Pricing American Call Option by the Black-Scholes Equation with a Nonlinear Volatility Function

Maria do Rosário Grossinho, Yaser Faghan Kord and Daniel Sevcovic

No 2017/18, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

Abstract: 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 (variationalinequalities) 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; PSORmethod (search for similar items in EconPapers)
Date: 2017-12
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Persistent link: https://EconPapers.repec.org/RePEc:ise:remwps:wp0182017

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