Pricing of reservations for time-limited spectrum leases under overbooking

With spectrum trading the owners of usage rights on wireless spectrum may transfer them temporarily to other users. A secondary market for spectrum may be implemented through the use of reservation mechanisms, by which prospective consumers of spectrum portions may first book them and decide later whether to actually buy the usage rights. A possible strategy for the owners of usage rights is to practise overbooking, i.e., to allow for more reservations than what they could sell (and then pay a penalty if they cannot satisfy the requests). A relevant problem for the owners of usage rights is to set the price for reservations. An algorithm is proposed here to price reservations in the presence of overbooking. The algorithm is based on the iterative use of the Cox-Ross-Rubinstein approach to price financial call options. The algorithm is then applied to a number of cases and the dependence of the price on the overbooking probability and the penalty is analysed.