A Semi-Lagrangian method for the weather options of mean-reverting Brownian motion with jump–diffusion

The weather options were created to enable companies to hedge against climate risks. However, the valuation of weather options is complex, since the underlying temperature process has no negotiable price. This paper presents a new weather option pricing model, which is governed by a stochastic underlying temperature following a mean-reverting Browning motion with jump–diffusion under the assumption of mean-self-financing. Consequently, a two-dimensional partial integro-differential equation (PIDE) is derived to value the weather-based options.