Modelling and Pricing communication networks services in Markets for Bandwidth

The subject of this thesis is pricing and modelling of communication network services in bandwidth markets, more precisely connections between two or more geographical locations, subject to a certain Quality of Service requirements. First, it is shown how network topology leads to additional arbitrage opportunities, like the so called network or geographical arbitrage, and how it influences hedging strategies. A solution to such a pricing problem is proposed on the simplest bandwidth topology, the triangle network, both for pricing and hedging strategy based on a risk-minimization criteria. Such solution is then applied to various underlying price processes, from a Cox-Ross-Rubinstein type model to a more complex Geometric Brownian Motion (GBM). Future developments for price models including spikes as typical features of non-storable commodities are then discussed. Second, the foundations for a realistic extension of results found in triangle networks to a global telecommunication network are laid. In addition, estimates for the correlation function between traffic activities on distant routes are derived. More precisely, it is found an upper bound for the exponential decay rate of space and time two-point correlation functions. Lastly, the analysis moves to real data. The dynamics of different forward contract prices are linked with a price process dynamics for a forward contract with fixed maturity. Subsequently, a truncated increments variation technique is used to detect and remove spike prices from real data, in order to estimate parameter values for a GBM process. Then a simple model for the price process, consisting of a GBM with Poissonian spikes, is proposed and simulated in order to mimic the empirical data.