THEORETICAL AND NUMERICAL VALUATION OF CALLABLE BONDS

This paper studies the value of a callable bond and the bond issuer’s optimal financial decision regarding whether to continue the investment on the market or call the bond. Assume the market investment return follows a stochastic model, the value of contract is formulated as a partial differential equation system embedded with a free boundary, defining the level of market return rate at which it is optimal for the issuer to call the bond. A fundamental solution of the partial differential equation is derived, and used to formulate the value of the bond. A bisection scheme is implemented to solve the problem numerically.