Pricing puttable convertible bonds with integral equation approaches

American-style puttable convertible bonds are often priced with various numerical solutions because the predominant complexity arises from the determination of the two free boundaries together with the bond price. In this paper, two forms of integral equations are derived to price a puttable convertible bond on a single underlying asset. The first form is obtained under the Black-Scholes framework by using an incomplete Fourier transform. However, this integral equation formulation possesses a discontinuity along both free boundaries. An even worse problem is that this representation contains two first-order derivatives of the unknown exercise prices, which demands a higher smoothness of the interpolation functions used in the numerical solution procedure. Thus, a second integral equation formulation is developed based on the first form to overcome those problems. Numerical experiments are conducted to show several interesting properties of puttable convertible bonds.