With short‐term and seasonal variations filtered out, the data for the climate is closer to stationary, predictable for some time in the future and can be approximated with a Markov process, thus demonstrating that climate and weather time series exhibit differing characteristics. Hence, based on statistical analysis of the temperature time series, we consider an Ornstein‐Uhlenbeck process for the dynamics of the global mean temperature and propose a realistic new semi‐empirical model for estimating the global sea level response. We then use the concept of absence of arbitrage opportunities and define a simple pricing rule with stochastic interest rates for evaluating climate derivatives. Finally, we discuss three financial products that enable different parties who feel vulnerable to climate change to hedge their risks or shoulder additional risks where a cost‐benefit advantage exists, and we describe their pricing formula. We first consider a digital coupon swap allowing two parties to bet on sea level rise at different fixing time and then introduce a climate default swap providing a party with protection against a rise in the sea‐level where the default is the first passage time of an up barrier. As a special case, we look at the pricing of a climate default bond or nature‐linked bond. Copyright © 2010 Wilmott Magazine Ltd.
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