Abstract: By applying equilibrium approach,this paper studies the pricing of convertible bonds with default risk when underlying assets follow the fractional Brownian motion.A mathematical pricing model for convertible bonds has been developed and an analytical solution has been proved by quasi-martingale method.An analysis on a numerical example is presented in the end of this paper.The conclusion is that the default risk and the long-range dependence of underlying asset are key factors for pricing convertible bonds.

Key words: convertible bonds, fractional Brownian motion, long-range dependence, call option, quasi-martingale