Barrier options are path-dependent options, and their return depends not only on the price of the underlying asset on the expiry date but also on whether the underlying asset reaches the prescribed barrier level during the contract's validity period. This paper mainly studies the barrier option pricing problem under the Ornstein–Uhlenbeck equa-tion model under an uncertain environment. Assuming that the stock price obeys the Ornstein–Uhlenbeck equation model, the pricing formulas of four European barrier options are derived. Finally, several numerical examples are used to verify the effectiveness of the model.

PURPOSES: This study evaluates the economic value of national highway construction projects using Real Option Pricing Models. METHODS : We identified the option premium for uncertainties associated with flexibilities according to the future's change in national highway construction projects. In order to evaluate value of future's underlying asset, we calculated the volatility of the unit price per year for benefit estimation such as VOTS, VOCS, VICS, VOPCS and VONCS that the “Transportation Facility Investment Evaluation Guidelines” presented. RESULTS: We evaluated the option premium of underlying asset through a case study of the actual national highway construction projects using ROPM. And in order to predict the changes in the option value of the future's underlying asset, we evaluated the changes of option premium for future's uncertainties by the defer of the start of construction work, the contract of project scale, and the abandon of project during pre-land compensation stages that were occurred frequently in the highway construction projects. Finally we analyzed the sensitivity of the underlying asset using volatility, risk free rate and expiration date of option. CONCLUSIONS: We concluded that a highway construction project has economic value even though static NPV had a negative(-) value because of the sum of the existing static NPV and the option premium for the future's uncertainties associated with flexibilities.

The binomial option pricing model is widely used to understand pricing an option which is a financial derivative. The Model presents very important characteristics in deciding a price of an option. First, a value of option is decided independently with probabilities that stock prices are ascending or fall. Second, an option pricing is not depend on investors' risk preferences. When an option is evaluated, this paper may clear that investors had to consider the probabilities of a stock price's movements and their own preferences for a risk.