Valuation of Carbon Emission Allowances and Related Derivatives Under a Closed Trading Phase

Abstract

This paper provides a complete-market valuation framework for emission allowances and related derivatives. In particular we present a structural model by assuming an emission rate with time-homogeneous parameters, where closed-form expressions are derived for allowances, allowance futures, and option prices. In addition, we also discuss the completeness of the allowance market and the source of incompleteness as supported by empirical evidence. While identifying limitations of the models, we present in detail their applications under information incompleteness, with a focus on deriving implied emission values from actual market data. Finally, the model is implemented using real world allowance data, based on which a comparative analysis is undertaken.

Keywords: Climate change, Carbon dioxide, Valuation of carbon emission allowances, Market completeness, Market and information incompleteness, Analytical Analysis, Numerical Analysis.

JEL Classification: C15, G13