Research on the improvement of Least-Square Monte Carlo pricing method of Convertible bond

Because of the multi-risks convertible bond is subject to and the significant path-dependent structure of it, Monte-Carlo method is now widely considered more favorable for convertible bond pricing, especially LSM is highly recommended for its convenience in implementation. However, some recent improvements of closed-form solution method and of PDE method have challenged some superiorities of Monte Carlo method, making further improvement necessary for Monte-Carlo pricing method of convertible bond. This paper first analyze and comment the improvements of LSM pricing method for American option by Rasmussen and Zheng Chengli, then propose to combine Rasmussen Improvements and Importance Sampling into LSM pricing method for convertible bond. The empirical study shows that these tentative improvements significantly reduce the simulation variance, making LSM more competitive when pricing convertible bond.