Valuation of Carbon Emission Allowances and Sustainable Investment

Rising awareness of the impacts of climate change is leading to a rapid development of emission trading schemes (ETS) globally as a market-based means of emission control. Under a typical ETS, emission allowances are issued to firms under predetermined quotas at the beginning of each year by regulators, a sufficient number of which must be surrendered at the end of the year to cover their emission amounts or a penalty must be paid. At the same time, allowances may be traded between firms, forming a secondary market of the instrument that is of interest to both the financial and actuarial industry seeking sustainable asset and liability portfolios. Research on an efficient allowance valuation model is therefore urgently called for. In this thesis, we present valuation frameworks and models for allowances and options under closed and open trading phases. A trading phase consists of multiple years. Within each phase, banking and borrowing of allowances are permitted. Existing studies on allowance valuation fail to differentiate between the two types of phases and their implications on the modeling approaches. An ETS operating in a closed phase imposes a lapse of unused allowances at the end of phase, introducing terminal conditions of allowance prices for which structural models are required. We present three closed-phase allowance valuation models based on different specifications of the aggregate emission process: an Arithmetic Brownian Motion (ABM) emission rate, a Vasicek emission amount, and a Vasicek emission rate. In contrast, an ETS operating in an open phase permits inter-phase banking of unused allowances, the price of which is conveniently captured by reduced-form models. We investigate three open-phase allowance option valuation models based on different specifications of the allowance price process: a Lognormal model, a skewness kurtosis adjusted Lognormal model, and a Mixture Lognormal model. Closed-form expressions are derived for allowances, futures, and options as applicable. Market completeness and model applications are discussed, supplemented by numerical illustrations of model performance using actual market price data. Furthermore, we extend the results of the open-phase models presented to the design and modeling of variable annuities backed by allowance-based managed funds and indexed annuities linked to the allowance markets. These products present an innovative yet feasible step forward for insurers and pensioners, as the allowance's non-lapsing feature and low return correlations with the stock market make it a suitable alternative asset for portfolio diversification. Analytical pricing, valuation, and hedging schemes are presented and numerically illustrated through semi-hypothetical examples. Finally, we introduce a systematic framework for the management of sustainable equity investment portfolios under climate change, where metrics and methods are proposed to quantify investment-related climate change risks. Inferior historical risk-adjusted performance of carbon-intensive sectors are empirically demonstrated to justify the recommended divestment from these industries. A method to generate equity return impact scenarios is proposed, which can be incorporated into scenario-based calculations and models in various actuarial practices. Using the generated scenarios as key inputs, we present and illustrate the construction of a sustainable portfolio under a hypothetical asset universe