# Institute of Mathematics

## DG method for numerical pricing of multi-asset Asian options - the case of options with floating strike

#### Jiří Hozman, Tomáš Tichý

###### Received September 29, 2016.  First published March 4, 2017.

Abstract:  Option 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.
Keywords:  option pricing; discontinuous Galerkin method; path-dependent option; basket option; floating strike
Classification MSC:  65M60, 35Q91, 91G60, 91G80

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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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