6.1 INTRODUCTION

In this chapter we derive an explicit formula for the value of the option to invest in a capital project, but where the option to do so has a finite life. The seminal and most often quoted papers in this area are those of Margrabe (1978) and McDonald and Siegel (1986), both of which solve the valuation problem by assuming that the benefits and costs associated with the capital project are generated by a geometric Brownian motion. Virtually all the subsequent work in the area, such as that by Myers and Majd (1990), Olsen and Stensland (1992), Quigg (1993), Carr (1988, 1995) and Schroder (1999), has continued with the Brownian motion assumption. There is growing evidence, however, that asset prices evolve in terms of distributions which possess fat tails when compared to the normal distribution on which the Brownian motion is based (Praetz, 1972; Blattberg and Gonedes, 1974; Theodossiou, 1998; Barndorff-Nielsen and Shephard, 2001). Hence, our purpose here is to present a closed-form solution for the value of the option to invest in a capital project when the difference between the benefits and costs of the investment decision are generated by a general class of Student distributions. These processes exhibit the fat tail properties that characterize the (probable) distributions of some R&D projects, which either fail after large expenditures in development and clinical trials, or succeed as blockbuster products. Section 6.2 develops the valuation formula and analyzes some of its more important properties. Section 6.3 contains our summary...