Integrating the risk and term structures of interest rates

Merton (1974) analysed the risk structure of corporate bonds under the assumption of a flat term structure of interest rates. We clarify his results and extend them to the case of stochastic interest rates. As a consequence we deal simultaneously with interest rate risk and with default risk. We investigate the price of a corporate bond and the various measures of the riskness of a corporate bond proposed by Merton ((i) the Yield difference between the corporate bond and a default free bond with the same characteristics, (ii) the standard deviation of the rate of return of a corporate bond). We demonstrate and we explain why several of Merton's conclusions are no longer valid in a stochastic term structure framework.