warner<\/strong> Inc (TWX), kter\u00e9 se obchoduje cca za 100 USD a m\u00e1 Implied Volatilitu na hodnot\u011b cca 10%, opce m\u00e1 23 dn\u016f do expirace. Cena opc\u00ed na strike 100 se pohybuje mezi 0,81 \u2013 1,20 USD<\/strong>.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0 \u00a0Na dal\u0161\u00edm obr\u00e1zku je vid\u011bt op\u010dn\u00ed \u0159et\u011bzec akciov\u00e9ho titulu Masimo Corp<\/strong>. (MASI), kter\u00fd se obchoduje za t\u00e9m\u011b\u0159 toto\u017enou cenu 100 USD, ov\u0161em hodnota Implied Volatility je zhruba 30%, tedy hodnota t\u0159ikr\u00e1t vy\u0161\u0161\u00ed ne\u017e u p\u0159edch\u00e1zej\u00edc\u00edho titulu, opce m\u00e1 op\u011bt 23 dn\u016f do expirace. Cena opc\u00ed na strike 100<\/strong> se pak pohybuje mezi 3,50 \u2013 4,50 USD<\/strong>.<\/span><\/p>\n

\"\"<\/span><\/p>\n

\u00a0 Cena opc\u00ed na stejn\u00e9m strike se stejnou expirac\u00ed za stejn\u00fdch \u00farokov\u00fdch podm\u00ednek a bez dividendy<\/strong> se pak diametr\u00e1ln\u011b odli\u0161uje<\/strong>. Hodnoty opc\u00ed u titulu s\u00a0vy\u0161\u0161\u00ed Implied Volatilitou jsou v\u00edce ne\u017e t\u0159ikr\u00e1t vy\u0161\u0161\u00ed. V\u0161e je zp\u016fsobeno pr\u00e1v\u011b touto Implied Volatilitou, v\u0161echny ostatn\u00ed podm\u00ednky pro v\u00fdpo\u010det ceny opc\u00ed jsou toti\u017e identick\u00e9.\u00a0<\/span><\/p>\n

