The Survival Zone for a Bond with Both Call and Put Options Embedded

We present a numerical method to price bonds that have multiple embedded options with an emphasis on the case with both long call and short put options. The valuation framework is a one-factor model for the term structure of interest rates where the instantaneous interest rate is allowed to follow a fairly general stochastic process. The equilibrium interest rates that define the free boundaries for the embedded call and put options are given. We demonstrate the survival zone within which a bond with both long call and short put options remains afloat. We show that even moderate levels of transaction costs can have a significant effect on exercise of options.