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Abstract
We introduce a general decision-tree framework to value an option to invest/divest in a project, focusing on the model risk inherent in the assumptions made by standard real option valuation methods. We examine how real option values depend on the dynamics of project value and investment costs, the frequency of exercise opportunities, the size of the project relative to initial wealth, the investor’s risk tolerance (and how it changes with wealth) and several other choices about model structure. For instance, contrary to stylised facts from previous literature, real option values can actually decrease with the volatility of the underlying project value and increase with investment costs. And large projects can be more or less attractive than small projects (ceteris paribus) depending on the risk tolerance of the investor, how this changes with wealth, and the structure of costs to invest in the project.
Highlights
The original definition of a real option, first stated by Myers (1977), is a decision opportunity for a corporation or an individual
This paper develops a general model for real option valuation—with a utility which encompasses all the standard utility functions and with a price process which has the standard geometric Brownian as a special case—by setting specific values for model parameters, we can assess the change in real option value arising from different decisions
We have shown that exponential utility option values are too low when the decision maker’s risk tolerance increases with wealth, which is a more realistic assumption than constant absolute risk aversion (CARA)
Summary
The original definition of a real option, first stated by Myers (1977), is a decision opportunity for a corporation or an individual. We allow general assumptions about: the market price of the project; the investment costs; the frequency of exercise opportunities; the size of the project relative to the decision-maker’s wealth; the. We do not assume that risks can be hedged by traded securities, but risk-neutral valuation techniques still apply in the special case of a linear utility function In this case, Grasselli (2011) proves that the time-flexibility of the opportunity to invest in a project still carries a positive option value for a risk-averse decision maker, so that the paradigm of real options can still be applied to value a decision where none of the risks can be hedged. An Appendix aids understanding of our framework with some illustrative examples
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