Crop Insurance as a Tool for Price and Yield Risk Management

Impact of copula choice on the modeling of crop yield basis risk

“…These results are also in conflict with those of recent studies by Anderson et al (2009) and Coble et al (2008), in which important differences are suggested to have been found in the performance of the PQH and IC procedures in the context of rating revenue and whole farm‐insurance products. This study indeed finds no significant performance differences between PQH and IC 5 .…”

“…When calibrated with the Spearman rank correlation, they performed virtually identical to the Gaussian copula (results not presented). Regarding the performance of PQH and IC, our results are consistent with the numerical results of Anderson et al (2009) and Coble et al (2008), who demonstrate that the differences between IC and PQH are essentially close to zero for all practical purposes.…”

“…The methods available for modeling dependence structures vary from parametric methods that produce spherical or nonspherical dependence structures, to ad hoc methods of inducing correlation, to nonparametric kernel methods. The agricultural insurance field has been dominated for many years by the use of ad hoc methods such as the Iman and Conover (IC, 1982) approach, and more recently advocated Phoon, Quek, and Huang procedure (PQH, 2004; see e.g., Anderson et al, 2009; Coble et al, 2008). Copulas, meanwhile, have received much less attention in agricultural insurance settings.…”

“…The PQH procedure (2004) is similar to the IC procedure in that it allows for simulation of correlated uniform random numbers with the desired rank correlation. Like the IC procedure, it is both easy to implement and computationally quite fast, but may be more effective at replicating the underlying correlation structure, according to Coble et al (2008) and Anderson et al (2009). It also uses the rank correlation measure as the primary calibration parameter, although again no guidance is typically given on which rank dependence measure is most desirable.…”

“…Yet, an important dimension of this modeling problem in multivariate contexts that has been mostly ignored is the nature of the dependence between random variables themselves—i.e., the underlying copula (Nelsen, 2006). With little exception (Vedenov, 2008; Zhu et al, 2008), studies in the agricultural economics literature have been dominated by methods that are based on linear correlation measures or that otherwise result in elliptical dependence structures, although this fact is rarely noticed nor stated explicitly (see e.g., Anderson et al, 2009; Babcock and Hennessy, 1996; Coble et al, 2000; Coble et al, 2008; Hart et al, 2006; Hennessy et al, 1997; Paulson and Babcock, 2008; Ramirez, 1997; Richardson and Condra, 1978; Woodard et al, 2010). Meanwhile, interest in the modeling of dependence structures and copulas in other areas of risk analysis such as financial engineering and actuarial mathematics has increased substantially in recent years.…”