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In this paper is investigated the pricing problem of options on bonds withcredit risk based on analysis on two kinds of solving problems for theBlack-Scholes equations. First, a solution representation of the Black-Scholesequation with the maturity payoff function which is the product of the powerfunction, normal distribution function and characteristic function is provided.Then a solution representation of a special terminal boundary value problem ofthe Black-Sholes equation is provided and its monotonicity is proved. Thesimplest case of the structural model of the credit bond is studied and itspricing formula is provided, and based on the results, the pricing model ofoption on corporate bond with credit risk is transformed into a terminalboundary value problem of the Black-Scholes equation with some special maturitypayoff functions and the solution formula is obtained. Using it, we provide thepricing formulae of the puttable and callable bonds with credit risk.

Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk