Climate risks and weather derivatives: A copula-based pricing model

The paper focuses on the role of climate and weather derivatives (CDs/WDs for short) as instruments to hedge climate risk. The aim of this paper is hence twofold: (i) we introduce a copula-based pricing methodology for multivariate CDs/WDs, whose flexible theoretical framework allows to be suited to any pricing application and possible structure of multivariate products, and (ii) we discuss the impact of CDs/WDs on climate risk and their implication for financial stability. Using the proposed framework, we illustrate a calibration example on a case study on data for 11 Italian cities, looking specifically at the joint hedge of rainfall (cumulated) and temperature (either cumulated CDD or HDD, depending on the season), across four different seasons of the year. We find that Archimedean copula functions characterized by left tail dependence (i.e. Clayton copulas) are generally more suitable to fit the data, depending on the season and the location. We also explore the advantages of using more sophisticated, i.e. rotated or multivariate, copulas and assess the improvement of fitting. We find that rotated copulas (specifically, a Rotated Gumbel) represent a first meaningful performance improvement; and multivariate copulas such as the bi-parametric Survival BB8 significantly improve fitting, but they also impose technical constraints due to the higher computational requirements. Subsequently, leveraging both the theoretical model and the empirical results, we discuss the relation between climate risk hedging and financial stability. Especially, we move from modeling complexities and limitations to illustrate how incorrect calculations (in the form of mispricings, or over/under estimations of capital at risk) can, alongside with climate change effect, increase rather than reduce the climate physical risk and hence the concerns for financial stability. Finally, we discuss this point in relation with the legislative framework, noting how, in the current context of uncertain legislation and imperfect pricing, climate hedging risks are likely to do more harm than good.