Abstract
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 modeling the residuals we also compare the prices of January out of the money call and put options under normally distributed disturbances and NIG and VG distributed disturbances. The results of numerical analysis demonstrate that the normal model fails to capture adequately tail risk, and consequently significantly misprices out of the money options. Thus one should take extreme care in choosing the appropriate statistical model.
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