Pricing Corporate Bond With Option On HJM Model And Structure Approach

In foreign countries, corporate bond is a common investment tool. It gives investor interests and par value of bond at maturity. This paper analyzes corporate bond valuation and optimal call and default rules when interest rates and firm value are stochastic, then concluded a class of PDE for corporate bond pricing.About interest rate, HJM model is a general interest rate model.Unfortunately, it is seldom used in corporate bond pricing for its defect.In this paper, we use Carverhill Theorem to make spot rate in this model to be Markovian, obtain some conditions of the volatility. About credit risk, We use Acharya and Carpenter(2002) for reference, regarding callable defaultable bonds as some embedded options on host bond.The structure of this paper as follow: Section1introduces the research background and the significance of this article, and then gives a brief review of previous studies theory. Section2reviews the theory of term structure of interest rate. Section3introduces the feature of them, then gives the advantages of choosing HJM model. The section4is choosing structural approach which has great theory meanings to build the model, studying the price of callable defaultable bonds. This is the core part of this article. We show the procedure of building model on Ito Theorem and no-arbitrage theory, apply mathematic approach such as change of Numeraire to give the simplification of PDE. In section5, we conclude the paper and discuss possible extension.