American option pricing under an extended slow-growth volatility model

Abstract

This paper extends the Slow Growth Volatility (SGV) model to American option pricing.  The SGV framework introduces a nonlinear, state-dependent volatility to reflect observed skew beyond classical models.  We establish existence and uniqueness for the penalized PDE and show convergence, as the penalty parameter vanishes, towards the solution of the associated linear complementarity formulation.  Numerical implementation employs a rational penalty method with finite difference discretization, and computational results confirm that the SGV framework remains consistent and competitive with Black--Scholes and CEV.