The existing telecommunications infrastructure in most of the world is adequate to deliver voice and text applications, but demand for broadband services such as streaming video and large file transfer (e.g., movies) is accelerating. The explosion in Internet use has created a huge demand for telecommunications capacity. However, this demand is extremely volatile, making network planning difficult. Modern financial option pricing methods are applied to the problem of network investment decision timing. In particular, we study the optimal decision problem of building new network capacity in the presence of stochastic demand for services. Adding new capacity requires a capital investment, which must be balanced by uncertain future revenues. We study the underlying risk factor in the bandwidth market and then apply real options theory to the upgrade decision problem. We notice that sometimes it is optimal to wait until the maximum capacity of a line is nearly reached before upgrading directly to the line with the highest known transmission rate (skipping the intermediate lines). It appears that past upgrade practice underestimates the conflicting effects of growth and volatility. This explains the current overcapacity in available bandwidth. To the best of our knowledge, this real options approach has not been used previously in the area of network capacity planning. Consequently, we believe that this methodology can offer insights for network management.

This work demonstrates that it is possible to obtain accurate values of callable bonds using a fully numerical approach, provided that the PDE is discretized appropriately. To facilitate comparisons with results reported by Buttler and Waldvogel (1996), we consider models with a single factor: the instantaneous risk free interest rate. We emphasize, however, that it is straightforward to extend the numerical methods described to cases where the Green's function cannot be determined analytically as well as to cases with time-dependent parameters (typically used to match current term structures of interest rates/interest rate volatilities), or multi-factor interest rate models.