European-Style Forward Derivatives for Telecom Commodities

Bandwidth commodity markets are developing, and (dark) fiber swaps are not uncommon. Derivatives, especially derivatives of forward contracts, are likely to be important for risk management
and hedging. However there is currently no method available to price contingent claims where the underlying asset is a claim on some part of a network and non-storable. To date, geographical (no-)arbitrage has not been included in the pricing of contingent claims on forwards. We present a method for pricing European-style contingent claims on forwards using both the usual no-arbitrage conditions and geographical no-arbitrage. We make appropriate allowances for the non-storability of the underlying asset (point-to-point) bandwidth and the storability of forward-based contingent claims. We give an example of pricing a call option on a forward contract with a range of underlying network topologies based on realistic forward prices. For this example, a call option on a 10 month forward, we find the option price to be relatively insensitive to the network topology (less than 10 %) for a range of strike prices. We speculate that this is due to the long date leading to geographical arbitrage effects being reduced to log-Normality by the Central Limit Theorem. This would imply that increasing differences might be observed for shorter-dated contingent claims. We conclude by discussing the steps required in forward curve modeling to move to any-style contingent claims on network capacity.