Pricing weather derivatives under a tri-variate stochastic model

Abstract

Weather derivatives are used to protect farmers in sub-Saharan Africa (SSA) from yield loss caused by climate change. However, mispricing these contracts poses a significant risk due to the interconnected nature and combined impact of the principal climate determinants of maize yield, including rainfall amount, daily temperature, and reference evapotranspiration. To address this issue, this research extends the pricing of derivatives to a joint stochastic process of the three variables, which captures the non-linearity and non-stationarity in the data. Tri-variate models constructed through copulas capture the interdependence properties of the dataset. Pricing models are derived from these processes in a manner that satisfies path integral and market-consistent properties, hence providing more realistic prices for weather derivatives for maize in Malawi. The analysis findings identify possible ranges within the stochastic process that align with varying levels of maize yield loss in the area. Under path integral formulation, call option prices increase with the severity of the tri-variate process, while put option or market environment consistent formulation prices decrease with severity. Thus, this research provides a framework for pricing weather derivatives that incorporates the joint stochastic nature of multiple climate variables, allowing for more accurate risk management for farmers in the area.