A Real Options Approach To Investment Pricing And Timing Under Uncertainty

In this paper, we attack the newest problems on investment under uncertainty. Several frameworks are developed in detail and one case study is also shown for the purpose of application.According to utility indifference prices and the ideas from real option pricing, we turn on the valuation and timing of the option to invest under uncertainty and without a perfect spanning asset. Firstly, we review two classical approaches of investment under uncertainty: the well known models of McDonald and Siegel(1986) and Dixit and Pindyck(1994), which value the investment decision as a perpetual American call option on the project value. However, the complete market in Dixit and Pindyck(1994) is a theoretical setting which often cannot be found in practice, and McDonald and Siegel(1986) does not recognizes private risks. Thus, we assume the markets are incomplete and recognize private risks by utility function. Utilizing stochastic dynamic programming and utility indifference prices, we obtain the methods of how to value and time the investment opportunity.Firstly, we assume utility is exponential and cashflows of a project follow a lognormal process with upper barrier without a perfect spanning asset. We deal with problems of timing and valuation of the project. By making use of stochastic control theory and a new verification, explicit solutions are derived to both the value and timing of the option to invest.Secondly, we propose a new model for the cash-flow of a project, an exponential mean-reverting process, in which there is much evidence in practice. We also acquire the explicit solutions by our new methods and solving a partial differential equation successfully.Thirdly, we assume utility is a function with the constant and relative risk aversion coefficients. Some results are derived about the value and timing of the option to invest. We conclude that both the pricing and timing are pertinent to the investor's amount of wealth in contrast to the exponential situation.Fourthly, we explore an application in a practical project. By means of the Matlab software, we discuss the effects of varied combination of parameters on the pricing and timing via comparative static and numerical examples. We show that by diagrams, which explain our theoretical results are right.