Analytical valuation of exotic double barrier options

This article derives the bivariate joint probability distribution functions of a geometric Brownian motion and the extreme values of another geometric Brownian. Based on the probability distribution functions, the authors develop the analytical pricing formulas of three exotic double barrier options (DBOs) with continuously monitored barriers, including rainbow DBOs, protected DBOs, and protected rainbow DBOs. By using the continuity correction of barriers proposed in research by Doobae Jun, the aforementioned pricing formulas can be further extended to price the three exotic DBOs with discretely monitored barriers. Some numerical examples are also provided for end-users to examine the pricing accuracy and efficiency and the properties of the exotic DBOs.