Publicação
Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
| Resumo: | 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. |
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| Autores principais: | Grossinho, Maria do Rosário |
| Outros Autores: | Kord, Yaser Faghan; Ševčovič, Daniel |
| Assunto: | American option pricing nonlinear Black-Scholes equation variable transaction costs PSOR method |
| Ano: | 2017 |
| País: | Portugal |
| Tipo de documento: | working paper |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | 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. |
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