A modified structural model for credit risk

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 corresponding pricing formulae for the valuation are obtained by Green’s function approach in a unified way. Finally, the numerical results show that the introduction of the new parameters like the risk aversion of the investor and the correlation between the tradeable and non‐tradeable assets may have a positive impact on the short‐term credit spread.