In this Master’s thesis we discuss and generalize one of the fundamental models in Credit Risk modelling, Merton’s Corporate Debt model, considering the possibility of cross-ownership over debt and equity in a multiple-firm system. In addition, we provide an assumption on different levels of debt seniority, along with various forms of financial derivatives on every firm’s equity and/or debt. By expanding Merton’s model with these assumptions, we aim to capture the complexity of cross-ownership and cross-shareholding among firms in real world networks. We develop a system of equations for determining non-arbitrage values of debt and equity for every member firm within a system, by assuming simultaneous maturity of all debt and obligations within a system, together with the possibility of different levels of debt seniority. Additional assumptions were made on cross-ownership structure and form of financial derivatives, both of which define claims on debt and equity of every member within and outside the system. These assumptions provide existence and/or uniqueness of a solution of the defined system of equations. The proof itself offers an algorithm for determining non-arbitrage values, by using Picard’s iterations. Also, we discuss the connection between recovery claims and their corresponding contingent claims, financial derivatives. Capital structure irrelevance theory based on Modigliani - Miller theorem, at the level of the whole system, still holds. No matter how complex the structure of cross-ownership is, value of the claims of system outsiders remains unaffected. We present balance sheet equations at the time of debt maturity for every firm within a system, as well as on the aggregate level. Using them, we define quantitative risk measures for the system, equivalent to financial leverage, internal financial leverage and degree of cross-ownership. Using all of the assumptions of the model along with Fundamental theorem for asset pricing, we derive values of debt and equity before the time of maturity. Furthermore, we analyse the differences between determined values when accounting for cross-ownership and the values provided by Merton’s model. We present the possibility of implementing weaker assumptions in system modelling, at the risk of losing the uniqueness of the solution for a given system of equations. Further developments of the model are proposed.