Pricing of spectrum reservation under overbooking

Reservations represent an alternative implementation of secondary markets for spectrum with respect to spot selling through auctions. In a previous paper we have shown that reservation mechanisms may be profitable to mobile operators, be they virtual or endowed with a network, assuming the reservation price as a parameter. Pricing reservations, when the owner of spectrum usage rights applies overbooking and pays a penalty if the reservation is not honoured, is still an open issue. Here we propose an iterative algorithm, based on tools derived from the field of financial markets, to set prices for reservations under overbooking. We analyse the sensitivity of the reservation price to a number of parameters (the purchase price, the expiration time of reservation, the overbooking probability, and the penalty value), and show that the reservation prices decay fast with the overbooking probability, and increase with the penalty value, but short expiration times may make the penalty ineffective.