Design and Pricing of Derivative Contracts in a Spectrum Market

36 Pages Posted: 14 Aug 2013  

Aparna Gupta

Rensselaer Polytechnic Institute (RPI)

Koushik Kar

Rensselaer Polytechnic Institute

Praveen Kumar Muthuswamy

Rensselaer Polytechnic Institute (RPI)

Date Written: August 13, 2013

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 article, 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 is modeled as driven by a fractional Brownian motion process owing to the self-similarity properties of the wireless traffic. Utilizing fractional stochastic calculus, we obtain the value of derivative contracts in the proposed spectrum market. The value of a derivative contract is expressed as the expected discounted payoff of the derivative contract under risk-neutral Brownian motion dynamics for the spot price. Finally, 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 the derivative contracts for changes in spot price volatility and the parameters that define the contracts.

Keywords: Financial Innovation, Derivative Instruments, Derivative Pricing Models, Fractional Brownian Motion

JEL Classification: L96, G12, G13

Suggested Citation

Gupta, Aparna and Kar, Koushik and Muthuswamy, Praveen Kumar, Design and Pricing of Derivative Contracts in a Spectrum Market (August 13, 2013). Available at SSRN: https://ssrn.com/abstract=2309386 or http://dx.doi.org/10.2139/ssrn.2309386

Aparna Gupta (Contact Author)

Rensselaer Polytechnic Institute (RPI) ( email )

Troy, NY 12180
United States

Koushik Kar

Rensselaer Polytechnic Institute ( email )

Troy, NY 12180
United States

Praveen Kumar Muthuswamy

Rensselaer Polytechnic Institute (RPI) ( email )

Troy, NY 12180
United States

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