Pricing american call option by the Black-Scholes equation with a nonlinear volatility function

Grossinho, Maria do Rosário; Kord, Yaser Faghan; Ševčovič, Daniel

http://hdl.handle.net/10400.5/15991

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Authors

Grossinho, Maria do Rosário

Kord, Yaser Faghan

Ševčovič, Daniel

Abstract(s)

In this paper we analyze a nonlinear Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We study the generalized Black-Scholes equation by means of transformation of the free boundary problem (variational inequalities) into the so-called Gamma equation for the new variable H = S@2SV . Moreover, we reformulate our new problem with PSOR method and construct an effective numerical scheme for discretization of the Gamma equation. Finally,we solve numerically our nonlinear complementarity problem applying PSOR method.

Keywords

American option pricing nonlinear Black-Scholes equation variable transaction costs PSOR method

URI

http://hdl.handle.net/10400.5/15991

Citation

Grossinho, Maria do Rosário, Yaser Faghan Kord e Daniel Ševčovič (2017). "Pricing american call option by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 018 - 2017