This thesis develops a model of closed end bond funds that helps us better understand a recent finding in the literature. In 2012 Elton et al. published an empirical study of closed end bond funds (CEBFs) and they suggested that the use of leverage in CEBFs could explain the fact that these funds had higher returns than those of comparable open end funds. This thesis provides a framework for estimating the impact of leverage on expected return and risk in this context. We use a Merton type approach to model both unlevered and levered CEBFs. The assets of a CEBF are primarily risky bonds. Each of these risky bonds can be analysed in terms of options under the Merton approach. We create an unlevered CEBF model by extending Merton's model to a multi-firm framework to represent a CEBF composed of several risky bonds. We then add leverage by assuming the CEBF issues debt. This permits us to model the securities of a levered closed end bond fund as compound options. The equity and debt of the CEBF can be decomposed into options on a portfolio of options. This framework enables us to compute the expected rate of return and standard deviation of an unlevered and levered CEBF. We obtain results that are comparable to those observed in Elton et al.