DGM for real options valuation: Options to change operating scale

Abstract

The real options approach interprets a flexibility value, embedded in a project, as an option premium. The object of interest is to valuate real options to change operating scale, typical for natural resources industry. The evolution of the project as well as option prices is decribed by partial differential equations of the Black-Scholes type, linked through a payoff function given by a type of the flexibility provided. The governing equations are discretized by the discontinuous Galerkin method over a finite element mesh and they are integrated in temporal variable by an implicit Euler scheme. The special attention is paid to the treatment of early exercise feature that is handled by additional penalty term. The capabilities of the approach presented are documented on the selected individual real options from the reference experiments using real market data.