首页|Price options on investment project expansion under commodity price and volatility uncertainties using a novel finite difference method
Price options on investment project expansion under commodity price and volatility uncertainties using a novel finite difference method
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NSTL
Elsevier
In this paper we develop a PDE-based mathematical model for valuing real options on the expansion of an investment project whose underlying commodity price and its volatility follow their respective geometric Brownian motions. This mathematical model is of the form of a 2-dimensional Black-Scholes equation whose payoff condition is determined also by a PDE system. A novel 9-point finite difference scheme is proposed for the discretiza-tion of the spatial derivatives and the fully implicit time-stepping scheme is used for the time discretization of the PDE systems. We show that the coefficient matrix of the fully discretized system is an M-matrix and prove that the solution generated by this finite dif-ference scheme converges to the exact one when the mesh sizes approach zero. To demon-strate the usefulness and effectiveness of the mathematical model and numerical method, we present a case study on a real option pricing problem in the iron-ore mining industry. Numerical experiments show that our model and methods are able to produce numerical results which are financially meaningful.(c) 2022 Elsevier Inc. All rights reserved.
Real option valuationFinite difference methodConvergenceStability2D Black-Scholes equationFinancial engineeringSTOCHASTIC VOLATILITYVALUATIONASSETS
NSTL
Elsevier
