The Valuation of Weather Derivatives Using One Sided Crank–Nicolson Schemes

Abstract

This paper prices weather derivatives of two typical processes: the Ornstein–Uhlenbeck process and the Ornstein–Uhlenbeck process with jump diffusions. Efficient one sided Crank–Nicolson schemes are developed to solve the convection dominated partial differential and integral-differential equation corresponding to the two processes, respectively. For second order convergence, the one sided Crank–Nicolson schemes may utilize piecewise cubic interpolations to approximate the jump conditions in degree days direction. The unconditional stability is then obtained through the local von Neumann analysis. As extensive numerical experiments shown, the schemes are highly efficient and accurate, and can serve as competitive and practical pricing instruments in weather derivative markets.