Accurate formulas for evaluating barrier options with dividends payout and the application in credit risk valuation

Abstract

To price the stock options with discrete dividend payout reasonably and consistently, the stock price falls due to dividend payout must be faithfully modeled. However, this will significantly increase the mathematical difficulty since the post-dividend stock price process, the stock price process after the price falls due to dividend payout, no longer follows the lognormal diffusion process. Analytical pricing formulas are hard to be derived even for the simplest vanilla options.