Pricing an Option on Revenue from an Innovation: An Application to Movie Box Office Revenue

We develop a model for valuing revenue streams from innovations. The stochastic properties of revenue from innovations create a more difficult environment in which to value options than when the underlying is a security. There is no initial revenue, and cumulative revenue cannot decrease. Revenues from innovations are characterized by different lives and different rates of the resolution of uncertainty. A common deterministic model for predicting revenue from an innovation is known as the Bass model. We embed the Bass model in a gamma process, resulting in a stochastic process with moments proportional to the mean of the Bass model. To illustrate this model we choose the valuation of options on movie box office revenue. These options enable film distributors to manage the risk of a movie, and they offer diversification opportunities for investors. We develop the econometric methodology for ex ante parameter estimation and a Bayesian updating scheme using Markov chain Monte Carlo simulation as data after release become available. Call prices obtained using the maximum likelihood (ML) parameter estimates from the full data set closely approximate the average discounted value of ex post call payouts that would have occurred at option maturity.