Description:
We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory. The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier Transform ("FFT") lower bound approximation to value the inherent real optionality and for robustness check, we compare the semi-analytical pricing accuracy with the Monte Carlo simulation. Model parameters are estimated from the historical monthly data, and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox-Ingersoll-Ross ("CIR") model.