The Tourinho model: neglected nugget or a receding relic?

Abstract

This article evaluates Tourinho's (1979b) work as one of the earliest contributors to the real options literature. His model pioneered the application of risk neutrality to uncertain investments, but his originality of introducing an option-holding cost albeit to overcome the extraction paradox is rarely imitated. We claim that the combination of a convenience yield and an option-holding cost produces a more satisfying representation. Moreover, variations in the holding cost give rise to a host of investment decisions ranging from the standard real option solution for a zero-holding cost to a net present value solution for an infinite-holding cost. Not only does the holding cost mediate between these two poles, but it provides the option seller (usually a landowner or a government) with a policy instrument for influencing the extraction timing and thus the extraction profit of the option buyer. We derive the holding cost that optimizes the landowner's combined value of the option premium, holding costs and eventual royalties.

Keywords:

• oil extraction
• real option-holding cost
• convenience yield
• escalating investment cost

JEL Classification: :

• D81
• G31

Acknowledgements

We wish to thank Alcino Azevedo, Mike Bowe, Michael Brennan, Michael Flanagan, Sydney Howell, Ser-Huang Poon, Artur Rodrigues, Mark Shackleton, Octavio Tourinho, Lenos Trigeogis, and the participants at the Real Options Conference, Rio, 2008, for helpful comments.

Notes

The Tourinho (1979b) thesis was not published, but the working paper (Tourinho 1979a) based on his research is available from the University of California, Berkeley, Institute of Business and Economic Research.

Tourinho notes in several places that exercise of an American perpetual stock option (and thus solving the standard differential equation) could be justified by dividends on the stock (p. 16), especially ‘proportional dividends which are paid out continuously’ (p. 74, which cites observations in Merton 1973, using Samuelson (1965 (sic)), which would be similar to considering a convenience yield). Immediate extraction precludes consideration of a convenience yield, but this is hardly realistic.