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Design and pricing of derivative contracts in a spectrum market

Author

Listed:
  • Aparna Gupta

    (Lally School of Management and Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, USA)

  • Koushik Kar

    (Lally School of Management and Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, USA)

  • Praveen K. Muthuswamy

    (Lally School of Management and Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, USA)

Abstract

We propose a secondary spectrum market that allows wireless providers to purchase spectrum access licenses of short duration in the form of spot contracts and derivative contracts on spectrum. A spot contract provides immediate access to one or more wireless channels and cannot be further traded. On the other hand, derivative contracts on spectrum typically involve purchase of spectrum licenses in the future for predefined terms, and they can play an important role in risk management objectives of wireless providers. In this paper, we utilize a model for the spot price of spectrum licenses in which the price increases with increasing congestion in spectrum usage caused by the primary demand for spectrum. The spot price process, modeled as driven by a fractional Brownian motion (fBm) process to capture the self-similarity properties of wireless traffic, is utilized in fractional stochastic calculus to obtain the value of derivative contracts. We design a variety of derivative contracts considering the risk profile of both the buyers and sellers of spectrum. Through a detailed numerical study, we examine the value of these derivative contracts for changes in spot price volatility and the parameters that define the contracts.

Suggested Citation

  • Aparna Gupta & Koushik Kar & Praveen K. Muthuswamy, 2015. "Design and pricing of derivative contracts in a spectrum market," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-25.
    • Handle: RePEc:wsi:jfexxx:v:02:y:2015:i:01:n:s2345768615500051
    DOI: 10.1142/S2345768615500051
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