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Fuzzy Real Options Theory and the Handling of Giga-Investments

Submitted by Christer Carlsson, 18.12.2001, IBA E


Very large investments, often called giga-investments, require a budget of 0.2-0.5 Bł and will typically have a life cycle of 15-25 years. The classical approach for decision support is to estimate the future cash inflows of the products (or services) produced through the investment, the future cash outflows caused by the investment and related operations and then to calculate the net present value (NPV) of these cash flows. If the NPV is significantly positive the investment decision is made and senior management will have to live with this decision for the life cycle of the giga-investment. In many cases this have been problematic, in some cases catastrophic.


The real options model offers a way to handle large investments with risky outcomes in a more flexible way than the NPV method. There is an option for senior manage-ment to invest capital or to wait for more and better information, and then commit capital. The classical real options model builds on the questionable assumption that an efficient market will discount the effect of the giga-investment by putting a realistic market value on the shares offered through the stock exchange. This is then used to estimate the market risk and to build a stochastic real options model. The assumption is questionable due to the very long life cycle involved. A better approach had to be found.

Status and results

The real options model was enhanced and developed with fuzzy numbers, which were used to replace the stochastic elements. Then it was possible to show that the Black-Scholes formula can be proved also with fuzzy numbers and that there is an options price for the added flexibility introduced with the fuzzy numbers. The fuzzy numbers were also used to update the dynamic decision tree, which now became more adaptive to changing market conditions. The fuzzy real options models were compared to the classical real options models and proved to be more general. The results when com-pared with the NPV models were significantly better.

Adaptivity and portability

The fuzzy real options methods adapt to changing market conditions if the decision tree is made dynamic and adaptive to changes in fuzzy numbers, i.e. it is allowed to change its structure on the basis of new information. In our case this information was produced with the Industry Foresight method. In terms of the EUNITE levels of adaptivity the real options model is of Level I.

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