The Valuation of Convertible Bonds with Numeraire Changes

The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market.We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper.A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time.We also consider a special case when the asset price follows GBM (Geometric Brownian Motion) and interest rate follows Vasicek’s model.