Abstract
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.
Funding source: National Basic Research Program
Award Identifier / Grant number: 2012CB955804
Funding source: Major Research Plan of the National Natural Science Foundation of China
Award Identifier / Grant number: 91430108
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11171251
Funding source: Major Program of Tianjin University of Finance and Economics
Award Identifier / Grant number: ZD1302
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