Pricing american call option by the Black-Scholes equation with a nonlinear volatility function
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 (va...
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| Other Authors: | , |
| Format: | workingPaper |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.5/15991 |
| Country: | Portugal |
| Oai: | oai:www.repository.utl.pt:10400.5/15991 |
| Summary: | 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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