A Study On Optimal Timing Of A Carbon Emission Reduction Policy Based On Real Option Theory

Global warming is an important and special social,political and economic issue.The uncertainties from a carbon emission reduction policy with sunk costs lie mainly in benefits of the policy and evolution of the ecological environment in the future.At the same time,due to the existence of sunk costs,the policy faces economic or ecological irreversibility.In the past,the standard framework for evaluating an environmental policy was the traditional cost-benefit analysis method,which just ignored the above two important factors: uncertainties and irreversibility.Therefore,the theory of real option applies to the study on environmental policy.However,there are still some deficiencies.In theory,the past models either assume a random state or two random state variables with simple randomness assumptions such as geometric Brownian motion.In practice,the empirical research of the social cost of carbon caused by the stock of externality lag behind the theory study,which limits the practical value of the model.As the social costs of carbon emission emissions continue to be studied,environmentalists have found that there could be a sharp rise in the social costs of carbon in the future.This makes the assumption of continuous random changes of carbon social cost(such as geometric Brownian motion)in past models no longer satisfied the reality.Based on the real option theory,this paper studies the optimal timing of adoption a carbon emission reduction policy under uncertainty and how uncertainties affect the optimal timing.This paper is not only considering the random variation in the economic state variable with discrete jump process,and joined the random variation of ecological state variable.In the numerical examples,this paper puts the social cost of carbon forward as reality basis of the state variable,and the numerical examples will be combined with the social cost of carbon concept.The research of this paper shows that: When there is continuous random fluctuation of economic status variables reflecting social cost of carbon,the optimal critical value is affected by factors such as discount rate,natural degradation rate of carbon dioxide and random volatility of carbon social cost.Specifically,the critical value is direct proportional to the discount rate r,the degradation rate and the variance parameters of random fluctuations,and affected by through the factor /(-1).But when the state variables reflecting the social cost of carbon have the possibility of discrete jumps in the future,the product of the arrival rate λ and the saltus of jump will enter the discount factor(--)through the factor /(-1),which will further affect the policy benefits.What’s more,under the double uncertainties,the critical value will be affected by the carbon dioxide stock and its random volatility: Firstly,compared with the case under a single uncertainty,policy threshold under double uncertainty condition is higher.Secondly,the influence of random fluctuations of the stock is direct proportional to the optimal critical value.Finally,the larger the current carbon dioxide stock,the weaker the impact of uncertainty.