A Study On The Theory And Approach To The Valuation Of Real Option

The dissertation mainly studies the pricing theory and approach to real option. Basing on the principle of arbitrage-free pricing theory, the basic tools of replicated pricing and dynamic programming approach, and under the guide of projection theory of Hilbert space, this paper focus on the issues of pricing and hedging of real option in incomplete markets. Compared with the finance option, what the real option valuation face are the main problems as follow: the underlying assets can not be traded; the value distribution does not follow GBM; and the uncertainties are endogenous. Many of the problems are relevant with the completeness of the markets. So this paper first describe the option pricing theory in the incomplete market. In general, we can only obtain an arbitrage-free interval for the real option in the incomplete markets. In order to obtain an unique valuation, we must add new pricing criterions, and the different pricing criterions will lead to different approximate valuation, but from the point of the theory of Hilbert space, no matter what kinds of approximate valuation, they can be view as the project of a vector from the Hilbert space to its closed subspace, the only difference is the different definitions of norm. As for the issues of non-traded assets, applying the approach of stochastic dynamic programming, and under the principle of No-Arbitrage, we obtain optimal strategy to hedge the real option in discrete and continuous conditions. And to the problems of special distribution of underlying assets, this paper analyzes the price movement of the underlying assets from the arrival of information, the market efficiency and the market mechanism which decide the price. It also studies the problem of real option pricing when the underlying assets follow the pure jump Poisson, mixed jump-diffusion Merton and mean-reversion model, and obtains the price formula or partial differential equation to price and hedge the real option. When the value of real option can not separate from the value of project, or the uncertainties are endogenous to real option holder, it is difficult to pricing the real option by the ways of No-Arbitrage. In this paper we present a approach named valuation with comparison, Its basic point is to value the project or program with flexibility by means of decision tree analysis (DTA) and stochastic dynamic programming (SDP), and the results are compared with that of non-flexibility, finally, the value of flexibility is obtained. As an application to the approach, this paper explores how to design and pricing the employment contract with flexibility. It show that to the important staffs, the firms must apply long contract, and to the subordinate staffs, it can employ short contract.