Pricing an Option on a Non-Decreasing Asset Value: An Application to Movie Revenue

Abstract

In recent years financial engineers have created instruments that facilitate the efficient transfer of the risk associated with certain forms of entertainment revenues. This paper focuses on one particular instrument, options on streams of movie revenues. These options enable film distributors to manage the risk of a movie, and they offer diversification opportunities for investors. Pricing the options is complicated by the fact that cumulative revenue is zero when the options are first offered, uncertainty is high at the start and quickly diminishes, and the underlying is non-decreasing. We propose a continuous time Gamma process to capture the underlying revenue stream and derive the option pricing formula. To estimate the parameters of the process before revenue observations are available, we propose a regression method using revenue data from a data base of earlier movies. With the arrival of the revenue observations, we update the initial estimates in a Bayesian framework. The fit of the revenue process and the option price formula to movie data as well as sensitivities of the option price with respect to the parameters are explored. We apply our method to a set of example movies.