6.3 SUMMARY CONCLUSIONS

Our purpose here has been to present a closed-form solution for the value of the option to invest in a capital project when the option to do so has a finite life. In doing so, we assume that the capital project's net present value evolves in terms of the Student distributions which exhibit the fat tail properties characterizing at least some of the empirical distributions of R&D. However, most analytical work conducted in this area assumes that the option to undertake an investment project has an infinite life (McDonald and Siegel, 1986). Unfortunately, many real-life investment opportunities are not infinitely lived but expire and become worthless at a known point in time. Probably the best example of this is a finitely lived patent, which gives the holder the option to invest at any time before a given expiration date. Our analysis provides an explicit closed-form solution for the valuation of finite-lived derivative securities of this kind.

Closed-form solutions, such as the one derived here, are, however, notoriously difficult to come by. Yet, despite the difficulties associated with obtaining closedform solutions, there is one variation to our analysis that is worthy of further investigation. This stems from the fact that many asset prices appear to evolve in terms of distributions which exhibit not only fat tails but also significant skewness (Theodossiou, 1998; Barndorff-Nielsen and Shephard, 2001). Here it is important to note that the symmetric Student distributions on which our analysis is based are a specific instance of...