Rafael Company1, Vera N. Egorova2, Lucas Jódar1,*, Ferran Fuster Valls3
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 493-508, 2020, DOI:10.32604/cmes.2020.010208
Abstract A numerical method for American options pricing on assets under the
Heston stochastic volatility model is developed. A preliminary transformation is
applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational costs. Free boundary is treated by the penalty
method. Transformed nonlinear partial differential equation is solved numerically
by using the method of lines. For full discretization the exponential time differencing method is used. Numerical analysis establishes the stability and positivity of
the proposed method. The numerical convergence behaviour and effectiveness are
investigated in extensive numerical experiments. More >
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