Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives

In this paper we model the daily average temperature via an extended version of the standard Ornstein Uhlenbeck process driven by a Levy noise with seasonally adjusted asymmetric ARCH process for volatility. More precisely, we model the disturbances with the Normal inverse Gaussian (NIG) and Variance gamma (VG) distribution. Besides modelling the residuals we also compare the prices of January 2010 out of the money call and put options for two of the Slovenian largest cities Ljubljana and Maribor under normally distributed disturbances and NIG and VG distributed disturbances. The results of our numerical analysis demonstrate that the normal model fails to capture adequately tail risk, and consequently significantly misprices out of the money options. On the other hand prices obtained using NIG and VG distributed disturbances fit well to the results obtained by bootstrapping the residuals. Thus one should take extreme care in choosing the appropriate statistical model.