In this paper, we modify classical structural models such as the Black-Cox model and Merton's model by indifference pricing. The reason of doing this is because the assets of a firm, which are traditionally regarded as the underlying and used to hedge the credit risk, are usually non-tradeable in the market. We introduce the firm's stock and a financial index in the market to hedge the credit risk and derive the price of the defaultable corporate bond by indifference valuation. The correspond...