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Pricing of digital and barrier options
Shyman, Pavlo ; Karlova, Andrea (advisor) ; Dostál, Petr (referee)
Xaxev pra'ce: Oeehovarn' hhiarmVh a barierovycl] opci' Autor: Pavlo Shy man Katedra: Katedra pravdepodobnusti a maternal icke statist iky Vedouei bakalafske prace: Mgr. Andrea Karlova e-mail vedouci': karlova'O'karlm.mff.cum.e/ A h s t r a k l : V predloxene praci slndnjeme /phsoby oreuovanf dvon druliu exol.iekyeh opci': binanii'eh a barirvuvyrli. klrn; patri k rasln obcluKluvanyui oprfni na trim finnnrnfcli do- rivjilu. '1'uio cjccnoviUif jc /.alo/riuj na molndarh /,ajist ovaiu cxutickyc-li opri pomort' ,slan- dnrdnfch plain vanilla call a. put upci. V pnici json pups/uiy dvr hlavnf mrfody stati(;k(;ho xajislovani bari(':rovy'')i opci f/ujist ovam ponun-/ htriko sprradh a calendar spreads) a uv^- doiiy shnnlacni al;.v.iriUny j)i'o o(.'onov;i.iif tochl.o npn, Takr jsou /dc popsiiny dve jjorUulia pro rcplikovain' liinarnu-li ra.sh-or-noi liin.» a asst'l-or-iiot liin^, opt;f. Sinmlami alguri!rny jstiii jia[)ro^ra.niiA';iiiy v ja/ycf Aiatlnanaiica ti a U'drcticlsVTni podkladv (oclito al^nrit nni melody Montr ('a.rlo. Tilh1: Pririm>' of r)iu,ila] and [Sarricr Options Author: Pavlo Sliyna.ni Doj>artmont: Department of Proba.hililv and Afalliematicaj Sl.atirilios Sui>ervi.sor: Mftr. Andrea Karlova Su]xj)A'isor's e-mail addre.-v-v k"arlova«karliii.niff.euni.e7 Abstract: In tlie {^resented work \ve study merhods...
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Obchodní strategie v neúplném trhu
Bunčák, Tomáš ; Karlova, Andrea (advisor) ; Štěpán, Josef (referee)
MASTER THESIS ABSTRACT TITLE: Trading Strategy in Incomplete Market AUTHOR: Tomáš Bunčák DEPARTMENT: Department of Probability and Mathematical Statistics, Charles University in Prague SUPERVISOR: Andrea Karlová We focus on the problem of finding optimal trading strategies (in a meaning corresponding to hedging of a contingent claim) in the realm of incomplete markets mainly. Although various ways of hedging and pricing of contingent claims are outlined, main subject of our study is the so-called mean-variance hedging (MVH). Sundry techniques used to treat this problem can be categorized into two approaches, namely a projection approach (PA) and a stochastic control approach (SCA). We review the methodologies used within PA in diversely general market models. In our research concerning SCA, we examine the possibility of using the methods of optimal stochastic control in MVH, and we study the problem of our interest in several settings of market models; involving cases of pure diffusion models and a jump- diffusion case. In order to reach an exemplary comparison, we provide solutions of the MVH problem in the setting of the Heston model via techniques of both of the approaches. Some parts of the thesis are accompanied with numerical illustrations.
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Options under Stable Laws
Karlová, Andrea ; Volf, Petr (advisor) ; Klebanov, Lev (referee) ; Witzany, Jiří (referee)
Title: Options under Stable Laws. Author: Andrea Karlová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. Petr Volf, CSc. Abstract: Stable laws play a central role in the convergence problems of sums of independent random variables. In general, densities of stable laws are represented by special functions, and expressions via elementary functions are known only for a very few special cases. The convenient tool for investigating the properties of stable laws is provided by integral transformations. In particular, the Fourier transform and Mellin transform are greatly useful methods. We first discuss the Fourier transform and we give overview on the known results. Next we consider the Mellin transform and its applicability on the problem of the product of two independent random variables. We establish the density of the product of two independent stable random variables, discuss the properties of this product den- sity and give its representation in terms of power series and Fox's H-functions. The fourth chapter of this thesis is focused on the application of stable laws into option pricing. In particular, we generalize the model introduced by Louise Bachelier into stable laws. We establish the option pricing formulas under this model, which we refer to as the Lévy Flight...
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Obchodní strategie v neúplném trhu
Bunčák, Tomáš ; Karlova, Andrea (advisor) ; Štěpán, Josef (referee)
MASTER THESIS ABSTRACT TITLE: Trading Strategy in Incomplete Market AUTHOR: Tomáš Bunčák DEPARTMENT: Department of Probability and Mathematical Statistics, Charles University in Prague SUPERVISOR: Andrea Karlová We focus on the problem of finding optimal trading strategies (in a meaning corresponding to hedging of a contingent claim) in the realm of incomplete markets mainly. Although various ways of hedging and pricing of contingent claims are outlined, main subject of our study is the so-called mean-variance hedging (MVH). Sundry techniques used to treat this problem can be categorized into two approaches, namely a projection approach (PA) and a stochastic control approach (SCA). We review the methodologies used within PA in diversely general market models. In our research concerning SCA, we examine the possibility of using the methods of optimal stochastic control in MVH, and we study the problem of our interest in several settings of market models; involving cases of pure diffusion models and a jump- diffusion case. In order to reach an exemplary comparison, we provide solutions of the MVH problem in the setting of the Heston model via techniques of both of the approaches. Some parts of the thesis are accompanied with numerical illustrations.
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Pricing of digital and barrier options
Shyman, Pavlo ; Dostál, Petr (referee) ; Karlova, Andrea (advisor)
Xaxev pra'ce: Oeehovarn' hhiarmVh a barierovycl] opci' Autor: Pavlo Shy man Katedra: Katedra pravdepodobnusti a maternal icke statist iky Vedouei bakalafske prace: Mgr. Andrea Karlova e-mail vedouci': karlova'O'karlm.mff.cum.e/ A h s t r a k l : V predloxene praci slndnjeme /phsoby oreuovanf dvon druliu exol.iekyeh opci': binanii'eh a barirvuvyrli. klrn; patri k rasln obcluKluvanyui oprfni na trim finnnrnfcli do- rivjilu. '1'uio cjccnoviUif jc /.alo/riuj na molndarh /,ajist ovaiu cxutickyc-li opri pomort' ,slan- dnrdnfch plain vanilla call a. put upci. V pnici json pups/uiy dvr hlavnf mrfody stati(;k(;ho xajislovani bari(':rovy'')i opci f/ujist ovam ponun-/ htriko sprradh a calendar spreads) a uv^- doiiy shnnlacni al;.v.iriUny j)i'o o(.'onov;i.iif tochl.o npn, Takr jsou /dc popsiiny dve jjorUulia pro rcplikovain' liinarnu-li ra.sh-or-noi liin.» a asst'l-or-iiot liin^, opt;f. Sinmlami alguri!rny jstiii jia[)ro^ra.niiA';iiiy v ja/ycf Aiatlnanaiica ti a U'drcticlsVTni podkladv (oclito al^nrit nni melody Montr ('a.rlo. Tilh1: Pririm>' of r)iu,ila] and [Sarricr Options Author: Pavlo Sliyna.ni Doj>artmont: Department of Proba.hililv and Afalliematicaj Sl.atirilios Sui>ervi.sor: Mftr. Andrea Karlova Su]xj)A'isor's e-mail addre.-v-v k"arlova«karliii.niff.euni.e7 Abstract: In tlie {^resented work \ve study merhods...
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