  In this paper is proposed a 2 factor structural PDE model of pricing puttable
bond with credit risk and derived the analytical pricing formula. To this end,
first, a 2 factor structural (PDE) model of pricing zero coupon bond with
credit risk is provided, the analytical pricing formula is derived under some
conditions for default boundary and default recovery, and the strict
monotonicity of the bond price function with respect to the firm value variable
is proved. Then a (2 factor) pricing model of the option on zero coupon bond
with credit risk is provided and under some condition on the exercise price its
analytical pricing formula is derived by transforming the 2 factor model into a
terminal boundary value problem for Black-Scholes equation with time dependent
coefficient using zero coupon bond as numeraire. Using it, we provide the
pricing formulae of the puttable and callable bonds with credit risk.
