Weather Derivative Pricing and the Normal Distribution: Fitting the Variance to Maximise Expected Predictive Log-Likelihood

7 Pages Posted: 27 Jun 2006

See all articles by Stephen Jewson

Stephen Jewson

Risk Management Solutions

Jeremy Penzer

London School of Economics

Date Written: June 23, 2006

Abstract

The normal distribution is commonly used to predict weather indices when pricing weather derivatives. The standard method for making such predictions involves calculating an unbiased estimator for the population variance. The variance of the prediction (the predictive variance) is then the unbiased estimator for the population variance with an adjustment to account for sampling error on the mean. This is not, however, the only way to model the predictive variance, and it is not necessarily the best way. We investigate an alternative method, based on adjusting the predictive variance so as to maximise the expected predictive log-likelihood. For the small sample sizes often used in weather derivative pricing the resulting predictive variances are significantly larger than those calculated using the standard method.

Keywords: weather derivatives, normal distribution, variance estimators

JEL Classification: G13

Suggested Citation

Jewson, Stephen and Penzer, Jeremy, Weather Derivative Pricing and the Normal Distribution: Fitting the Variance to Maximise Expected Predictive Log-Likelihood (June 23, 2006). Available at SSRN: https://ssrn.com/abstract=911569 or http://dx.doi.org/10.2139/ssrn.911569

Stephen Jewson

Risk Management Solutions ( email )

London EC3R 8NB
United Kingdom

Jeremy Penzer (Contact Author)

London School of Economics ( email )

Houghton Street
London WC2A 2AE
United Kingdom

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