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Genetic algorithms for the optimisation of the Schwartz–Smith two-factor model: a case study on a copper deposit

Abstract Mining companies typically seek ways to hedge risks affecting their production. One useful instrument to mitigate the financial risk is the futures contracts on commodity prices. Information from the transactions in futures markets is publicly available and can be analysed with the Schwartz–Smith two-factor model (SSTF). However, finding the parameters governing this model can be very challenging. This step is done using a deterministic optimisation approach called the Expectation–Maximisation algorithm (EM). The starting values of the model will have a significant effect on the convergence of the EM. To ensure the solution does not get stuck in a local maximum, the EM algorithm is performed multiple times with different starting values. This paper assesses the value of genetic algorithms (GA) to optimise the parameters of the SWTF model. Although they are slower than EM algorithms because they use random number generators to search for the optimal solution, GA optimise a population of solutions instead of working on only one solution at the time. Moreover, a constraint on the range parameter can be applied to ensure the parameter has a sound economic meaning. Once the SWTF parameters have been calibrated on the observation of futures contracts, the model can be used for the simulation of spot and futures prices. To demonstrate the performance of the proposed approach, a case study was conducted on a copper deposit. The simulations based on the SWTF model whose parameters are determined by GA are used. An active management strategy of the stockpile, dependent on discrepancies in commodity futures prices is tested. Results show that the active management strategy produces positive returns over the passive investment approach.