Solution of option pricing equations using orthogonal polynomial expansion

@article{Baustian2019SolutionOO,
  title={Solution of option pricing equations using orthogonal polynomial expansion},
  author={Falko Baustian and Katerina Filipov{\'a} and Jan Posp{\'i}sil},
  journal={ArXiv},
  year={2019},
  volume={abs/1912.06533}
}
In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of Heston model at the boundary with vanishing… 
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