Optimal timing of investments modeled as perpetual American options in a Levy market

Abstract

Using a real option approach, this paper models an arbitrary real life investment, which typically has a long maturity date, as a perpetual American call option in a Levy market. Expressions for the moments, characteristic function and infinitesimal generator of the associated jump-diffusion Levy process, defined by two independent compound Poisson processes and two correlated standard Brownian motions, are derived and these fundamental results are employed to determine the optimal time for investment. An application of the results to a Build Operate and Transfer investment is furnished.