This paper examines the term structures of default probabilities that are generated by the Collin-Dufresne and Goldstein model and a dynamic-leverage-ratio model. The dynamic-leverage-ratio model is capable of producing term structures of default probabilities which are consistent with some...

In this paper we present a simple and easy-to-use method for computing accurate estimates (in closed form) of Black-Scholes barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds (in closed form) for the exact barrier option...