# Institute of Mathematics

## DG method for the numerical pricing of two-asset European-style Asian options with fixed strike

#### Jiří Hozman, Tomáš Tichý

###### Received June 30, 2017.   First published December 11, 2017.

Abstract:  The 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.
Keywords:  option pricing; discontinuous Galerkin method; Asian option; basket option; fixed strike
Classification MSC:  65M60, 35Q91, 91G60, 91G80
DOI:  10.21136/AM.2017.0176-17

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Affiliations:   Jiří Hozman, Technical University of Liberec, Faculty of Science, Humanities and Education, Department of Mathematics and Didactics of Mathematics, Studentská 1402/2, 461 17 Liberec, Czech Republic, e-mail: jiri.hozman@tul.cz; Tomáš Tichý, VŠB - Technical University of Ostrava, Faculty of Economics, Department of Finance, Sokolská třída 33, 702 00 Ostrava, Czech Republic, e-mail: tomas.tichy@vsb.cz

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