The valuation of convertible bonds with numeraire changes

Abstract

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.

Pricing Warrant Bonds with Credit Risk under a Jump Diffusion Process

“…Liao and Huang [3] considered the pricing of convertible bond with credit risk under the geometric Brownian motion model. Zhou and Wang [4] assumed that the interest rate follows the geometric Brownian motion and obtained the valuation of convertible bond by the method of measure transformation. Laura and Ioannis [5] defined the firm's optimal call policy and proposed the pricing framework for convertible bond based on a structural default model.…”