This article builds a new structural default model under the assumption that a firm’s assets return follows a dynamics displaying jumps of both signs. In essence, we expand the work of Hilberink and Rogers (itself an extension of the Leland and Toft framework), which deals only with negative jumps. In contrast, we make use of stable Lévy processes, and we compute the values of the firm, debt and equity under this assumption. Theoretical credit spreads can also be obtained in our framework. They prove to be consistent with the empirical credit spreads observed in financial markets.