Pricing Climate Derivatives With Nonlinear Models

Given the large number of processes affecting global temperature in the climate system and the fact that these processes operate on different time scales, one cannot assume that a single time scale characterises either the interannual variability of climate or the response of climate to radiative forcing imposed over decades to centuries. Therefore, when modelling climate, we must consider different regimes for the time scale depending on the external forcing. We do this by introducing uncertainty to the characteristic time and to the sensitivity of climate to the stock of greenhouse gases in the atmosphere. We also make allowance for the possibility of non-linear diffusion term representing the weather and add jumps in global temperature. As a result, we improve a simple model introduced in earlier work by presenting three different jump-diffusion models for solving the estimated time constant problem and accounting for non-linear climate forcings. Copyright © 2012 Wilmott Magazine Ltd.