The Option Value of Government Guarantee in Highway Based on Utility Indifference Pricing

Government guarantee is one of important measures to attract investment in infrastructure for developing countries. Most of existing researches are based on the hypothesis of complete market, but this paper has broken traditional risk neutral hypothesis. Considering investors' risk attitude in incomplete market, the utility indifference pricing has been introduced to the option value of minimum traffic guarantee in highway. This paper constructs the European option pricing model in government guarantee and offers partial differential equation for utility indifference pricing point. Meanwhile, through the analysis of partial differential equation for utility indifference pricing under CARA utility functions, the pricing method given by this paper has been proved consistent with traditional B-S equation pricing method under the condition of investors being risk neutral. In the end, through the numerical solution to partial differential equation, an interesting relation between option price of minimum traffic guarantee and investors' risk attitude has been revealed.