DG method for the numerical pricing of two-asset European-style Asian options with fixed strike
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Date
2017
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematics of the Academy of Sciences of the Czech Republic
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.
Description
Subject(s)
option pricing, discontinuous Galerkin method, Asian option, basket option, fixed strike
Citation
ISSN
0862-7940