Real Options, Options Pricing Of Incomplete Market And The Investment Decisions

The topic of option pricing not only be a very important problem in the finance market, but also make a very important role on the really firm's investment decision. Because in the really investing projectors, firms have various management flexibilities (real option), as option to wait investment, option to temporarily shut down, option to abandon for salvage value, option to expand, option to default and option to R&D. Using stochastic analysis, stochastic optimal control, game theory and such mathematical method with the real option theory, the research is focused on the issue of the option pricing and investment decision models. At the same time on the incomplete finance market, it was discoursed about the issue of the option pricing and the optimal investment profiles. The main ideas and contributions of this thesis are as follows:1. When the output price follows a geometric Brownian motion and the investment has a partly reversibility, the firm has the real options to the investment project. Once on the output price reaches some trigger price, the firm invests the project, after entry, if the output price full to another trigger price, the firm may temporarily suspend or abandon the project. The entry, temporary suspension and exit decisions as managerial flexibility have the values of real option. In particular when the project salvage isn't enough large, the trigger price for temporary suspension is larger than the trigger price for exit, so, in the period of temporary suspension, the firm have two different real options: the waiting–option for reproducing and the option to abandon the project for obtaining the salvage.2. The model about environment pollution with stochastic harmfulness was established. By analyzing, the optimal environment controlling strategy was obtained. The flexibility values with the strategy were concluded.3. In extant real option literatures, the focus is mainly on the optimal timing of initiating a given project. Actually, once the firm enters into the project, the firm sometimes immediately obtains additional real option, e.g., R&D. Based on a new established model, this paper analyzes the valuation of R&D option and the optimal timing of firm's entry and R&D. We demonstrate that the firm makes investment to begin the project only if output price reaches some threshold, but subsequent R&D is initiated only if the output price reaches another trigger point. Furthermore, the first trigger price is irrelevant to the R&D option, but the option value of investment waiting is positively correlated with the R&D option.4. In fact, the payback criterion are commonly observed instrument, but in the standard literature on investment decisions about R&D projects, it are criticized as it does not lead to a maximization of expected profits. By using the read option approach to investment under uncertainty, we show that it can be rational for the investor to use the payback criterion as a rule of thumb, because a shorter payback period indicates lower values of waiting option and implies higher returns of unit capital. So, by using the payback criterion not only come to the same conclusion as using the strategies net-present values, but also takes much information: How many years the investment is paid back. It be of momentous current significance for the investor without abundant funds.5. With a simple model, it can be used to analyze the ploblems of firm endogenous default and strategic default. Throughout the chapter, it is assumed that the firm makes the decisions thatlie in the best interest of equity holders. Combining the pricing theory and analysis of option, with the game theory, it analyzes the firm's capital structure and the endogenous default and strategic default, computing the optimal bankruptcy-triggering value under maximizing the value of equity claim. It also compares the equity value of endogenous default with the equity value of strategic default, result that the equity value of strategic default is more than the other one.6. A stochastic volatility model is established. Under a condition of utility maximum, the problem of optimal portfolio choice is solved with the self-financing strategies. The analytical formation of the expected utility is obtained.7. Introduce the notion of a market-free-lunch that depends on the preferences of all agents participating in the market. In semi-martingale models of securities markets, it characterizes no arbitrage (NA) and no-free-lunch-with-vanishing-risk (NFLVR). By using some kinds utility functions, the relation of three notions are obtain, on the other hand, using the mean-variance utility function and indifference argument, the contingent claim studied. It was proved that the price of contingent claims does not depend on the initial capital, and is not linear in the number of claims. The selling (buying) price of contingent claimed is positively (negatively) correlative with the variance of the non-hedge able part of contingent claims. The higher the risk of the non-hedge able part of contingent claims, the higher (lower) it's selling (buying) price, and the formula of pricing the contingent claim in complete market has been implied.