\u00a0\u00a0 Proto\u017ee zn\u00e1me ceny jednotliv\u00fdch opc\u00ed a zn\u00e1me v\u0161echny ostatn\u00ed parametry, d\u00e1 se pak pomoc\u00ed matematick\u00e9ho oce\u0148ovac\u00edho modelu vypo\u010d\u00edtat, jak\u00e1 je pr\u00e1v\u011b hodnota t\u00e9to Implied Volatility<\/strong>. Tyto hodnoty mohou b\u00fdt velmi u\u017eite\u010dn\u00e9 k\u00a0obchodn\u00edmu pou\u017eit\u00ed, proto\u017ee obchodov\u00e1n\u00ed opc\u00ed je p\u0159edev\u0161\u00edm o obchodov\u00e1n\u00ed volatility. Vzorec a technika v\u00fdpo\u010dtu Implied Volatility podle BS modelu je dosti sofistikovan\u00e1, na\u0161t\u011bst\u00ed jsou v\u0161ak voln\u011b k\u00a0dispozici aplikace, kter\u00e9 n\u00e1m podle zadan\u00fdch podm\u00ednek takovou hodnotu Implied Volatility vypo\u010d\u00edtaj\u00ed. Nap\u0159\u00edklad na Livevol<\/a><\/strong>\u00a0m\u016f\u017eeme jednu takovou naj\u00edt. Na obr\u00e1zku je vid\u011bt v\u00fdpo\u010det takov\u00e9 Impied Volatility pr\u00e1v\u011b u titulu Time Warner pro strike 100 za ceny opce ve v\u00fd\u0161i 1,20 USD. Po zad\u00e1n\u00ed expirace a \u00farok\u016f vid\u00edme v\u00fdpo\u010det moment\u00e1ln\u00ed Implied Volatility t\u00e9to opce<\/strong> ve v\u00fd\u0161i 9,85%<\/strong>, co\u017e odpov\u00edd\u00e1 \u00fadaj\u016fm\u00a0<\/span>z\u00a0p\u0159edch\u00e1zej\u00edc\u00edch obr\u00e1zk\u016f.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0 Obchodov\u00e1n\u00ed opc\u00ed vypad\u00e1 mnohdy velmi komplikovan\u00e9 a jakoby teoreticky n\u00e1ro\u010dn\u00e9. Mysl\u00edm si, \u017ee nen\u00ed t\u0159eba se takov\u00fdch vlastnost\u00ed v\u016fbec ob\u00e1vat a nen\u00ed zase tak obt\u00ed\u017en\u00e9 jim alespo\u0148 jednodu\u0161e porozum\u011bt. Excel s\u00a0teoretick\u00fdm v\u00fdpo\u010dtem op\u010dn\u00edch cen, o kter\u00e9m psal v\u00a0tomto \u010dl\u00e1nku, si m\u016f\u017eete st\u00e1hnou zde\u00a0Teoretick\u00fd v\u00fdpo\u010det ceny opc\u00ed<\/a><\/span>\u00a0<\/strong>a vyzkou\u0161et si n\u011bkter\u00e9 popisovan\u00e9 funkcionality nebo se pod\u00edvat na jednoduch\u00fd VBA k\u00f3d v\u00fdpo\u010dt\u016f a funkc\u00ed.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0Obchodovat opce lze tak, \u017ee na p\u0159\u00edslu\u0161n\u00fd po\u017eadovan\u00fd op\u010dn\u00ed kontrakt jednodu\u0161e kliknu do sv\u00e9 obchodn\u00ed platformy a zad\u00e1m p\u0159\u00edkaz k\u00a0jeho n\u00e1kupu. To dnes ch\u00e1pe ka\u017ed\u00fd. Kde se ale berou v\u0161echna ta \u010d\u00edsla s\u00a0cenami jednotliv\u00fdch kontrakt\u016f na jednotliv\u00fdch strikes\u00a0a v\u00a0jednotliv\u00fdch expirac\u00edch a jak jsou vlastn\u011b stanovov\u00e1na? Generuj\u00ed je burzovn\u00ed servery, Continue Reading<\/i><\/a><\/p>\n","protected":false},"author":1,"featured_media":256,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_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}},"categories":[2],"tags":[17,18],"class_list":["post-245","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-opcni-zaklady","tag-black-scholes","tag-implied-volatility"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/dobretrejdy.com\/wp-content\/uploads\/2017\/04\/numbers.jpg","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8zd8A-3X","jetpack-related-posts":[{"id":27,"url":"https:\/\/dobretrejdy.com\/?p=27","url_meta":{"origin":245,"position":0},"title":"Z\u00e1kladn\u00ed op\u010dn\u00ed pojmy","author":"dobretrejdy :c)","date":"29.3.2017","format":false,"excerpt":"\u00a0 \u00a0Za\u010d\u00ednaj\u00edc\u00ed op\u010dn\u00ed trader mus\u00ed pochopit a zcela vst\u0159ebat z\u00e1kladn\u00ed pojmoslov\u00ed, definice a principy, kter\u00e9 jsou s takov\u00fdmi obchody spojeny. Pochopen\u00edm takov\u00fdch z\u00e1klad\u016f je absolutn\u00edm p\u0159edpokladem pro dal\u0161\u00ed \u00fasp\u011b\u0161n\u00fd v\u00fdvoj op\u010dn\u00edho obchodn\u00edka. Jak\u00fdm pojm\u016fm by m\u011bl tedy ka\u017ed\u00fd porozum\u011bt? Uvedu z\u00e1kladn\u00ed pojmy v jejich obecn\u00e9 definici, abych v budoucnu ka\u017ed\u00fd\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\/03\/main-1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/03\/main-1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/03\/main-1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2017\/03\/main-1.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1686,"url":"https:\/\/dobretrejdy.com\/?p=1686","url_meta":{"origin":245,"position":1},"title":"Vnit\u0159n\u00ed hodnota a Pr\u00e9mium","author":"dobretrejdy :c)","date":"8.4.2018","format":false,"excerpt":"\u00a0\u00a0\u00a0 Homonymum \u201eSink Or Swim\u201c zn\u00ed t\u00e9m\u011b\u0159 stejn\u011b jako n\u00e1zev skv\u011bl\u00e9 op\u010dn\u00ed analytick\u00e9 platformy z\u00a0minul\u00e9ho \u010dl\u00e1nku a zcela p\u0159esn\u011b vystihuje dialektiku tradingu, bu\u010f se mi poda\u0159\u00ed na trz\u00edch plavat nebo na nich utonu. Nev\u00edm, jestli vyn\u00e1lezci n\u00e1zvu t\u00e9to aplikace m\u011bli na mysli pr\u00e1v\u011b tyto protikladn\u00e9 procesy p\u0159e\u017eit\u00ed, ale platforma thinkorswim\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\/2018\/04\/main.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2018\/04\/main.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2018\/04\/main.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2018\/04\/main.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":3810,"url":"https:\/\/dobretrejdy.com\/?p=3810","url_meta":{"origin":245,"position":2},"title":"Delta Neutral \u2013 XI.","author":"dobretrejdy :c)","date":"27.10.2019","format":false,"excerpt":"\u00a0\u00a0 Pozn\u00e1n\u00ed princip\u016f Delta Neutral obchodov\u00e1n\u00ed ve v\u0161ech nuanc\u00edch nen\u00ed jednoduch\u00e9, p\u0159esto\u017ee se to tak m\u016f\u017ee na prvn\u00ed pohled zd\u00e1t. V p\u0159edchoz\u00edch \u010dl\u00e1nc\u00edch jsem popisoval, jak lze od sebe odli\u0161it takov\u00e9 obchody nap\u0159\u00edklad podle hodnoty znam\u00e9nka u parametru Gamma a se zaslou\u017eenou pozornost\u00ed jsem v n\u011bkolika dal\u0161\u00edch \u010dl\u00e1nc\u00edch popisoval obchodov\u00e1n\u00ed\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\/10\/main.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/10\/main.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/10\/main.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2019\/10\/main.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":574,"url":"https:\/\/dobretrejdy.com\/?p=574","url_meta":{"origin":245,"position":3},"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":267,"url":"https:\/\/dobretrejdy.com\/?p=267","url_meta":{"origin":245,"position":4},"title":"Je opce levn\u00e1 nebo drah\u00e1?","author":"dobretrejdy :c)","date":"28.4.2017","format":false,"excerpt":"\u00a0\u00a0 V\u00a0minul\u00e9m \u010dl\u00e1nku Cena opce\u00a0jsem se pokusil popsat, jak je mo\u017en\u00e9 si alespo\u0148 zjednodu\u0161en\u011b p\u0159edstavit zcela zevrubnou stavbu stanoven\u00ed ceny op\u010dn\u00edho kontraktu. 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