A PDE Based Weather Derivative Pricing Method

As an innovative management tool,the main function of a weather derivative is to avoid non-catastrophic weather risks.In the research of weather derivatives,weather derivative pricing is the key issue.Therefore,exploring new pricing methods will surely provide references and significances for developing weather derivative markets in China.Observing the trend of the daily average temperature data of Zhengzhou City from 1951 to 2017,this paper constructs temperature models with the mean value recovery O-U model.Firstly,we consider the difference between weather derivatives pricing and classical Black-Scholes option pricing model.and introduce a market price of risk in the model to establish a temperature derivative pricing model.We estimate the parameters and derive the partial differential pricing equation followed by the HDD index.Secondly,the central difference method is used to solve the PDE and compared with the results calculated by Alaton approximate pricing formula.As shown,the two models basically agree with each other when the temperature range is small,but serious deviations can be observed when the temperature range is large.It is because that the model is a convection-dominated convection-diffusion PDE,which is different from the classical option pricing model.Finally,in order to eliminate the errors,we develop a one-sided finite difference scheme for the pricing model.Through numerical comparison,it is shown that the agreement is good when the temperature range is large.To summarize,the temperature-based weather derivatives can be reasonably used by this method and this PDE based method can be used to pricing weather derivatives reasonably.