Abstract:

In the recent literature of corporate finance, some two-barrier models have been proposed to measure the liquidation risk of a firm subject to both Chapter 7 (Liquidation) and Chapter 11 (Reorganization) of the U.S. bankruptcy code. We establish explicit formulas for the probability of liquidation in such two-barrier models in which the firm value is modeled by a time-homogeneous diffusion process or a jump-diffusion process. The formulas offer a quantitative understanding about how the capital structures before and during bankruptcy affect the probability of liquidation. Since our formulas involve regularity of some well-known probabilities in risk theory, which is a long-standing theoretical issue in the literature, we employ regularity theory of partial differential equations to propose optimal conditions under which these probabilities are classical solutions of associated equations. Finally, we introduce two hybrid Barrier-Parisian options and study their pricing formulas. The new hybrid options overcome disadvantages of both regular Barrier options and Parisian options.