Abstract
This paper means to price weather derivatives through solving the Partial Differential Equation (PDE) of the Ornstein–Uhlenbeck process. Since the PDE is convection dominated, a finite difference scheme with adaptively adjusted one-sided difference is proposed to discretize the PDE without causing spurious oscillations. We compare the finite difference scheme with both the Monte Carlo simulations and Alaton’s approximate formulas. It is shown by extensive numerical experiments that the PDE based approach is accurate, efficient and practical for weather derivative pricing.In addition, we point out that the PDE approach developed for discretely sampled temperature is essentially equivalent to the Semi-Lagrangian time stepping based method. A corresponding Semi-Lagrangian method is also proposed to price weather derivatives of continuously sampled temperature.
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