Price options on investment project expansion under commodity price and volatility uncertainties using a novel finite difference method

Nan Li, Song Wang and Kai Zhang

Applied Mathematics and Computation, 2022, vol. 421, issue C

Abstract: 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 discretization 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 difference scheme converges to the exact one when the mesh sizes approach zero. To demonstrate 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.

Keywords: Real option valuation; Finite difference method; Convergence; Stability; 2D Black-Scholes equation; Financial engineering (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000236

DOI: 10.1016/j.amc.2022.126937

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