The Pricing of Revenue Assurance: Reply

Abstract

In their comment, Yin and Turvey (YT) suggest an approach to overcome a potential problem with Stokes, Nayda, and English’s (SNE’s) methodology for valuing revenue insurance. The problem, as discussed in SNE and YT, is that farm gross revenue is not a traded asset. Therefore, revenue insurance, which is itself a derivative security (i.e., a security that derives its value from the value of another asset—in this case, farm gross revenue), is difficult to price using standard asset pricing methods because buying and selling the underlying asset to hedge away risk is not possible. SNE assume an equilibrium pricing function exists and, and in doing so, are left with one unobservable parameter in their pricing formula. YT’s comment is essentially to propose a method for eliminating this unknown parameter. The problem is that an underlying asset, for which a derivative security is written against, is not tradable. The importance of tackling this issue cannot be over emphasized and YT are to be commended for their efforts. Indeed, virtually no other research besides SNE and YT approaches the problem of premium determination for agricultural insurance from the perspective of treating the insurance as a derivative security. 1 The importance of doing so is that one gains access to contemporary asset pricing methodology. In this reply, we focus on two important issues related to the problems created by nontradability. First, we clarify the tradable versus nontradable distinction in terms of its implications for arbitrage free pricing. The results we present provide the necessary background for motivating YT’s equation (1). Whereas YT begin their comment by assuming an economy that justifies their equation (1), we provide a mathematical characterization of the economy that insures the equation holds. Taking this approach gives us the opportunity to define the issues YT raise more clearly because the mathJ.R. Stokes is assistant professor at the Pennsylvania State University, University Park, PA; W.I. Nayda is Manager of Financial Analysis and Development at Capital One, Inc., McLean, VA. 1 Counter examples include research by Turvey and Amanor