Weather Derivative Pricing and the Normal Distribution: Comparing Three Fitting Schemes Using the Out-of-Sample Log-Likelihood Scoring System

Abstract

Many common weather indices are very close to being normally distributed, and it may be reasonable to assume they are exactly normally distributed for the purpose of pricing weather derivatives. Given that assumption, how should the indices be modelled? We use the expected out-of-sample log-likelihood score to compare 3 schemes: standing normal fitting, adjusted variance normal fitting, and the t-distribution.

Keywords: weather derivatives, normal distribution, variance estimators, t-distribution

JEL Classification: G13