D. Lvov, A.B. Yigitbasioglu, and N. El Bachir (UK)
Convertible bonds, Monte-Carlo, Simulations, Regres sions.
Convertible bonds are complex hybrid securities subject to multiple sources of risk. Many exhibit exotic path de pendent features. Monte Carlo simulation methods are usually the favorite choice for solving high-dimensional problems and pricing path dependent securities. This pa per breaks away from the tradition established in the lit erature of pricing convertible bonds with finite difference and lattice methods, and suggests a simulation methodol ogy for convertible bond pricing. We introduce the divi dend process for convertible bonds, and formulate the pric ing problem according to the probabilistic martingale ap proach. The proposed methodology deals with callable and puttable convertible bonds. The early exercise rules are es timated by means of least squares regressions as in [1]. The accuracy of the simulation algorithm is tested in the context of a two factor model. The algorithm performs fairly well, and shows potential for further extension to include many complexities inherent in convertible bonds, as well as addi tional risk factors.
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