Modelling and Pricing Temperature Using Ornstein-Uhlenbeck Process with Stochastic Speed of Mean Reversion

Abstract

In this paper, we focus on Ornstein-Uhlenbeck (OU) process with stochastic speed of mean reversion to model the temperature variations. The OU model may explains well the temperature’s behaviour, but some empirical studies evidenced the problem of the constant mean reversion rate. Thus, this study suggests to represent the speed of mean reversion as an OU-type stochastic process driven by an independent pure-jump
increasing L´evy process. The analytical solution of the process is defined under Skorohod integral and the change of the (log) OU process is defined under normal inverse Gaussian family of distribution. Next, we price the cumulative average temperature (CAT) futures analytically using the spot-forward relationship framework. In addition, we also provide numerical pricing of the CAT futures using Monte-Carlo simulation method. The empirical findings in this study are based on the temperature data collected in Subang, Malaysia.