Abstract
Weather derivatives are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rain using the mean reverting process. The Ornstein Uhlenbeck Process was proposed in [29] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equation(PDE) that governs the price of an option. We apply the Lie analysis theory to solve this PDE, we provide the group classification and we use it to find the invariant analytical solutions.
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