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

- 186 Downloads

## 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.

## Keywords

Kalman filter Iron ore futures Maximum likelihood optimization Schwartz (1997) model Commodity prices NPV valuation## Notes

### Acknowledgements

The authors gratefully thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for support (Project No. 435661).

## References

- Aiube, F. A. L., & Samanez, C. P. (2014). On the comparison of Schwartz and Smith’s two- and three-factor models on commodity prices.
*Applied Economics*,*46*, 3736–3749.CrossRefGoogle Scholar - Basu, D., & Miffre, J. (2013). Capturing the risk premium of commodity futures: The role of hedging pressure.
*Journal of Banking & Finance*,*37*, 2652–2664.CrossRefGoogle Scholar - Bertisen, J., & Davis, G. A. (2008). Bias and error in mine project capital cost estimation.
*The Engineering Economist*,*53*, 118–139.CrossRefGoogle Scholar - Brennan, M. J., & Schwartz, E. S. (1985). Evaluating natural resource investments.
*Journal of Business*,*58*, 135–157.CrossRefGoogle Scholar - Chicago Mercantile Exchange. (2015).
*Futures and options trading for risk management*. Retrieved January 4, 2017 from www.cmegroup.com. - Erb, P., Luethi, D., Hinz, J., & Otziger, S. (2014).
*schwartz97: A package on the Schwartz two-factor commodity model*. R package version 0.0.6.Google Scholar - Geman, H. (2009).
*Commodities and commodity derivatives: Modeling and pricing for agriculturals, metals and energy. The Wiley finance series*. West Sussex: Wiley.Google Scholar - Gibson, R., & Schwartz, E. S. (1990). Stochastic convenience yield and the pricing of oil contingent claims.
*The Journal of Finance*,*45*(3), 959–976.CrossRefGoogle Scholar - Haque, M. A., Topal, E., & Lilford, E. (2015). Iron ore prices and the value of the Australian dollar.
*Mining Technology*,*124*, 107–120.CrossRefGoogle Scholar - Haque, A., Topal, E., & Lilford, E. (2016). Estimation of mining project values through real option valuation using a combination of hedging strategy and a mean reversion commodity price.
*Natural Resources Research*,*25*, 459–471.CrossRefGoogle Scholar - Harvey, A. C. (1990).
*Forecasting, structural time series models and the Kalman filter*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Hurst, L. (2015). Assessing the competitiveness of the supply side response to China’s iron ore demand shock.
*Resources Policy*,*45*, 247–254.CrossRefGoogle Scholar - marketrealist.com. (2015).
*China’s steel production is greatly influencing iron ore prices*.Google Scholar - Masteika, S., Rutkauskas, A. V., & Alexander, J. A. (2012). Continuous futures data series for back testing and technical analysis. In
*Conference proceedings, 3rd international conference on financial theory and engineering*(Vol. 29, pp. 265–269).Google Scholar - McTaggart, R., Daroczi, G., & Leung, C. (2015).
*Quandl: API Wrapper for Quandl.com*. R package version 2.7.0.Google Scholar - Nejadi, S., Trivedi, J., & Leung, J. Y. (2015). Estimation of facies boundaries using categorical indicators with P-Field simulation and ensemble Kalman filter (EnKF).
*Natural Resources Research*,*24*, 121–138.CrossRefGoogle Scholar - Othman, J., & Jafari, Y. (2012). Accounting for depletion of oil and gas resources in Malaysia.
*Natural Resources Research*,*21*, 483–494.CrossRefGoogle Scholar - Patiño Douce, A. E. (2016). Metallic mineral resources in the twenty-first century: II. Constraints on future supply.
*Natural Resources Research*,*25*, 97–124.CrossRefGoogle Scholar - Platts. (2016). The Steel Index. Retrieved September 28, 2016 from https://www.thesteelindex.com.
- R Core Team. (2015).
*R: A language and environment for statistical computing*. Vienna: R Foundation for Statistical ComputingGoogle Scholar - Ribeiro, D. R. & Hodges, S. D. (2004).
*A two-factor model for commodity prices and futures valuation*. EFMA 2004 Basel Meetings Paper.Google Scholar - Rogers, C. D., & Robertson, K. (1987). Long term contracts and market stability: The case of iron ore.
*Resources Policy*,*13*, 3–18.CrossRefGoogle Scholar - Rudenno, V. (1998).
*The mining valuation handbook*. Elsternwick: Wrightbooks.Google Scholar - Schwartz, E. S. (1997). The stochastic behavior of commodity prices: Implications for valuation and hedging.
*The Journal of Finance*,*52*, 923–973.CrossRefGoogle Scholar - Schwartz, E., & Smith, J. E. (2000). Short-term variations and long-term dynamics in commodity prices.
*Management Science*,*46*, 893–911.CrossRefGoogle Scholar - U.S. Commodity Futures Trading Commission. (2015).
*Weekly commitment of traders reports*. Retrieved March 16, 2016 from www.cftc.gov. - Wilson, J. D. (2012). Chinese resource security policies and the restructuring of the Asia-Pacific iron ore market.
*Resources Policy*,*37*, 331–339.CrossRefGoogle Scholar - Zhang, K., & Kleit, A. N. (2016). Mining rate optimization considering the stockpiling—A theoretical economics and real option model.
*Resources Policy*,*47*, 87–94.CrossRefGoogle Scholar - Zhang, K., Nieto, A., & Kleit, A. N. (2014). The real option value of mining operations using mean-reverting commodity prices.
*Mineral Economics*,*28*, 11–22.CrossRefGoogle Scholar