Trinomial tree model of the real options approach used in mining investment price forecast and analysis

In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybdenum ore as an example, a theoretical model for the hurdle price under the optimal investment timing is constructed. Based on the example data, the op- tion price model is simulated. By the model, mine investment price can be computed and forecast effectively. According to the characteristics of mine investment, cut-off grade, reserve estimation and mine life in different price also can be quantified. The result shows that it is reliable and practical to enhance the accuracy for mining investment decision.

Study on the investment value and investment opportunity of renewable energies under the carbon trading system

China has promised to start the national carbon trading system in 2017.In the carbon trading system,the renewable energy projects may obtain additional benefits through the Certified Carbon Emission Reduction(CCER) trade.As the carbon price fluctuates along with the market conditions,such fluctuation enables the renewable power projects to acquire the rights of an option,i.e.it may contain an even higher value due to the uncertainties in the future.While making an investment decision,the renewable power companies may choose to make the investment immediately,or postpone the investment and accumulate more information to increase the return of investment;and for immediate investments,the return must be sufficient to exceed the potential value of a waiting option.To study the investment in renewable power projects subject to the fluctuation of carbon price,this paper adopts the trinomial tree model of real options to estimate the net present value(NPV) and real option value(ROV) of three types of renewable power projects;according to the decision-making rules of real options to defer,all the three types of projects will exercise the option to postpone the investment decision.This thesis also calculates the benchmark prices of the three types of renewable projects at different times,in the two situations of having no government subsidy and having the government subsidy,so as to determine the investment opportunity of a project.The benchmark price decreases gradually along with the increase of government subsidy,indicating that the government subsidy will stimulate the investment in renewable projects.The benchmark price also increases gradually along with the lapse of time,indicating that the uncertainty will increase together with the time span and thus requires an even higher carbon price to determine the investment opportunity.This thesis also analyzes the sensitivity of factors affecting the investment in renewable projects and draws the conclusion that the fluctuation of carbon price is positively related with the benchmark price of renewable power projects,which indicates that the fluctuation of carbon price increases the option value of an investment but postpones the time of investment.As the China's carbon trading system improves gradually,the carbon price will reach a stable status,thus stimulate the power companies to invest in the renewable projects.

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.