Browsing by Author "Tichý Tomáš"
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- ItemA discontinuous Galerkin method for pricing of two-asset options(University of West Bohemia, 2016-01-01) Hozman Jiří; Tichý Tomáš
- ItemA discontinuous Galerkin method for two-dimensional PDE models of Asian options(2016-01-01) Hozman Jiří; Tichý Tomáš; Cvejnová Daniela
- ItemComparison of Selected Advanced Numerical Methods for Greeks Calculation of Vanilla Options(IRANIAN SOCIETY OF OPERATIONS RESEARCH, 2018-01-01) Kresta Aleš; Hozman Jiří; Holčapek Michal; Tichý Tomáš; Valášek Radek
- ItemComparison of several alternatives to numerical pricing of options(VŠB - Technical University of Ostrava, 2017-01-01) Tichý Tomáš; Holčapek Michal; Hozman Jiří; Kresta Aleš
- ItemDG Approach to Numerical Pricing of Local Volatility Basket Options(Technical University of Liberec, 2016-01-01) Hozman Jiří; Tichý Tomáš
- ItemA DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model(2017-01-01) Hozman Jiří; Tichý Tomáš
- ItemDG framework for pricing European options under one-factor stochastic volatility models(Elsevier Science BV, 2018-01-01) Hozman Jiří; Tichý Tomáš
- ItemDG method for numerical pricing of multi-asset Asian options - A case of options with floating strike(Institute of Mathematics of the Academy of Sciences of the Czech Republic, 2017-01-01) Hozman Jiří; Tichý TomášOption pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two assets. Further, we focus only on one subclass - Asian options with floating strike - and introduce the concept of the dimensionality reduction with respect to the payoff leading to PDE with two spatial variables. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed and some theoretical results are also mentioned. Finally, the aforementioned model is supplemented with numerical results on real market data.
- ItemDG Method for Pricing European Options under Merton Jump-Diffusion Model(Institute of Mathematics, Czech Academy of Sciences, 2019-01-01) Hozman Jiří; Tichý Tomáš; Vlasák Miloslav
- ItemDG method for the Hull-White option pricing model(VŠB - Technical University of Ostrava, 2017-01-01) Hozman Jiří; Tichý Tomáš
- ItemDG method for the numerical pricing of two-asset European-style Asian options with fixed strike(Institute of Mathematics of the Academy of Sciences of the Czech Republic, 2017-01-01) Hozman Jiří; Tichý TomášThe evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and extends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution of European-style Asian option contracts on two assets, whose payoff depends on the difference of the strike price and the average value of the basket of two underlying assets during the life of the option. Further, a suitable transformation of variables respecting this complex form of a payoff function reduces the problem to a two-dimensional equation belonging to the class of convection-diffusion problems and the discontinuous Galerkin (DG) method is applied to it in order to utilize its solving potentials. The whole procedure is accompanied with theoretical results and differences to the floating strike case are discussed. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on Asian options.
- ItemDG solver for one-factor and two-factor Black-Scholes models(VŠB - Technical University of Ostrava, 2016-01-01) Hozman Jiří; Tichý Tomáš
- ItemThe discontinuous Galerkin method for discretely observed Asian options(John Wiley & Sons, Ltd., 2020-01-01) Hozman Jiří; Tichý Tomáš
- ItemA discontinuous Galerkin method for numerical pricing of European options under Heston stochastic volatility(2017-01-01) Hozman Jiří; Tichý Tomáš
- ItemA Note on Several Alternatives to Numerical Pricing of Options(Technical University of Liberec, 2017-01-01) Tichý Tomáš; Hozman Jiří; Holčapek Michal
- ItemNumerical Pricing of American-Style Options within the Black and Scholes Framework(VŠB TU Ostrava, 2018-01-01) Hozman Jiří; Kresta Aleš; Tichý Tomáš
- ItemNumerical pricing of European basket options with discrete barrier via the discontinuous Galerkin method(VSB TU Ostrava, 2016-01-01) Hozman Jiří; Tichý Tomáš
- ItemNumerical valuation of options by DG method: a study of boundary condition formulation(Institute of Electrical and Electronics Engineers Inc., 2016-01-01) Hozman Jiří; Tichý Tomáš
- ItemOn the Discontinuous Galerkin Method for Numerical Pricing of Basket Spread Options with the Average Strike(2017-01-01) Hozman Jiří; Tichý Tomáš
- ItemOn the impact of various formulations of the boundary condition within numerical option valuation by DG method(University of Nis, 2016-01-01) Hozman Jiří; Tichý Tomáš