A Fitted Finite-Volume Method Combined with the Lagrangian Derivative for the Weather Option Pricing Model

The purpose of weather option is to allow companies to insure themselves against fluctuations in the weather. However, the valuation of weather option is complex, since the underlying process has no negotiable price. Under the assumption of mean-self-financing, by hedging with a correlated asset which follows a geometric Brownian motion with a jump diffusion process, this paper presents a new weather option pricing model on a stochastic underlying temperature following a mean-reverting Brownian motion. Consequently, a two-dimensional partial differential equation is derived to value the weather option. The numerical method applied in this paper is based on a fitted finite-volume technique combined with the Lagrangian derivative. In addition, the monotonicity, stability, and the convergence of the discrete scheme are also derived. Lastly, some numerical examples are provided to value a series of European HDD-based weather put options, and the effects of some parameters on weather option prices are discussed.