An Application of Financial Mathematics, using Real Option Analysis, on Coal Production and Logistics

Abstract

We present an application of Financial Mathematics (using Real Option Analysis) to value the inherent optionality a coal producer has when mining and processing thermal coal. The pay-off of the physical option can be modelled as a spread option, whereby both the underlyings, and more unusually, the strike all follow stochastic processes. The volatilities for each are modelled to be stochastic. We derive a lower bound approximation to value the inherent optionality and compare this to Monte Carlo simulation.

Keywords: Stochastic volatility; option-pricing theory; real option theory; black-scholes formula; spread-option, rainbow option, FFT method, coal, Monte-Carlo, closed-form solution, fat-tails