Real (investment) options with multiple sources of rare events

We value real (investment) options when the underlying asset follows a mixed jump-diffusion process involving various types (sources) of rare events (jumps). These jumps are assumed independent of each other, with each type having a log-normally distributed jump size and a random (Poisson-distributed) arrival time. They may represent uncertainties about the arrival and impact (on the underlying investment) of new information concerning technological innovation, competition, political risk, regulatory effects and other sources. An analytic solution is presented for European claims (call or put options) with multiple sources of jumps. A discrete-time (Markov-chain) methodology (implemented within a finite-difference scheme) is proposed for the valuation of American as well as European options. The approach is also applicable to financial options with multiple types of rare events. The approach is illustrated through valuing complex real options with compound features involving interactions between optimal investment and subsequent operating decisions. Specifically, we value a growth option and an extension option.