The Tourinho Model:

1
The Tourinho Model Neglected Nugget or a
Receding Relic?
by Roger Adkins and Dean Paxson
Correspondence r.adkins_at_salford.ac.uk
2
The Issue
Rubinstein thesis
Insufficient attribution given to the pioneers of
corporate finance theory
Does this apply to real option theory? Is
Tourinho a victim?
Number of citations on Google Scholar
Tourinho predates others, but without similar
recognition! Why?
Rubinstein, M. (2006). A History of the Theory of
Investments My Annotated Bibliography. John
Wiley Sons, Inc.
Tourinho, O. A. F. (1979). The valuation of
reserves of natural resources an option pricing
approach University of California, Berkeley.
(Available now as download)
3
The Outline
Extraction Paradox
Resolved through introducing
Holding cost
Rising extraction cost
Storage cost not very significant
Omission of convenience yield
Revise the model to include convenience yield
Effect of holding cost on investment decision for
revised model
Effect of holding cost and rising extraction cost
on investment decision for revised model
Conclusion
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Extraction Paradox
Asset price S follows gBm
Risk neutral valuation relationship (RNVR) for
option value C on 1 unit of asset
Solution
Unit extraction cost
Value matching condition
Solution

• Resource is never extracted! Solution is to
  introduce
• Option holding cost
• Time increasing extraction cost

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Holding Cost
Option holding cost H per unit of time, required
to keep option open
RNVR
S
Solution
Acquire at zero cost an option to extract 1 unit
of asset when SZ
W
Exercise option to extract 1 unit of asset when
SW
Z
Time
Feasible solution
Option holding cost
Note
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Convenience Yield
Introduce a convenience yield Brennan Schwartz
(1986)
Solution
Resolves the extraction paradox
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Convenience Yield and Holding Cost
RNVR
Solution
Values of W and Z
No closed form solution exists Solve numerically
When H0, solution simplifies to
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Effect of Holding Cost on Optimal Solution
Zero holding cost
Optimal Values
Infinite holding cost
Real option solution
NPV solution
Holding Cost
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Effect of Holding Cost on Optimal Solution
Effect of an option holding cost is to yield a
solution between real option and NPV solutions
Optimal Values
Condition is not required for
revised model
Holding Cost
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Effect of Holding Cost and Convenience Yield on
Optimal Solution
Optimal Values
Increasing convenience yield lowers W
But, has less effect on Z
Holding Cost
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Effect of Holding Cost and Volatility on Optimal
Solution
Optimal Values
Decreasing volatility lowers W
But, has less effect on Z
Holding Cost
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Effect of Holding Cost and Extraction Cost on
Optimal Solution
Optimal Values
Increasing extraction cost raises W
But, has less effect on Z
Holding Cost
13
Effect of Volatility on Optimal Solution
Optimal Values
Deterministic Solution
Volatility increases raises W
But, effect on Z is less
Volatility
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The Effect of Increasing Extraction Cost and
Holding Costs
Similar result as before
The presence of an option holding cost is
To raise the asset price trigger when option to
extract is acquired at zero cost
To lower the asset price trigger when option is
exercised and the extraction process starts
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The Limitations of Tourinho Model
Omission of convenience yield
Absence of temporary suspension opportunities
Brennan Schwartz (1985)
The operating extraction cost and investment cost
are combined
Excludes the possibility of any managerial
flexibility after extraction starts
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The Merits of Tourinho Model
The first continuous time real option analysis of
real-world application using risk neutrality
Predates all subsequent analysis
Introduces concept of option holding cost
Examples Land rent before extraction
(construction) starts Tax on unexploited
resources
Cost of maintaining leading edge
technology before market launch
Innovative and apparently, not repeated
Introduces concept of rising extraction
(investment) cost
McDonald Siegel (1986) examine stochastic
investment cost
Introduces concept of storage cost
Uses finite difference method to generate solution
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Conclusion
Tourinho model is the earliest contribution to
risk neutral real option analysis using a
real-world application
It warrants due acknowledgement
But, it does ignore the convenience yield
Tourinho model introduces the concept of the
option holding cost
Holding cost value of zero produces a RO solution
Holding cost value of infinity produces a NPV
solution
Holding cost (like competition, cash flow rate,
volatility) mediates between RO and NPV solutions
Conceptually, option holding cost has practical
ramifications
Tourinho model is a neglected nugget
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