Grossinho, Maria do RosárioKord, Yaser FaghanŠevčovič, Daniel2018-11-142018-11-142017-12Grossinho, Maria do Rosário, Yaser Faghan Kord e Daniel Ševčovič (2017). "Pricing perpetual put options by the Black-Scholes equation with a nonlinear volatility function". Instituto Superior de Economia e Gestão – REM Working paper nº 019 - 20172184-108Xhttp://hdl.handle.net/10400.5/16343We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.engOption pricingnonlinear Black-Scholes equationperpetual American put optionearly exercise boundaryworking paper