Continuous rainbow options on commodity outputs: what is the real value of switching facilities?

Abstract

We develop real rainbow option models to value an operating asset with the flexibility to choose between two commodity outputs. We provide a quasi-analytical solution and a numerical lattice solution to a model with continuous switching opportunities between two commodity outputs, taking into account operating and switching costs. The models are applied to an illustrative case, demonstrating that the quasi-analytical solution and the lattice approach provide near identical results for the asset valuation and optimal switching boundaries. We find that the switching boundaries generally narrow as prices decline. In the presence of operating costs and temporary suspension, however, the thresholds diverge for low enough prices. A fertilizer plant with flexibility between selling ammonia and urea is valued in an empirical section using our real option models. Despite the high correlation between the two alternative commodities, ammonia and urea, there is significant value in the flexibility to choose between the two. Both strategic and policy implications for stakeholders in flexible assets are discussed, with some generalisations outside the fertilizer industry.

Keywords:

• rainbow option
• continuous switching
• temporary suspension
• operating flexibility

JEL Classification :

• D81
• G31

Acknowledgements

We thank Roger Adkins, Luiz Brandão, Paul Johnson, Tim Mennel, Peter Oliver, Lenos Trigeorgis and participants at the ZEW Real Options Conference 2008 and at the Real Options Conference 2009 for helpful comments.

Notes