Kalman Filtering-Based Approach for Project Valuation of an Iron Ore Mining Project Through Spot Price and Long-Term Commitment Contracts

Abstract

Iron ore was traditionally traded using long-term commitment (LTC) contracts. In the last decade, with the surging demand from China, a futures market was created for iron ore. In this paper, using historical information from this futures market, we focus on modeling market dynamics of Iron Fine 62% Fe—CFR Tianjin Port (China) futures contracts to determine optimal parameter values of the Schwartz (J Financ 52:923–973, 1997) two-factor model. A new approach using LTC and futures contracts is proposed to assess the Net Present Value (NPV) of an iron ore mining project. We apply Kalman filtering techniques to calibrate the two-factor commodity model to iron ore futures for the January 2014–November 2016 period. The Kalman filter is useful to infer unobservable variables from noisy measurements. In the Schwartz (1997) two-factor model, the unobservable spot price and convenience yield are inferred from futures contracts transactions. Model parameters are fitted using maximum likelihood optimization. Using parameters derived from the Kalman filtering and the maximum likelihood approach, spot price simulations for the next 7 years are made for three scenarios. The NPV of a mining project is calculated for each scenario. Then, both LTC and futures markets are treated separately and the mining company can choose which proportion of its production to sell in each market. Results show that the calibration and NPV simulation workflow can be effectively used to assess the profitability of a mining project, accounting for the exposure to futures markets.

Appendix

Let ${y_1},\ldots ,{y_T}$ be a set of independent and identically distributed observations. The joint density function is given by (Harvey 1990):

$$\begin{aligned} L(y;\psi ) = \prod \limits _{t = 1}^T {p({y_t}|{Y_{t - 1}})} \end{aligned}$$

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where ${p({y_t}|{Y_{t - 1}})}$ is the conditional distribution of $y_t$ knowing all available information at time $t-1$. The measurement equation of the Kalman filter can be written as:

$$\begin{aligned} {y_t} = {Z_t}{a_t}_{|t - 1} + {Z_t}\left( {\alpha _t} - {a_t}_{|t - 1}\right) + {d_t} + {\varepsilon _t} \end{aligned}$$

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The conditional distribution of $y_t$ is normal with a mean:

$$\begin{aligned} E({y_t}) = {Z_t}{a_t}_{|t - 1} + {d_t} \end{aligned}$$

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and a covariance matrix given by:

$$\begin{aligned} {F_t} = {Z_t}{P_{t|t - 1}}Z_t' + {H_t} \end{aligned}$$

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For a Gaussian model, the likelihood function can be written as:

$$\begin{aligned} \hbox {Log}\,L = - \frac{{NT}}{2}\log (2\pi ) - \frac{1}{2}\sum \nolimits _{t = 1}^T {\log |{F_t}|} - \frac{1}{2}\sum \limits _{t = 1}^T {\nu 'F_t^{ - 1}} {v_t} \end{aligned}.$$

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