Pricing American Parisian Options and ITS Application in the Valuation of Convertible Bonds

In this paper, we study the problem of pricing American Parisian options based on the forward shooting grid method. We verify the validity of forward shooting grid method by exploiting the relationships among option values of American cumulative Parisian option, American moving window Parisian option and American consecutive Parisian option. We also consider the effects of the trigger conditions and volatilities on the option prices. Then using the simulation method proposed, we present an empirical pricing study of the Chinese convertible bonds market. The results show that the simulated values agree much better with the market values.